Ordering based decision making - A survey
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paper_title: Computing with Words in Risk Assessment

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This paper presents a comprehensive overview of currently known applications of computing with words (CWW) in risk assessment. It is largely grouped into the following 5 categories: (1) fuzzy number based risk assessment; (2) fuzzy rule-based risk assessment; (3) fuzzy extension of typical probabilistic risk assessment; (4) ordinal linguistic approach for risk assessment; and (5) miscellaneous applications. In addition, the role of CWW within the broad area of risk assessment is briefly characterized.
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paper_title: Reasoning with multiple-source information in a possibilistic logic framework q

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This paper addresses the problem of merging uncertain information in the framework of possibilistic logic. It presents several syntactic combination rules to merge possibilistic knowledge bases, provided by different sources, into a new possibilistic knowledge base. These combination rules are first described at the meta-level outside the language of possibilistic logic. Next, an extension of possibilistic logic, where the combination rules are inside the language, is proposed. A proof system in a sequent form is given, sound and complete with respect to the possibilistic logic semantics. Possibilistic fusion modes are illustrated on an example inspired from an application of a localization of a robot in an uncertain environment.
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paper_title: Reasoning With Partially Ordered Information in a Possibilistic Logic Framework

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In many applications, the reliability relation associated with available information is only partially defined, while most of existing uncertainty frameworks deal with totally ordered pieces of knowledge. Partial pre-orders offer more flexibility than total pre-orders to represent incomplete knowledge. Possibilistic logic, which is an extension of classical logic, deals with totally ordered information. It offers a natural qualitative framework for handling uncertain information. Priorities are encoded by means of weighted formulas, where weights are lower bounds of necessity measures. This paper proposes an extension of possibilistic logic for dealing with partially ordered pieces of knowledge. We show that there are two different ways to define a possibilistic logic machinery which both extend the standard one.
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paper_title: Ranking and screening multiple criteria alternatives with partial information and use of ordinal and cardinal strength of preferences

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This paper consists of three parts: 1) some theories and an efficient algorithm for ranking and screening multicriteria alternatives when there exists partial information on the decision maker's preferences; 2) generation of partial information using variety of methods; and 3) the existence of ordinal and cardinal functions based on and strengths of preferences. We demonstrate that strengths of preference concept can be very effectively used to generate the partial information on preferences. We propose axioms for ordinal and cardinal (measurable) value functions. An algorithm is developed for ranking and screening alternatives when there exists partial information about the preferences and the ordering of alternatives. The proposed algorithm obtains the same information very efficiently while by solving one mathematical programming problem many alternatives can be ranked and screened. Several examples are discussed and results of some computational experiments are reported.
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paper_title: CP-nets: A Tool for Representing and Reasoning withConditional Ceteris Paribus Preference Statements

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Information about user preferences plays a key role in automated decision making. In many domains it is desirable to assess such preferences in a qualitative rather than quantitative way. In this paper, we propose a qualitative graphical representation of preferences that reflects conditional dependence and independence of preference statements under a ceteris paribus (all else being equal) interpretation. Such a representation is often compact and arguably quite natural in many circumstances. We provide a formal semantics for this model, and describe how the structure of the network can be exploited in several inference tasks, such as determining whether one outcome dominates (is preferred to) another, ordering a set outcomes according to the preference relation, and constructing the best outcome subject to available evidence.
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paper_title: Multiperson decision-making based on multiplicative preference relations

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A multiperson decision-making problem, where the information about the alternatives provided by the experts can be presented by means of diAerent preference representation structures (preference orderings, utility functions and multiplicative preference relations) is studied. Assuming the multiplicative preference relation as the uniform element of the preference representation, a multiplicative decision model based on fuzzy majority is presented to choose the best alternatives. In this decision model, several transformation functions are obtained to relate preference orderings and utility functions with multiplicative preference relations. The decision model uses the ordered weighted geometric operator to aggregate information and two choice degrees to rank the alternatives, quantifier guided dominance degree and quantifier guided non-dominance degree. The consistency of the model is analysed to prove that it acts coherently. ” 2001 Elsevier Science B.V. All rights reserved.
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paper_title: Multi-criteria decision making with fuzzy linguistic preference relations

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Abstract Although the analytic hierarchy process (AHP) and the extent analysis method (EAM) of fuzzy AHP are extensively adopted in diverse fields, inconsistency increases as hierarchies of criteria or alternatives increase because AHP and EAM require rather complicated pairwise comparisons amongst elements (attributes or alternatives). Additionally, decision makers normally find that assigning linguistic variables to judgments is simpler and more intuitive than to fixed value judgments. Hence, Wang and Chen proposed fuzzy linguistic preference relations (Fuzzy LinPreRa) to address the above problem. This study adopts Fuzzy LinPreRa to re-examine three numerical examples. The re-examination is intended to compare our results with those obtained in earlier works and to demonstrate the advantages of Fuzzy LinPreRa. This study demonstrates that, in addition to reducing the number of pairwise comparisons, Fuzzy LinPreRa also increases decision making efficiency and accuracy.
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paper_title: Linguistic Values Based Intelligent Information Processing: Theory, Methods and Applications

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This book focuses on systematic and intelligent information processing theories and methods based on linguistic values. The main contents include topics such as the 2-tuple model of linguistic values, 2-tuple linguistic aggregation operator hedge algebras, complete hedge algebras and linguistic value reasoning, reasoning with linguistic quantifiers, linguistic reasoning based on a random set, the fuzzy number model of linguistic values, linguistic value aggregation based on the fuzzy number model, extraction of linguistic proposition from a database and handling of linguistic information on the Internet, linguistic truth value lattice implication algebras, linguistic truth value resolution automatic reasoning, linguistic truth value reasoning based on lattice implication algebra, and related applications in decision-making and forecast.
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paper_title: Fuzzy sets and decision analysis

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Abstract This survey points out recent advances in multiple attribute decision making methods dealing with fuzzy or ill-defined information. Fuzzy MAUT as well as fuzzy outranking methods are reviewed. Aggregation procedures, choice problems and treatment of interactive attributes are covered. Trends in research and open problems are indicated.
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paper_title: Rational choice and security studies : Stephen Walt and his critics

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Formal theories and rational choice methods have become increasingly prominent in most social sciences in the past few decades. Proponents of formal theoretical approaches argue that these methods are more scientific and sophisticated than other approaches, and that formal methods have already generated significant theoretical progress. As more and more social scientists adopt formal theoretical approaches, critics have argued that these methods are flawed and that they should not become dominant in most social-science disciplines.Rational Choice and Security Studies presents opposing views on the merits of formal rational choice approaches as they have been applied in the subfield of international security studies. This volume includes Stephen Walt's article "Rigor or Rigor Mortis? Rational Choice and Security Studies," critical replies from prominent political scientists, and Walt's rejoinder to his critics.Walt argues that formal approaches have not led to creative new theoretical explanations, that they lack empirical support, and that they have contributed little to the analysis of important contemporary security problems. In their replies, proponents of rational choice approaches emphasize that formal methods are essential for achieving theoretical consistency and precision.
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paper_title: Incomplete fuzzy linguistic preference relations under uncertain environments

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When addressing decision-making problems, decision-makers typically express their opinions using fuzzy preference relations. In some instances, decision-makers may have to deal with the problems in which only partial information is available. Consequently, decision-makers embody their preferences as incomplete fuzzy preference relations. The values of incomplete fuzzy preference relations have been considered crisp in recent studies. To allow decision-makers to provide vague or imprecise responses, this study proposes a novel method, called incomplete fuzzy linguistic preference relations, that uses fuzzy linguistic assessment variables instead of crisp values of incomplete fuzzy preference relations to ensure comparison consistency. The proposed method reflects an environment in which some uncertainty or vagueness exists. Examples are included that illustrate the effectiveness of the proposed method.
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paper_title: Group decision making based on multiple types of linguistic preference relations

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In this paper, we investigate group decision making problems with multiple types of linguistic preference relations. The paper has two parts with similar structures. In the first part, we transform the uncertain additive linguistic preference relations into the expected additive linguistic preference relations, and present a procedure for group decision making based on multiple types of additive linguistic preference relations. By using the deviation measures between additive linguistic preference relations, we give some straightforward formulas to determine the weights of decision makers, and propose a method to reach consensus among the individual preferences and the group's opinion. In the second part, we extend the above results to group decision making based on multiple types of multiplicative linguistic preference relations, and finally, a practical example is given to illustrate the application of the results.
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paper_title: Multi-criteria decision making with fuzzy linguistic preference relations

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Abstract Although the analytic hierarchy process (AHP) and the extent analysis method (EAM) of fuzzy AHP are extensively adopted in diverse fields, inconsistency increases as hierarchies of criteria or alternatives increase because AHP and EAM require rather complicated pairwise comparisons amongst elements (attributes or alternatives). Additionally, decision makers normally find that assigning linguistic variables to judgments is simpler and more intuitive than to fixed value judgments. Hence, Wang and Chen proposed fuzzy linguistic preference relations (Fuzzy LinPreRa) to address the above problem. This study adopts Fuzzy LinPreRa to re-examine three numerical examples. The re-examination is intended to compare our results with those obtained in earlier works and to demonstrate the advantages of Fuzzy LinPreRa. This study demonstrates that, in addition to reducing the number of pairwise comparisons, Fuzzy LinPreRa also increases decision making efficiency and accuracy.
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paper_title: The Computational Complexity of Dominance and Consistency in CP-Nets

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We investigate the computational complexity of testing dominance and consistency in CP-nets. Previously, the complexity of dominance has been determined for restricted classes in which the dependency graph of the CP-net is acyclic. However, there are preferences of interest that define cyclic dependency graphs; these are modeled with general CP-nets. In our main results, we show here that both dominance and consistency for general CP-nets are PSPACE-complete. We then consider the concept of strong dominance, dominance equivalence and dominance incomparability, and several notions of optimality, and identify the complexity of the corresponding decision problems. The reductions used in the proofs are from STRIPS planning, and thus reinforce the earlier established connections between both areas.
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paper_title: A lattice-valued linguistic-based decision making method

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The subject of this work is to establish a mathematical framework that provides the basis and tool for synthesis and evaluation analysis in decision making, especially from the logic point of view. This paper focuses on a flexible and realistic approach, i.e., the use of linguistic assessment in decision making, specially, the symbolic approach acts by direct computation on linguistic values. A lattice-valued linguistic algebra model, which is based on a logical algebraic structure, i.e., lattice implication algebra, is applied to represent imprecise information and deal with both comparable and incomparable linguistic values (i.e., non-ordered linguistic values). Within this framework, some known weighted aggregation functions are analyzed and extended to deal with these kinds of lattice-value linguistic information.
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paper_title: An overview on the 2-tuple linguistic model for computing with words in decision making: Extensions, applications and challenges

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Many real world problems need to deal with uncertainty, therefore the management of such uncertainty is usually a big challenge. Hence, different proposals to tackle and manage the uncertainty have been developed. Probabilistic models are quite common, but when the uncertainty is not probabilistic in nature other models have arisen such as fuzzy logic and the fuzzy linguistic approach. The use of linguistic information to model and manage uncertainty has given good results and implies the accomplishment of processes of computing with words. A bird's eye view in the recent specialized literature about linguistic decision making, computing with words, linguistic computing models and their applications shows that the 2-tuple linguistic representation model [44] has been widely-used in the topic during the last decade. This use is because of reasons such as, its accuracy, its usefulness for improving linguistic solving processes in different applications, its interpretability, its ease managing of complex frameworks in which linguistic information is included and so forth. Therefore, after a decade of extensive and intensive successful use of this model in computing with words for different fields, it is the right moment to overview the model, its extensions, specific methodologies, applications and discuss challenges in the topic.
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paper_title: From Computing With Numbers To Computing With Words From Manipulation Of Measurements To Manipulation of Perceptions

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Discusses a methodology for reasoning and computing with perceptions rather than measurements. An outline of such a methodology-referred to as a computational theory of perceptions is presented in this paper. The computational theory of perceptions, or CTP for short, is based on the methodology of CW. In CTP, words play the role of labels of perceptions and, more generally, perceptions are expressed as propositions in a natural language. CW-based techniques are employed to translate propositions expressed in a natural language into what is called the Generalized Constraint Language (GCL). In this language, the meaning of a proposition is expressed as a generalized constraint, N is R, where N is the constrained variable, R is the constraining relation and isr is a variable copula in which r is a variable whose value defines the way in which R constrains S. Among the basic types of constraints are: possibilistic, veristic, probabilistic, random set, Pawlak set, fuzzy graph and usuality. The wide variety of constraints in GCL makes GCL a much more expressive language than the language of predicate logic. In CW, the initial and terminal data sets, IDS and TDS, are assumed to consist of propositions expressed in a natural language. These propositions are translated, respectively, into antecedent and consequent constraints. Consequent constraints are derived from antecedent constraints through the use of rules of constraint propagation. The principal constraint propagation rule is the generalized extension principle. The derived constraints are retranslated into a natural language, yielding the terminal data set (TDS). The rules of constraint propagation in CW coincide with the rules of inference in fuzzy logic. A basic problem in CW is that of explicitation of N, R, and r in a generalized constraint, X is R, which represents the meaning of a proposition, p, in a natural language.
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paper_title: Computing with Words in Decision support Systems: An overview on Models and Applications

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Decision making is inherent to mankind, as human beings daily face situations in which they should choose among different alternatives by means of reasoning and mental processes. Many of these decision problems are under uncertain environments with vague and imprecise information. This type of information is usually modelled by linguistic information because of the common use of language by the experts involved in the given decision situations, originating linguistic decision making. The use of linguistic information in decision making demands processes of Computing with Words to solve the related decision problems. Different methodologies and approaches have been proposed to accomplish such processes in an accurate and interpretable way. The good performance of linguistic computing dealing with uncertainty has caused a spread use of it in different types of decision based applications. This paper overviews the more significant and extended linguistic computing models due to its key role in linguistic decision making and a wide range of the most recent applications of linguistic decision support models.
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paper_title: AN EXTENDED HIERARCHICAL LINGUISTIC MODEL FOR DECISION‐MAKING PROBLEMS

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In multi-expert decision making (MEDM) problems the experts provide their preferences about the alternatives according to their knowledge. Because they can have different knowledge, educational backgrounds, or experiences, it seems logical that they might use different evaluation scales to express their opinions. In the present article, we focus on decision problems defined in uncertain contexts where such uncertainty is modeled by means of linguistic information, therefore the decision makers would use different linguistic scales to express their evaluations on the alternatives, i.e., multigranular linguistic scales. Several computational approaches have been presented to manage multigranular linguistic scales in decision problems. Although they provide good results in some cases, still present limitations. A new approach, so-called extended linguistic hierarchies, is presented here for managing multigranular linguistic scales to overcome those limitations, an MEDM case study is given to illustrate the proposed method.
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paper_title: Hesitant Fuzzy Linguistic Term Sets for Decision Making

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Dealing with uncertainty is always a challenging problem, and different tools have been proposed to deal with it. Recently, a new model that is based on hesitant fuzzy sets has been presented to manage situations in which experts hesitate between several values to assess an indicator, alternative, variable, etc. Hesitant fuzzy sets suit the modeling of quantitative settings; however, similar situations may occur in qualitative settings so that experts think of several possible linguistic values or richer expressions than a single term for an indicator, alternative, variable, etc. In this paper, the concept of a hesitant fuzzy linguistic term set is introduced to provide a linguistic and computational basis to increase the richness of linguistic elicitation based on the fuzzy linguistic approach and the use of context-free grammars by using comparative terms. Then, a multicriteria linguistic decision-making model is presented in which experts provide their assessments by eliciting linguistic expressions. This decision model manages such linguistic expressions by means of its representation using hesitant fuzzy linguistic term sets.
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paper_title: Extended hedge algebras and their application to fuzzy logic

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This paper continues our investigation on hedge albebras (6). We extend hedge algebras by two additional operations corresponding to infimum and supremum of the so-called concept category of an element x, i.e. the set which is generated from x by means of the hedge operations. It is shown that every extended hedge algebra with a lattice of the primary generators is a lattice. In the symmetrical extended hedge algebras we are able to define negation and implication, called concept-negation and concept- implication. Furthermore, it is proved that there exists an isomorphism from a subaigebra of a symmetrical extended hedge algebra of a linguistic truth variable into the closed unit interval (0, 1), under which the concept-negation and the concept-implication correspond to the negation and a kind of implication in multiple-valued logic based on the unit- interval (0, 1).
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paper_title: On aggregation operations of linguistic labels

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This article is devoted to defining some aggregation operations between linguistic labels. First, from some remarks about the meaning of label addition, a formal and general definition of a label space is introduced. After, addition, difference, and product by a positive real number are formally defined on that space. the more important properties of these operations are studied, paying special attention to the convex combination labels. the article concludes with some numerical examples. © 1993 John Wiley Sons, Inc.
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paper_title: The 2-tuple linguistic computational model. Advantages of its linguistic description, accuracy and consistency.

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The Fuzzy Linguistic Approach has been applied successfully to different areas. The use of linguistic information for modelling expert preferences implies the use of processes of Computing with Words. To accomplish these processes different approaches has been proposed in the literature: (i) Computational model based on the Extension Principle, (ii) the symbolic one(also called ordinal approach), and (iii) the 2-tuple linguistic computational model. The main problem of the classical approaches, (i) and (ii), is the loss of information and lack of precision during the computational processes. In this paper, we want to compare the linguistic description, accuracy and consistency of the results obtained using each model over the rest ones. To do so, we shall solve a Multiexpert Multicriteria Decision-Making problem defined in a multigranularity linguistic context using the different computational approaches. This comparison helps us to decide what model is more adequated for computing with words.
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paper_title: Fuzzy logic = computing with words

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As its name suggests, computing with words (CW) is a methodology in which words are used in place of numbers for computing and reasoning. The point of this note is that fuzzy logic plays a pivotal role in CW and vice-versa. Thus, as an approximation, fuzzy logic may be equated to CW. There are two major imperatives for computing with words. First, computing with words is a necessity when the available information is too imprecise to justify the use of numbers, and second, when there is a tolerance for imprecision which can be exploited to achieve tractability, robustness, low solution cost, and better rapport with reality. Exploitation of the tolerance for imprecision is an issue of central importance in CW. In CW, a word is viewed as a label of a granule; that is, a fuzzy set of points drawn together by similarity, with the fuzzy set playing the role of a fuzzy constraint on a variable. The premises are assumed to be expressed as propositions in a natural language. In coming years, computing with words is likely to evolve into a basic methodology in its own right with wide-ranging ramifications on both basic and applied levels.
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paper_title: Fuzzy sets and decision analysis

paper_content:

Abstract This survey points out recent advances in multiple attribute decision making methods dealing with fuzzy or ill-defined information. Fuzzy MAUT as well as fuzzy outranking methods are reviewed. Aggregation procedures, choice problems and treatment of interactive attributes are covered. Trends in research and open problems are indicated.
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paper_title: Fuzziness measure on complete hedge algebras and quantifying semantics of terms in linear hedge algebras

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In the paper, we shall examine the fuzziness measure (FM) of terms or of complete and linear hedge algebras of a linguistic variable. The notion of semantically quantifying mappings (SQMs) previously examined by the first author will be redefined more generally and a closed relation between the FM of linguistic terms and a family of SQMs with the parameters to be the FM of primary terms and linguistic hedges will be established. A semantics-based topology of hedge algebras and a closed and interesting relation between this topology, the FM and the above family of SQMs will be discovered and examined. An applicability of the FM and SQMs will be shown by an examination of some application examples.
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paper_title: Induced ordered weighted geometric operators and their use in the aggregation of multiplicative preference relations

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In this article, we introduce the induced ordered weighted geometric (IOWG) operator and its properties. This is a more general type of OWG operator, which is based on the induced ordered weighted averaging (IOWA) operator. We provide some IOWG operators to aggregate multiplicative preference relations in group decision-making (GDM) problems. In particular, we present the importance IOWG (I-IOWG) operator, which induces the ordering of the argument values based on the importance of the information sources; the consistency IOWG (C-IOWG) operator, which induces the ordering of the argument values based on the consistency of the information sources; and the preference IOWG (P-IOWG) operator, which induces the ordering of the argument values based on the relative preference values associated with each one of them. We also provide a procedure to deal with “ties” regarding the ordering induced by the application of one of these IOWG operators. This procedure consists of a sequential application of the aforementioned IOWG operators. Finally, we analyze the reciprocity and consistency properties of the collective multiplicative preference relations obtained using IOWG operators. © 2004 Wiley Periodicals, Inc.
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paper_title: Integrating Three Representation Models in Fuzzy Multipurpose Decision Making Based on Fuzzy Preference Relations

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Abstract The purpose of this paper is to study a fuzzy multipurpose decision making problem, where the information about the alternatives provided by the experts can be of a diverse nature. the information can be represented by means of preference orderings, utility functions and fuzzy preference relations, and our objective is to establish a general model which cover all possible representations. Firstly, we must make the information uniform, using fuzzy preference relations as uniform preference context. Secondly, we present some selection processes for multiple preference relations based on the concept of fuzzy majority. Fuzzy majority is represented by a fuzzy quantifier, and applied in the aggregation, by means of an OWA operator whose weights are calculated by the fuzzy quantifier. We use two quantifier guided choice degrees of alternatives, a dominance degree used to quantify the dominance that one alternative has over all the others, in a fuzzy majority sense, and a non dominance degree, that generalises Orlovski's non dominated alternative concept. The application of the two above choice degrees can be carried out according to two different selection processes, a sequential selection process and a conjunction selection process.
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paper_title: Integrating multiplicative preference relations in a multipurpose decision-makingmodel based on fuzzy preference relations

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The aim of this paper is to study the integration of multiplicative preference relation as a preference representation structure in fuzzy multipurpose decision-makingproblems. Assumingfuzzy multipurpose decision-makingproblems under di4erent preference representation structures (ordering, utilities and fuzzy preference relations) and using the fuzzy preference relations as uniform representation elements, the multiplicative preference relations are incorporated in the decision problem by means of a transformation function between multiplicative and fuzzy preference relations. A consistency study of this transformation function, which demonstrates that it does not change the informative content of multiplicative preference relation, is shown. As a consequence, a selection process based on fuzzy majority for multipurpose decision-makingproblems under multiplicative preference relations is presented. To design it, an aggregation operator of information, called ordered weighted geometric operator, is introduced, and two choice degrees, the quanti7er-guided dominance degree and the quanti7er-guided non-dominance degree, are de7ned for multiplicative preference relations. c 2001 Elsevier Science B.V. All rights reserved.
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paper_title: Multiperson decision-making based on multiplicative preference relations

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A multiperson decision-making problem, where the information about the alternatives provided by the experts can be presented by means of diAerent preference representation structures (preference orderings, utility functions and multiplicative preference relations) is studied. Assuming the multiplicative preference relation as the uniform element of the preference representation, a multiplicative decision model based on fuzzy majority is presented to choose the best alternatives. In this decision model, several transformation functions are obtained to relate preference orderings and utility functions with multiplicative preference relations. The decision model uses the ordered weighted geometric operator to aggregate information and two choice degrees to rank the alternatives, quantifier guided dominance degree and quantifier guided non-dominance degree. The consistency of the model is analysed to prove that it acts coherently. ” 2001 Elsevier Science B.V. All rights reserved.
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paper_title: On the Multi-Utility Representation of Preference Relations

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We develop the ordinal theory of (semi)continuous multi-utility representation for incomplete preference relations. We investigate the cases in which the representing sets of utility functions are either arbitrary or finite, and those cases in which the maps contained in these sets are required to be (semi)continuous. With the exception of the case where the representing set is required to be finite, we find that the requirements of such representations are surprisingly weak, pointing to a wide range of applicability of the representation theorems reported here. Some applications to decision theory under uncertainty and consumer theory are also considered.
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paper_title: Fuzzy multiple attributes group decision-making based on fuzzy preference relations

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In this paper, we present a new approach for fuzzy multiple attributes group decision-making based on fuzzy preference relations. First, we construct fuzzy importance matrices for decision-makers with respect to attributes and construct fuzzy evaluating matrices for decision-makers with respect to the attributes of the alternatives. Based on the fuzzy importance matrices and the fuzzy evaluating matrices, we construct fuzzy rating vectors for decision-makers with respect to the alternatives. Then, we defuzzify the trapezoidal fuzzy numbers in the constructed fuzzy rating vectors to get the rating vectors for the decision-makers. Based on the rating vectors, we construct fuzzy preference relations for the decision-makers with respect to the alternatives. Based on the fuzzy preference relations, we calculate the average rating value of each decision-maker with respect to the alternatives. Then, we sort these average rating values in a descending sequence and assign them different scores. Then, we calculate the summation values of the scores of the alternatives with respect to each decision-maker, respectively. The larger the summation values of the scores, the better the choice of the alternative. The proposed method is simpler than Chen's method (2000) and Li's method (2007) for handling fuzzy multiple attributes group decision-making problems. It provides us with a useful way to handle fuzzy multiple attributes group decision-making problems.
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paper_title: Probabilistic Borda rule voting

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An alternative voting system, referred to as probabilistic Borda rule, is developed and analyzed. The winning alternative under this system is chosen by lottery where the weights are determined from each alternative’s Borda score relative to all Borda points possible. Advantages of the lottery include the elimination of strategic voting on the set of alternatives under consideration and breaking the tyranny of majority coalitions. Disadvantages include an increased incentive for strategic introduction of new alternatives to alter the lottery weights, and the possible selection of a Condorcet loser. Normative axiomatic properties of the system are also considered. It is shown this system satisfies the axiomatic properties of the standard Borda procedure in a probabilistic fashion.
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paper_title: Rank-ordering of risk preferences with conventional and discrete measures

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When the functional form of utility is unknown, conventional measures of risk aversion are often approximated by applying a Taylor series expansion to expected utility. This is shown to produce counterintuitive rank-orderings of risk preferences for individuals who are willing to pay equal reservation prices in lotteries with different prizes. Moreover, individuals who are unwilling to participate in favorable lotteries may be incorrectly identified as having a finite aversion to risk. Correct orderings are obtained by applying a discrete measure of relative risk aversion. The contrast between the conventional and discrete measures is illustrated with data from three Dutch surveys.
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paper_title: How to make a decision: The analytic hierarchy process

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Abstract This paper serves as an introduction to the Analytic Hierarchy Process — A multicriteria decision making approach in which factors are arranged in a hierarchic structure. The principles and the philosophy of the theory are summarized giving general background information of the type of measurement utilized, its properties and applications.
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paper_title: A Consensus Support System Model for Group Decision-Making Problems With Multigranular Linguistic Preference Relations

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The group decision-making framework with linguistic preference relations is studied. In this context, we assume that there exist several experts who may have different background and knowledge to solve a particular problem and, therefore, different linguistic term sets (multigranular linguistic information) could be used to express their opinions. The aim of this paper is to present a model of consensus support system to assist the experts in all phases of the consensus reaching process of group decision-making problems with multigranular linguistic preference relations. This consensus support system model is based on i) a multigranular linguistic methodology, ii) two consensus criteria, consensus degrees and proximity measures, and iii) a guidance advice system. The multigranular linguistic methodology permits the unification of the different linguistic domains to facilitate the calculus of consensus degrees and proximity measures on the basis of experts' opinions. The consensus degrees assess the agreement amongst all the experts' opinions, while the proximity measures are used to find out how far the individual opinions are from the group opinion. The guidance advice system integrated in the consensus support system model acts as a feedback mechanism, and it is based on a set of advice rules to help the experts change their opinions and to find out which direction that change should follow in order to obtain the highest degree of consensus possible. There are two main advantages provided by this model of consensus support system. Firstly, its ability to cope with group decision-making problems with multigranular linguistic preference relations, and, secondly, the figure of the moderator, traditionally presents in the consensus reaching process, is replaced by the guidance advice system, and in such a way, the whole group decision-making process is automated
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paper_title: DECISION-MAKING WITH A FUZZY PREFERENCE RELATION

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Abstract In most decisio-making problems a preference relation in the set of alternatives is of a fuzzy nature, reflecting for instance on the fuzziness of experts estimates of the preferences. In this paper, the corresponding fuzzy equivalence and strict preference relations are defined for a given fuzzy non-strict preference relation in an unfuzzy set of alternatives which are used to introduce in a natural way the fuzzy set of nondominated alternatives. Two types of linearity of a fuzzy relation are introduced and the equivalence of the unfuzzy nondominated alternatives is studied. It is shown that unfuzzy nondominated solutions to the decision-making problem exist, provided the original fuzzy relation satisfies some topological requirements. A simple method of calculating these solutions is indicated.
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paper_title: Valued preference structures

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Abstract An approach to the axiomatics of valued preference modelling is suggested. In the framework of this approach, general definitions of strict preference, indifference and incomparability relations associated with a valued preference relation are established via solving a system of functional equations. Any solution of this system satisfies most of the classical properties. Characterizations of important particular solutions are also proved.
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paper_title: Incomplete linguistic preference relations and their fusion

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Various linguistic preference relations, including incomplete linguistic preference relation, consistent incomplete linguistic preference relation and acceptable incomplete linguistic preference relation, are introduced. Some desirable properties of the incomplete linguistic preference relation are studied. Based on the operational laws of the linguistic evaluation scale, and the acceptable incomplete linguistic preference relation with the least judgments, we develop a simple and practical method for constructing a consistent complete linguistic preference relation by using the additive transitivity property. The method not only relieves the decision maker of time pressure and makes sufficiently using of the provided preference information, but also maintains the decision maker's consistency level and avoids checking the consistency of linguistic preference relation. Furthermore, an approach to multi-person decision making based on incomplete linguistic preference relations is developed. The approach fuses all the consistent complete linguistic preference relations, constructed by using the individual acceptable incomplete linguistic preference relations with the least judgments, into a collective complete linguistic preference relation, and then the overall information corresponding to each decision alternative is aggregated. Finally, an illustrative example is given.
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paper_title: The Analytic Hierarchy Process

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This chapter provides an overview of Analytic Hierarchy Process (AHP), which is a systematic procedure for representing the elements of any problem hierarchically. It organizes the basic rationality by breaking down a problem into its smaller constituent parts and then guides decision makers through a series of pair-wise comparison judgments to express the relative strength or intensity of impact of the elements in the hierarchy. These judgments are then translated to numbers. The AHP includes procedures and principles used to synthesize the many judgments to derive priorities among criteria and subsequently for alternative solutions. It is useful to note that the numbers thus obtained are ratio scale estimates and correspond to so-called hard numbers. Problem solving is a process of setting priorities in steps. One step decides on the most important elements of a problem, another on how best to repair, replace, test, and evaluate the elements, and another on how to implement the solution and measure performance.
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paper_title: Uncertainty and rank order in the analytic hierarchy process

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Abstract The Analytic Hierarchy Process uses paired comparisons to derive a scale of relative importance for alternatives. We investigate the effect of uncertainty in judgment on the stability of the rank order of alternatives. The uncertainty experienced by decision makers in making comparisons is measured by associating with each judgment an interval of numerical values. The approach leads to estimating the probability that an alternative or project exchanges rank with other projects. These probabilities are then used to calculate the probability that project would change rank at all. We combine the priority of importance of each project with the probability that it does not change rank, to obtain the final ranking.
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paper_title: Induced ordered weighted geometric operators and their use in the aggregation of multiplicative preference relations

paper_content:

In this article, we introduce the induced ordered weighted geometric (IOWG) operator and its properties. This is a more general type of OWG operator, which is based on the induced ordered weighted averaging (IOWA) operator. We provide some IOWG operators to aggregate multiplicative preference relations in group decision-making (GDM) problems. In particular, we present the importance IOWG (I-IOWG) operator, which induces the ordering of the argument values based on the importance of the information sources; the consistency IOWG (C-IOWG) operator, which induces the ordering of the argument values based on the consistency of the information sources; and the preference IOWG (P-IOWG) operator, which induces the ordering of the argument values based on the relative preference values associated with each one of them. We also provide a procedure to deal with “ties” regarding the ordering induced by the application of one of these IOWG operators. This procedure consists of a sequential application of the aforementioned IOWG operators. Finally, we analyze the reciprocity and consistency properties of the collective multiplicative preference relations obtained using IOWG operators. © 2004 Wiley Periodicals, Inc.
---
paper_title: Some hybrid weighted averaging operators and their application to decision making

paper_content:

Two new hybrid weighted averaging operators for aggregating crisp and fuzzy information are proposed, some of which desirable properties are studied. These operators helps us to overcome the drawback in the existed reference. With respect to the proposed operators, three special types of preferred centroid of triangular fuzzy number are defined. On the base of these preferred centroid, we develop two algorithms to deal with decision making problems. Two numerical examples are provided to illustrate the practicality and validity of the proposed methods.
---
paper_title: Direct approach processes in group decision making using linguistic OWA operators

paper_content:

In a linguistic framework, several group decision making processes by direct approach are presented. These processes are designed using the linguistic ordered weighted averaging (LOWA) operator. To do so, first a study is made of the properties and the axiomatic of LOWA operator, showing the rationality of its aggregation way. And secondly, we present the use of LOWA operator to solve group decision making problems from individuals linguistic preference relations.
---
paper_title: The use of fuzzy outranking relations in preference modelling

paper_content:

This paper deals with preference modelling in the context of Decision Aid. In this framework, conflicting systems of logic, uncertain knowledge, ambiguous positions are always present. In order to tackle this problem, a multiple criteria methodology is proposed, mainly based on fuzzy outranking relations introduced both at one-dimensional and multi-dimensional levels. Some properties of outranking relations are investigated. Such relations are then combined using fuzzy logical connectives to generate relational systems of fuzzy preferences that are shown to be very useful to reflect the vagueness of information in the various preference situations that may be considered in the modelling process.
---
paper_title: Integrating Three Representation Models in Fuzzy Multipurpose Decision Making Based on Fuzzy Preference Relations

paper_content:

Abstract The purpose of this paper is to study a fuzzy multipurpose decision making problem, where the information about the alternatives provided by the experts can be of a diverse nature. the information can be represented by means of preference orderings, utility functions and fuzzy preference relations, and our objective is to establish a general model which cover all possible representations. Firstly, we must make the information uniform, using fuzzy preference relations as uniform preference context. Secondly, we present some selection processes for multiple preference relations based on the concept of fuzzy majority. Fuzzy majority is represented by a fuzzy quantifier, and applied in the aggregation, by means of an OWA operator whose weights are calculated by the fuzzy quantifier. We use two quantifier guided choice degrees of alternatives, a dominance degree used to quantify the dominance that one alternative has over all the others, in a fuzzy majority sense, and a non dominance degree, that generalises Orlovski's non dominated alternative concept. The application of the two above choice degrees can be carried out according to two different selection processes, a sequential selection process and a conjunction selection process.
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paper_title: Families of OWA operators

paper_content:

We introduce the ordered weighted averaging (OWA) operators. We look at some semantics and applications associated with these operators. We discuss the problem of obtaining the associated weighting parameters. We discuss the connection between OWA operators and linguistic quantifiers. We introduce a number of parametrized families of OWA operators; maximum entropy, S-OWA, step and window are among the most important of these families. We study the evaluation of quantified propositions using these operators. We introduce the idea of aggregate dependent weights.
---
paper_title: A new method of obtaining the priority weights from an interval fuzzy preference relation

paper_content:

In analyzing a multiple criteria decision-making problem, the decision maker may express her/his opinions as an interval fuzzy or multiplicative preference relation. Then it is an interesting and important issue to investigate the consistency of the preference relations and obtain the reliable priority weights. In this paper, a new consistent interval fuzzy preference relation is defined, and the corresponding properties are derived. The transformation formulae between interval fuzzy and multiplicative preference relations are further given, which show that two preference relations, consistent interval fuzzy and multiplicative preference relations, can be transformed into each other. Based on the transformation formula, the definition of acceptably consistent interval fuzzy preference relation is given. Furthermore a new algorithm for obtaining the priority weights from consistent or inconsistent interval fuzzy preference relations is presented. Finally, three numerical examples are carried out to compare the results using the proposed method with those using other existing procedures. The numerical results show that the given procedure is feasible, effective and not requisite to solve any mathematical programing.
---
paper_title: Learning valued preference structures for solving classification problems

paper_content:

This paper introduces a new approach to classification which combines pairwise decomposition techniques with ideas and tools from fuzzy preference modeling. More specifically, our approach first decomposes a polychotomous classification problem involving m classes into an ensemble of binary problems, one for each ordered pair of classes. The corresponding classifiers are trained on the relevant subsets of the (transformed) original training data. In the classification phase, a new query is submitted to every binary learner. The output of each classifier is interpreted as a fuzzy degree of preference for the first in comparison with the second class. By combining the outputs of all classifiers, one thus obtains a fuzzy preference relation which is taken as a point of departure for the final classification decision. This way, the problem of classification is effectively reduced to a problem of decision making based on a fuzzy preference relation. Corresponding techniques, which have been investigated quite intensively in the field of fuzzy set theory, hence become amenable to the task of classification. In particular, by decomposing a preference relation into a strict preference, an indifference, and an incomparability relation, this approach allows one to quantify different types of uncertainty in classification and thereby supports sophisticated classification and postprocessing strategies.
---
paper_title: Multi-criteria Decision Making with Incomplete Linguistic Preference Relations

paper_content:

When there are n criteria or alternatives in a decision matrix, a pairwise comparison methodology of analytic hierarchy process (AHP) with the time of n(n-1)/2 is frequently used to select, evaluate or rank the neighboring alternatives. But while the number of criteria or comparison level increase, the efficiency and consistency of a decision matrix decrease. To solve such problems, this study therefore uses horizontal, vertical and oblique pairwise comparisons algorithm to construct multi-criteria decision making with incomplete linguistic preference relations model (InLinPreRa). The use of pairwise comparisons will not produce the inconsistency, even allows every decision maker to choose an explicit criterion or alternative for index unrestrictedly. When there are n criteria, only n-1 pairwise comparisons need to be carried out, then one can rest on incomplete linguistic preference relations to obtain the priority value of alternative for the decision maker's reference. The decision making assessment model that constructed by this study can be extensively applied to every field of decision science and serves as the reference basis for the future research.
---
paper_title: Incomplete fuzzy linguistic preference relations under uncertain environments

paper_content:

When addressing decision-making problems, decision-makers typically express their opinions using fuzzy preference relations. In some instances, decision-makers may have to deal with the problems in which only partial information is available. Consequently, decision-makers embody their preferences as incomplete fuzzy preference relations. The values of incomplete fuzzy preference relations have been considered crisp in recent studies. To allow decision-makers to provide vague or imprecise responses, this study proposes a novel method, called incomplete fuzzy linguistic preference relations, that uses fuzzy linguistic assessment variables instead of crisp values of incomplete fuzzy preference relations to ensure comparison consistency. The proposed method reflects an environment in which some uncertainty or vagueness exists. Examples are included that illustrate the effectiveness of the proposed method.
---
paper_title: Families of relations modelling preferences under incomplete information

paper_content:

Let us consider a preferential information of type preference-indifference-incomparability (P,Â I,Â J), with additional information about differences in attractiveness between pairs of alternatives. The present paper offers a theoretical framework for the study of the "level of constraint" of this kind of partial preferential information. It suggests a number of structures as potential models being less demanding than the classical one in which differences in utilities can be used to represent the comparison of differences in attractiveness. The models are characterized in the more general context of families of non-complete preference structures, according to two different perspectives (called "semantico-numerical" and "matrix"). Both perspectives open the door to further practical applications connected with elicitation of the preferences of a decision maker.
---
paper_title: Fuzzy Preference Modelling and Multicriteria Decision Support

paper_content:

Note: Index. Bibliogr. : p. 239-251 Reference Record created on 2004-09-07, modified on 2016-08-08
---
paper_title: Interval multiplicative transitivity for consistency, missing values and priority weights of interval fuzzy preference relations

paper_content:

In this paper, the concept of multiplicative transitivity of a fuzzy preference relation, as defined by Tanino T. Tanino, Fuzzy preference orderings in group decision-making, Fuzzy Sets and Systems 12 (1984) 117-131, is extended to discover whether an interval fuzzy preference relation is consistent or not, and to derive the priority vector of a consistent interval fuzzy preference relation. We achieve this by introducing the concept of interval multiplicative transitivity of an interval fuzzy preference relation and show that, by solving numerical examples, the test of consistency and the weights derived by the simple formulas based on the interval multiplicative transitivity produce the same results as those of linear programming models proposed by Xu and Chen Z.S. Xu, J. Chen, Some models for deriving the priority weights from interval fuzzy preference relations, European Journal of Operational Research 184 (2008) 266-280. In addition, by taking advantage of interval multiplicative transitivity of an interval fuzzy preference relation, we put forward two approaches to estimate missing value(s) of an incomplete interval fuzzy preference relation, and present numerical examples to illustrate these two approaches.
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paper_title: Cardinal Consistency of Reciprocal Preference Relations: A Characterization of Multiplicative Transitivity

paper_content:

Consistency of preferences is related to rationality, which is associated with the transitivity property. Many properties suggested to model transitivity of preferences are inappropriate for reciprocal preference relations. In this paper, a functional equation is put forward to model the ldquocardinal consistency in the strength of preferencesrdquo of reciprocal preference relations. We show that under the assumptions of continuity and monotonicity properties, the set of representable uninorm operators is characterized as the solution to this functional equation. Cardinal consistency with the conjunctive representable cross ratio uninorm is equivalent to Tanino's multiplicative transitivity property. Because any two representable uninorms are order isomorphic, we conclude that multiplicative transitivity is the most appropriate property for modeling cardinal consistency of reciprocal preference relations. Results toward the characterization of this uninorm consistency property based on a restricted set of (n-1) preference values, which can be used in practical cases to construct perfect consistent preference relations, are also presented.
---
paper_title: Group decision making based on multiple types of linguistic preference relations

paper_content:

In this paper, we investigate group decision making problems with multiple types of linguistic preference relations. The paper has two parts with similar structures. In the first part, we transform the uncertain additive linguistic preference relations into the expected additive linguistic preference relations, and present a procedure for group decision making based on multiple types of additive linguistic preference relations. By using the deviation measures between additive linguistic preference relations, we give some straightforward formulas to determine the weights of decision makers, and propose a method to reach consensus among the individual preferences and the group's opinion. In the second part, we extend the above results to group decision making based on multiple types of multiplicative linguistic preference relations, and finally, a practical example is given to illustrate the application of the results.
---
paper_title: Utility theory for decision making

paper_content:

Abstract : The book presents a concise yet mathematically complete treatment of modern utility theories that covers nonprobabilistic preference theory, the von Neumann-Morgenstern expected-utility theory and its extensions, and the joint axiomatization of utility and subjective probability.
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paper_title: Multiperson decision-making based on multiplicative preference relations

paper_content:

A multiperson decision-making problem, where the information about the alternatives provided by the experts can be presented by means of diAerent preference representation structures (preference orderings, utility functions and multiplicative preference relations) is studied. Assuming the multiplicative preference relation as the uniform element of the preference representation, a multiplicative decision model based on fuzzy majority is presented to choose the best alternatives. In this decision model, several transformation functions are obtained to relate preference orderings and utility functions with multiplicative preference relations. The decision model uses the ordered weighted geometric operator to aggregate information and two choice degrees to rank the alternatives, quantifier guided dominance degree and quantifier guided non-dominance degree. The consistency of the model is analysed to prove that it acts coherently. ” 2001 Elsevier Science B.V. All rights reserved.
---
paper_title: Multi-criteria decision making with fuzzy linguistic preference relations

paper_content:

Abstract Although the analytic hierarchy process (AHP) and the extent analysis method (EAM) of fuzzy AHP are extensively adopted in diverse fields, inconsistency increases as hierarchies of criteria or alternatives increase because AHP and EAM require rather complicated pairwise comparisons amongst elements (attributes or alternatives). Additionally, decision makers normally find that assigning linguistic variables to judgments is simpler and more intuitive than to fixed value judgments. Hence, Wang and Chen proposed fuzzy linguistic preference relations (Fuzzy LinPreRa) to address the above problem. This study adopts Fuzzy LinPreRa to re-examine three numerical examples. The re-examination is intended to compare our results with those obtained in earlier works and to demonstrate the advantages of Fuzzy LinPreRa. This study demonstrates that, in addition to reducing the number of pairwise comparisons, Fuzzy LinPreRa also increases decision making efficiency and accuracy.
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paper_title: Fuzzy multiple attributes group decision-making based on fuzzy preference relations

paper_content:

In this paper, we present a new approach for fuzzy multiple attributes group decision-making based on fuzzy preference relations. First, we construct fuzzy importance matrices for decision-makers with respect to attributes and construct fuzzy evaluating matrices for decision-makers with respect to the attributes of the alternatives. Based on the fuzzy importance matrices and the fuzzy evaluating matrices, we construct fuzzy rating vectors for decision-makers with respect to the alternatives. Then, we defuzzify the trapezoidal fuzzy numbers in the constructed fuzzy rating vectors to get the rating vectors for the decision-makers. Based on the rating vectors, we construct fuzzy preference relations for the decision-makers with respect to the alternatives. Based on the fuzzy preference relations, we calculate the average rating value of each decision-maker with respect to the alternatives. Then, we sort these average rating values in a descending sequence and assign them different scores. Then, we calculate the summation values of the scores of the alternatives with respect to each decision-maker, respectively. The larger the summation values of the scores, the better the choice of the alternative. The proposed method is simpler than Chen's method (2000) and Li's method (2007) for handling fuzzy multiple attributes group decision-making problems. It provides us with a useful way to handle fuzzy multiple attributes group decision-making problems.
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paper_title: Characterizable fuzzy preference structures

paper_content:

In this paper, we study the existence, construction and reconstruction of fuzzy preferencestructures. Starting from the definition of a classical preference structure, we propose anatural definition of a fuzzy preference structure, merely requiring the fuzzification of theset operations involved. Upon evaluating the existence of these structures, we discover thatthe idea of fuzzy preferences is best captured when fuzzy preference structures are definedusing a L U ukasiewicz triplet. We then proceed to investigate the role of the completenesscondition in these structures. This rather extensive investigation leads to the proposal of astrongest completeness condition, and results in the definition of a one-parameter class offuzzy preference structures. Invoking earlier results by Fodor and Roubens, the constructionof these structures from a reflexive binary fuzzy relation is then easily obtained. Thereconstruction of such a structure from its fuzzy large preference relation inevitable toobtain a full characterization of these structures in analogy to the classical case is morecumbersome. The main result of this paper is the discovery of a non-trivial characterizingcondition that enables us to fully characterize the members of a two-parameter class offuzzy preference structures in terms of their fuzzy large preference relation. As a remarkableside-result, we discover three limit classes of characterizable fuzzy preference structures,traces of which are found throughout the preference modelling literature. Copyright Kluwer Academic Publishers 1998
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paper_title: Group decision making with linguistic preference relations with application to supplier selection

paper_content:

Linguistic preference relation is a useful tool for expressing preferences of decision makers in group decision making according to linguistic scales. But in the real decision problems, there usually exist interactive phenomena among the preference of decision makers, which makes it difficult to aggregate preference information by conventional additive aggregation operators. Thus, to approximate the human subjective preference evaluation process, it would be more suitable to apply non-additive measures tool without assuming additivity and independence. In this paper, based on @l-fuzzy measure, we consider dependence among subjective preference of decision makers to develop some new linguistic aggregation operators such as linguistic ordered geometric averaging operator and extended linguistic Choquet integral operator to aggregate the multiplicative linguistic preference relations and additive linguistic preference relations, respectively. Further, the procedure and algorithm of group decision making based on these new linguistic aggregation operators and linguistic preference relations are given. Finally, a supplier selection example is provided to illustrate the developed approaches.
---
paper_title: Probabilistic Borda rule voting

paper_content:

An alternative voting system, referred to as probabilistic Borda rule, is developed and analyzed. The winning alternative under this system is chosen by lottery where the weights are determined from each alternative’s Borda score relative to all Borda points possible. Advantages of the lottery include the elimination of strategic voting on the set of alternatives under consideration and breaking the tyranny of majority coalitions. Disadvantages include an increased incentive for strategic introduction of new alternatives to alter the lottery weights, and the possible selection of a Condorcet loser. Normative axiomatic properties of the system are also considered. It is shown this system satisfies the axiomatic properties of the standard Borda procedure in a probabilistic fashion.
---
paper_title: A consistency and consensus based decision support model for group decision making with multiplicative preference relations

paper_content:

In group decision making (GDM) with multiplicative preference relations (also known as pairwise comparison matrices in the Analytical Hierarchy Process), to come to a meaningful and reliable solution, it is preferable to consider individual consistency and group consensus in the decision process. This paper provides a decision support model to aid the group consensus process while keeping an acceptable individual consistency for each decision maker. The concept of an individual consistency index and a group consensus index is introduced based on the Hadamard product of two matrices. Two algorithms are presented in the designed support model. The first algorithm is utilized to convert an unacceptable preference relation to an acceptable one. The second algorithm is designed to assist the group in achieving a predefined consensus level. The main characteristics of our model are that: (1) it is independent of the prioritization method used in the consensus process; (2) it ensures that each individual multiplicative preference relation is of acceptable consistency when the predefined consensus level is achieved. Finally, some numerical examples are given to verify the effectiveness of our model.
---
paper_title: Induced uncertain linguistic OWA operators applied to group decision making

paper_content:

The ordered weighted averaging (OWA) operator was developed by Yager [IEEE Trans. Syst., Man, Cybernet. 18 (1998) 183]. Later, Yager and Filev [IEEE Trans. Syst., Man, Cybernet.--Part B 29 (1999) 141] introduced a more general class of OWA operators called the induced ordered weighted averaging (IOWA) operators, which take as their argument pairs, called OWA pairs, in which one component is used to induce an ordering over the second components which are exact numerical values and then aggregated. The aim of this paper is to develop some induced uncertain linguistic OWA (IULOWA) operators, in which the second components are uncertain linguistic variables. Some desirable properties of the IULOWA operators are studied, and then, the IULOWA operators are applied to group decision making with uncertain linguistic information.
---
paper_title: Applying fuzzy linguistic preference relations to the improvement of consistency of fuzzy AHP

paper_content:

The lack of consistency in decision making can lead to inconsistent conclusions. In fuzzy analytic hierarchy process (fuzzy AHP) method, it is difficult to ensure a consistent pairwise comparison. Furthermore, establishing a pairwise comparison matrix requires nx(n-1)2 judgments for a level with n criteria (alternatives). The number of comparisons increases as the number of criteria increases. Therefore, the decision makers judgments will most likely be inconsistent. To alleviate inconsistencies, this study applies fuzzy linguistic preference relations (Fuzzy LinPreRa) to construct a pairwise comparison matrix with additive reciprocal property and consistency. In this study, the fuzzy AHP method is reviewed, and then the Fuzzy LinPreRa method is proposed. Finally, the presented method is applied to the example addressed by Kahraman et al. [C. Kahraman, D. Ruan, I. Dogan, Fuzzy group decision making for facility location selection, Information Sciences 157 (2003) 135-153]. This study reveals that the proposed method yields consistent decision rankings from only n-1 pairwise comparisons, which is the same result as in Kahraman et al. research. The presented fuzzy linguistic preference relations method is an easy and practical way to provide a mechanism for improving consistency in fuzzy AHP method.
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paper_title: The ordered weighted geometric averaging operators

paper_content:

The ordered weighted averaging (OWA) operator was introduced by Yager.1 The fundamental aspect of the OWA operator is a reordering step in which the input arguments are rearranged in descending order. In this article, we propose two new classes of aggregation operators called ordered weighted geometric averaging (OWGA) operators and study some desired properties of these operators. Some methods for obtaining the associated weighting parameters are discussed, and the relationship between the OWA and DOWGA operators is also investigated. © 2002 Wiley Periodicals, Inc.
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paper_title: The continuous ordered weighted geometric operator and its application to decision making

paper_content:

The aim of this paper is to develop a continuous ordered weighted geometric (C-OWG) operator, which is based on the continuous ordered weighted averaging (C-OWA) operator recently introduced by the author and the geometric mean. We study some desirable properties of the C-OWG operator, and present its application to decision making with interval multiplicative preference relation, and finally, an illustrative example is pointed out.
---
paper_title: The weighted OWA operator

paper_content:

One of the properties that the OWA operator satisfies is commutativity. This condition, that is not satisfied by the weighted mean, stands for equal reliability of all the information sources that supply the data. In this article we define a new combination function, the WOWA (Weighted OWA), that combines the advantages of the OWA operator and the ones of the weighted mean. We study some of its properties and show how it can be extended to deal with linguistic labels. © 1997 John Wiley & Sons, Inc.
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paper_title: Group Decision-Making Model With Incomplete Fuzzy Preference Relations Based on Additive Consistency

paper_content:

In decision-making problems there may be cases in which experts do not have an in-depth knowledge of the problem to be solved. In such cases, experts may not put their opinion forward about certain aspects of the problem, and as a result they may present incomplete preferences, i.e., some preference values may not be given or may be missing. In this paper, we present a new model for group decision making in which experts' preferences can be expressed as incomplete fuzzy preference relations. As part of this decision model, we propose an iterative procedure to estimate the missing information in an expert's incomplete fuzzy preference relation. This procedure is guided by the additive-consistency (AC) property and only uses the preference values the expert provides. The AC property is also used to measure the level of consistency of the information provided by the experts and also to propose a new induced ordered weighted averaging (IOWA) operator, the AC-IOWA operator, which permits the aggregation of the experts' preferences in such a way that more importance is given to the most consistent ones. Finally, the selection of the solution set of alternatives according to the fuzzy majority of the experts is based on two quantifier-guided choice degrees: the dominance and the nondominance degree
---
paper_title: A View of Averaging Aggregation Operators

paper_content:

Aggregation operators have been used and studied for a long time. More than ten different types of means (including the arithmetic, geometric, and harmonic ones) were already studied 2000 years ago. Nevertheless, this topic has gained relevance in recent years. This is partly due to the increasing need of methods and operators for fusing information within computer programs. In this paper, we will present a personal view of the field, focusing on the application issues and on averaging aggregation operators. We will point out some research topics and open lines for future research.
---
paper_title: Social Choice and Individual Values

paper_content:

Originally published in 1951, Social Choice and Individual Values introduced "Arrow's Impossibility Theorem" and founded the field of social choice theory in economics and political science. This new edition, including a new foreword by Nobel laureate Eric Maskin, reintroduces Arrow's seminal book to a new generation of students and researchers. "Far beyond a classic, this small book unleashed the ongoing explosion of interest in social choice and voting theory. A half-century later, the book remains full of profound insight: its central message, 'Arrow's Theorem,' has changed the way we think."-Donald G. Saari, author of Decisions and Elections: Explaining the Unexpected
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paper_title: Reasoning with multiple-source information in a possibilistic logic framework q

paper_content:

This paper addresses the problem of merging uncertain information in the framework of possibilistic logic. It presents several syntactic combination rules to merge possibilistic knowledge bases, provided by different sources, into a new possibilistic knowledge base. These combination rules are first described at the meta-level outside the language of possibilistic logic. Next, an extension of possibilistic logic, where the combination rules are inside the language, is proposed. A proof system in a sequent form is given, sound and complete with respect to the possibilistic logic semantics. Possibilistic fusion modes are illustrated on an example inspired from an application of a localization of a robot in an uncertain environment.
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paper_title: Social choice axioms for fuzzy set aggregation

paper_content:

The problem of aggregating n fuzzy sets F1, F2,.., Fn on a set ω is viewed as one of merging the opinions of n individuals (e.g. experts) that rate objects belonging to ω. This approach contrasts with the pure set-theoretic point of view, and leads to interpreting already known axioms underlying fuzzy connectives in a way different from that of multiple criteria aggregation. Various natural properties of a voting procedure, including the ones proposed by Arrow are expressed in the fuzzy set setting. A number of conditions limiting the choice of fuzzy set operations are proposed and classified according to whether they are imperative, mainly technical, or facultative. Families of solutions are obtained that include those proposed in earlier works. The case of non-homogeneous groups is briefly examined. Lastly the application of the voting paradigm to the management of antagonistic local decision rules in knowledge-based systems is outlined.
---
paper_title: Situation Assessment in Disaster Management

paper_content:

We present a framework for decision-making in relation to disaster management with a focus on situation assessment during disaster management monitoring. The use of causality reasoning based on the temporal evolution of a scenario provides a natural way to chain meaningful events and possible states of the system. There are usually different ways to analyse a problem and different strategies to follow as a solution and it is also often the case that information originating in different sources can be inconsistent or unreliable. Therefore we allow the specification of possibly conflicting situations as they are typical elements in disaster management. A decision procedure to decide on those conflicting situations is presented which not only provides a framework for the assistance of one decision-maker but also how to handle opinions from a hierarchy of decision-makers.
---
paper_title: Hard and soft constraints for reasoning about qualitative conditional preferences

paper_content:

Many real life optimization problems are defined in terms of both hard and soft constraints, and qualitative conditional preferences. However, there is as yet no single framework for combined reasoning about these three kinds of information. In this paper we study how to exploit classical and soft constraint solvers for handling qualitative preference statements such as those captured by the CP-nets model. In particular, we show how hard constraints are sufficient to model the optimal outcomes of a possibly cyclic CP-net, and how soft constraints can faithfully approximate the semantics of acyclic conditional preference statements whilst improving the computational efficiency of reasoning about these statements.
---
paper_title: A Logic of Soft Constraints based on Partially Ordered Preferences

paper_content:

Representing and reasoning with an agent's preferences is important in many applications of constraints formalisms. Such preferences are often only partially ordered. One class of soft constraints formalisms, semiring-based CSPs, allows a partially ordered set of preference degrees, but this set must form a distributive lattice; whilst this is convenient computationally, it considerably restricts the representational power. This paper constructs a logic of soft constraints where it is only assumed that the set of preference degrees is a partially ordered set, with a maximum element 1 and a minimum element 0. When the partially ordered set is a distributive lattice, this reduces to the idempotent semiring-based CSP approach, and the lattice operations can be used to define a sound and complete proof theory. A generalised possibilistic logic, based on partially ordered values of possibility, is also constructed, and shown to be formally very strongly related to the logic of soft constraints. It is shown how the machinery that exists for the distributive lattice case can be used to perform sound and complete deduction, using a compact embedding of the partially ordered set in a distributive lattice.
---
paper_title: A CP-Nets-Based Model and Verification for Consumer-Centric Information Service Composition

paper_content:

A CP-nets-based model for consumer-centric information service composition is proposed. Moreover, an algorithm was provided to construct the model. The model can explicitly express the diversity and individuality of users' needs, and the combinational logic between services graphically, and verify the correctness of services composition by using the reachability, safeness, boundedness, liveness and fairness of CP-nets. Finally, there is an example, a concrete consumer-centric information service composition for a system is modeled and validated based on CP-nets method. It shows that this modeling approach has enough capability of expressing and verifying consumer-centric information service composition.
---
paper_title: CP-nets: A Tool for Representing and Reasoning withConditional Ceteris Paribus Preference Statements

paper_content:

Information about user preferences plays a key role in automated decision making. In many domains it is desirable to assess such preferences in a qualitative rather than quantitative way. In this paper, we propose a qualitative graphical representation of preferences that reflects conditional dependence and independence of preference statements under a ceteris paribus (all else being equal) interpretation. Such a representation is often compact and arguably quite natural in many circumstances. We provide a formal semantics for this model, and describe how the structure of the network can be exploited in several inference tasks, such as determining whether one outcome dominates (is preferred to) another, ordering a set outcomes according to the preference relation, and constructing the best outcome subject to available evidence.
---
paper_title: UCP-Networks: A Directed Graphical Representation of Conditional Utilities

paper_content:

We propose a directed graphical representation of utility functions, called UCP-networks, that combines aspects of two existing preference models: generalized additive models and CP-networks. The network decomposes a utility function into a number of additive factors, with the directionality of the arcs reflecting conditional dependence in the underlying (qualitative) preference ordering under a ceteris paribus interpretation. The CP-semantics ensures that computing optimization and dominance queries is very efficient. We also demonstrate the value of this representation in decision making. Finally, we describe an interactive elicitation procedure that takes advantage of the linear nature of the constraints on "tradeoff weights" imposed by a UCP-network.
---
paper_title: Incompleteness and Incomparability in Preference Aggregation

paper_content:

We consider how to combine the preferences of multiple agents despite the presence of incompleteness and incomparability in their preference orderings. An agent's preference ordering may be incomplete because, for example, there is an ongoing preference elicitation process. It may also contain incomparability as this is useful, for example, in multi-criteria scenarios. We focus on the problem of computing the possible and necessary winners, that is, those outcomes which can be or always are the most preferred for the agents. Possible and necessary winners are useful in many scenarios including preference elicitation. First we show that computing the sets of possible and necessary winners is in general a difficult problem as is providing a good approximation of such sets. Then we identify general properties of the preference aggregation function which are sufficient for such sets to be computed in polynomial time. Finally, we show how possible and necessary winners can be used to focus preference elicitation.
---
paper_title: Majority Judgment: Measuring, Ranking, and Electing

paper_content:

In Majority Judgment, Michel Balinski and Rida Laraki argue that the traditional theory of social choice offers no acceptable solution to the problems of how to elect, to judge, or to rank. They find that the traditional model--transforming the "preference lists" of individuals into a "preference list" of society--is fundamentally flawed in both theory and practice. Balinski and Laraki propose a more realistic model. It leads to an entirely new theory and method--majority judgment--proven superior to all known methods. It is at once meaningful, resists strategic manipulation, elicits honesty, and is not subject to the classical paradoxes encountered in practice, notably Condorcet's and Arrow's. They offer theoretical, practical, and experimental evidence--from national elections to figure skating competitions--to support their arguments. Drawing on insights from wine, sports, music, and other competitions, Balinski and Laraki argue that the question should not be how to transform many individual rankings into a single collective ranking, but rather, after defining a common language of grades to measure merit, how to transform the many individual evaluations of each competitor into a single collective evaluation of all competitors. The crux of the matter is a new model in which the traditional paradigm--to compare--is replaced by a new paradigm--to evaluate.
---
paper_title: LCP-Nets: A Linguistic Approach for Non-functional Preferences in a Semantic SOA Environment

paper_content:

This paper addresses the problem of expressing preferences among non- functional properties of services in a Web service architecture. In such a context, seman- tic and non-functional annotations are required on service declarations and business process calls to services in order to select the best available service for each invoca- tion. To cope with these multi-criteria decision problems, conditional and unconditional preferences are managed using a new variant of conditional preference networks (CP- nets), taking into account uncertainty related to the preferences to achieve a better satisfaction rate. This variant, called LCP-nets, uses fuzzy linguistic information in- side the whole process, from preference elicitation to outcome query computation, a qualitative approach that is more suitable to business process programmers. Indeed, in LCP-nets, preference variables and utilities take linguistic values while conditional pref- erence tables are considered as fuzzy rules which interdependencies may be complex. The expressiveness of the graphical model underlying CP-nets provides for solutions to gather all the preferences under uncertainty and to tackle interdependency problems. LCP-nets are applied to the problem of selecting the best service among a set of of- fers, given their dynamic non-functional properties. The implementation of LCP-nets is presented step-by-step through a real world example.
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paper_title: Semiring-based constraint satisfaction and optimization

paper_content:

We introduce a general framework for constraint satisfaction and optimization where classical CSPs, fuzzy CSPs, weighted CSPs, partial constraint satisfaction, and others can be easily cast. The framework is based on a semiring structure, where the set of the semiring specifies the values to be associated with each tuple of values of the variable domain, and the two semiring operations (+ and X) model constraint projection and combination respectively. Local consistency algorithms, as usually used for classical CSPs, can be exploited in this general framework as well, provided that certain conditions on the semiring operations are satisfied. We then show how this framework can be used to model both old and new constraint solving and optimization schemes, thus allowing one to both formally justify many informally taken choices in existing schemes, and to prove that local consistency techniques can be used also in newly defined schemes.
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paper_title: Semiring-based constraint logic programming: syntax and semantics

paper_content:

We extend the Constraint Logic Programming (CLP) formalism in order to handle semiring-based constraints. This allows us to perform in the same language both constraint solving and optimization. In fact, constraints based on semirings are able to model both classical constraint solving and more sophisticated features like uncertainty, probability, fuzziness, and optimization. We then provide this class of languages with three equivalent semantics: model-theoretic, fix-point, and proof-theoretic, in the style of classical CLP programs.
---
paper_title: Probabilistic Borda rule voting

paper_content:

An alternative voting system, referred to as probabilistic Borda rule, is developed and analyzed. The winning alternative under this system is chosen by lottery where the weights are determined from each alternative’s Borda score relative to all Borda points possible. Advantages of the lottery include the elimination of strategic voting on the set of alternatives under consideration and breaking the tyranny of majority coalitions. Disadvantages include an increased incentive for strategic introduction of new alternatives to alter the lottery weights, and the possible selection of a Condorcet loser. Normative axiomatic properties of the system are also considered. It is shown this system satisfies the axiomatic properties of the standard Borda procedure in a probabilistic fashion.
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paper_title: The Computational Complexity of Dominance and Consistency in CP-Nets

paper_content:

We investigate the computational complexity of testing dominance and consistency in CP-nets. Previously, the complexity of dominance has been determined for restricted classes in which the dependency graph of the CP-net is acyclic. However, there are preferences of interest that define cyclic dependency graphs; these are modeled with general CP-nets. In our main results, we show here that both dominance and consistency for general CP-nets are PSPACE-complete. We then consider the concept of strong dominance, dominance equivalence and dominance incomparability, and several notions of optimality, and identify the complexity of the corresponding decision problems. The reductions used in the proofs are from STRIPS planning, and thus reinforce the earlier established connections between both areas.
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paper_title: Logical Preference Representation and Combinatorial Vote

paper_content:

We introduce the notion of combinatorial vote, where a group of agents (or voters) is supposed to express preferences and come to a common decision concerning a set of non-independent variables to assign. We study two key issues pertaining to combinatorial vote, namely preference representation and the automated choice of an optimal decision. For each of these issues, we briefly review the state of the art, we try to define the main problems to be solved and identify their computational complexity.
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paper_title: Geometry of Voting

paper_content:

It is shown how simple geometry can be used to analyze and discover new properties about pairwise and positional voting rules as well as for those rules (e.g., runoffs and Approval Voting) that rely on these methods. The description starts by providing a geometric way to depict profiles, which simplifies the computation of the election outcomes. This geometry is then used to motivate the development of a “profile coordinate system,” which evolves into a tool to analyze voting rules. This tool, for instance, completely explains various longstanding “paradoxes,” such as why a Condorcet winner need not be elected with certain voting rules. A different geometry is developed to indicate whether certain voting “oddities” can be dismissed or must be taken seriously, and to explain why other mysteries, such as strategic voting and the no-show paradox (where a voter is rewarded by not voting), arise. Still another use of geometry extends McGarvey's Theorem about possible pairwise election rankings to identify the actual tallies that can arise (a result that is needed to analyze supermajority voting). Geometry is also developed to identify all possible positional and Approval Voting election outcomes that are admitted by a given profile; the converse becomes a geometric tool that can be used to discover new election relationships. Finally, it is shown how lessons learned in social choice, such as the seminal Arrow's and Sen's Theorems and the expanding literature about the properties of positional rules, provide insights into difficulties that are experienced by other disciplines.
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paper_title: From Computing With Numbers To Computing With Words From Manipulation Of Measurements To Manipulation of Perceptions

paper_content:

Discusses a methodology for reasoning and computing with perceptions rather than measurements. An outline of such a methodology-referred to as a computational theory of perceptions is presented in this paper. The computational theory of perceptions, or CTP for short, is based on the methodology of CW. In CTP, words play the role of labels of perceptions and, more generally, perceptions are expressed as propositions in a natural language. CW-based techniques are employed to translate propositions expressed in a natural language into what is called the Generalized Constraint Language (GCL). In this language, the meaning of a proposition is expressed as a generalized constraint, N is R, where N is the constrained variable, R is the constraining relation and isr is a variable copula in which r is a variable whose value defines the way in which R constrains S. Among the basic types of constraints are: possibilistic, veristic, probabilistic, random set, Pawlak set, fuzzy graph and usuality. The wide variety of constraints in GCL makes GCL a much more expressive language than the language of predicate logic. In CW, the initial and terminal data sets, IDS and TDS, are assumed to consist of propositions expressed in a natural language. These propositions are translated, respectively, into antecedent and consequent constraints. Consequent constraints are derived from antecedent constraints through the use of rules of constraint propagation. The principal constraint propagation rule is the generalized extension principle. The derived constraints are retranslated into a natural language, yielding the terminal data set (TDS). The rules of constraint propagation in CW coincide with the rules of inference in fuzzy logic. A basic problem in CW is that of explicitation of N, R, and r in a generalized constraint, X is R, which represents the meaning of a proposition, p, in a natural language.
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paper_title: Reasoning with multiple-source information in a possibilistic logic framework q

paper_content:

This paper addresses the problem of merging uncertain information in the framework of possibilistic logic. It presents several syntactic combination rules to merge possibilistic knowledge bases, provided by different sources, into a new possibilistic knowledge base. These combination rules are first described at the meta-level outside the language of possibilistic logic. Next, an extension of possibilistic logic, where the combination rules are inside the language, is proposed. A proof system in a sequent form is given, sound and complete with respect to the possibilistic logic semantics. Possibilistic fusion modes are illustrated on an example inspired from an application of a localization of a robot in an uncertain environment.
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paper_title: Rational choice and security studies : Stephen Walt and his critics

paper_content:

Formal theories and rational choice methods have become increasingly prominent in most social sciences in the past few decades. Proponents of formal theoretical approaches argue that these methods are more scientific and sophisticated than other approaches, and that formal methods have already generated significant theoretical progress. As more and more social scientists adopt formal theoretical approaches, critics have argued that these methods are flawed and that they should not become dominant in most social-science disciplines.Rational Choice and Security Studies presents opposing views on the merits of formal rational choice approaches as they have been applied in the subfield of international security studies. This volume includes Stephen Walt's article "Rigor or Rigor Mortis? Rational Choice and Security Studies," critical replies from prominent political scientists, and Walt's rejoinder to his critics.Walt argues that formal approaches have not led to creative new theoretical explanations, that they lack empirical support, and that they have contributed little to the analysis of important contemporary security problems. In their replies, proponents of rational choice approaches emphasize that formal methods are essential for achieving theoretical consistency and precision.
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paper_title: On the consistency of rule bases based on lattice-valued first-order logic LF(X)

paper_content:

The consistency of a rule base is an essential issue for rule-based intelligent information processing. Due to the uncertainty inevitably included in the rule base, it is necessary to verify the consistency of the rule base while investigating, designing, and applying a rule-based intelligent system. In the framework of the lattice-valued first-order logic system LF(X), which attempts to handle fuzziness and incomparability, this article focuses on how to verify and increase the consistency degree of the rule base in the intelligent information processing system. First, the representations of eight kinds of rule bases in LF(X) as the generalized clause set forms based on these rule bases' nonredundant generalized Skolem standard forms are presented. Then an α-automated reasoning algorithm in LF(X), also used as an automated simplification algorithm, is proposed. Furthermore, the α-consistency and the α-simplification theories of the rule base in LF(X) are formulated, and especially the coherence between these two theories is proved. Therefore, the verification of the α-consistency of the rule base, often an infinity problem that is difficult to solve, can be transformed into a finite and achievable α-simplification problem. Finally, an α-simplification stepwise search algorithm for verifying the consistency of the rule base as well as a kind of filtering algorithm for increasing the consistency level of the rule base are proposed. © 2006 Wiley Periodicals, Inc. Int J Int Syst 21: 399–424, 2006.
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paper_title: A Logical Reasoning With Preference

paper_content:

In a decision making context, multiple choices of actions are usually offered to solve a particular problem. Consequently, the question of preferences among the actions will occur. The ordering of recommended actions by preference is made by taking into account the states of the universe of discourse. We develop here a logic Lp for reasoning about preferences in such circumstances. The language of the logic is propositional extended with a special binary relation of preference among formulae. The model theory of the logic is studied and the soundness and completeness theorem is established.
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paper_title: Reasoning With Partially Ordered Information in a Possibilistic Logic Framework

paper_content:

In many applications, the reliability relation associated with available information is only partially defined, while most of existing uncertainty frameworks deal with totally ordered pieces of knowledge. Partial pre-orders offer more flexibility than total pre-orders to represent incomplete knowledge. Possibilistic logic, which is an extension of classical logic, deals with totally ordered information. It offers a natural qualitative framework for handling uncertain information. Priorities are encoded by means of weighted formulas, where weights are lower bounds of necessity measures. This paper proposes an extension of possibilistic logic for dealing with partially ordered pieces of knowledge. We show that there are two different ways to define a possibilistic logic machinery which both extend the standard one.
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paper_title: Weak completeness of resolution in a linguistic truth-valued propositional logic

paper_content:

In the present paper, the weak completeness of alpha-resolution principle for a latticevalued logic (L(n)xL(2))P(X) with truth value in a logical algebra - lattice implication algebra L(n)xL(2), is established. Accordingly, the weak completeness of (Exactly, True)-resolution principle for a linguistic truth-valued propositional logic l based on the linguistic truth-valued lattice implication algebra L-LIA is derived.
---
paper_title: Some Views on Information Fusion and Logic Based Approaches in Decision Making under Uncertainty

paper_content:

Decision making under uncertainty is a key issue in information fusion and logic based reasoning approaches. The aim of this paper is to show noteworthy theoretical and applicational issues in the area of decision making under uncertainty that have been already done and raise new open research related to these topics pointing out promising and challenging research gaps that should be addressed in the coming future in order to improve the resolution of decision making problems under uncertainty. Keyword: decision making, uncertainty, information fusion, logics, uncertain information processing, computing with words Categories: I.1, I.2, M.4, F.4.1
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paper_title: A Linguistic Truth-Valued Uncertainty Reasoning Model Based on Lattice-Valued Logic

paper_content:

The subject of this work is to establish a mathematical framework that provide the basis and tool for uncertainty reasoning based on linguistic information. This paper focuses on a flexible and realistic approach, i.e., the use of linguistic terms, specially, the symbolic approach acts by direct computation on linguistic terms. An algebra model with linguistic terms, which is based on a logical algebraic structure, i.e., lattice implication algebra, is applied to represent imprecise information and deals with both comparable and incomparable linguistic terms (i.e., non-ordered linguistic terms). Within this framework, some inferential rules are analyzed and extended to deal with these kinds of lattice-valued linguistic information.
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paper_title: A Logic of Soft Constraints based on Partially Ordered Preferences

paper_content:

Representing and reasoning with an agent's preferences is important in many applications of constraints formalisms. Such preferences are often only partially ordered. One class of soft constraints formalisms, semiring-based CSPs, allows a partially ordered set of preference degrees, but this set must form a distributive lattice; whilst this is convenient computationally, it considerably restricts the representational power. This paper constructs a logic of soft constraints where it is only assumed that the set of preference degrees is a partially ordered set, with a maximum element 1 and a minimum element 0. When the partially ordered set is a distributive lattice, this reduces to the idempotent semiring-based CSP approach, and the lattice operations can be used to define a sound and complete proof theory. A generalised possibilistic logic, based on partially ordered values of possibility, is also constructed, and shown to be formally very strongly related to the logic of soft constraints. It is shown how the machinery that exists for the distributive lattice case can be used to perform sound and complete deduction, using a compact embedding of the partially ordered set in a distributive lattice.
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paper_title: From Semantic to Syntactic Approaches to Information Combination in Possibilistic Logic

paper_content:

This paper proposes syntactic combination rules for merging uncertain propositional knowledge bases provided by different sources of information, in the framework of possibilistic logic. These rules are the counterparts of combination rules which can be applied to the possibility distributions (defined on the set of possible worlds), which represent the semantics of each propositional knowledge base. Combination modes taking into account the levels of conflict, the relative reliability of the sources, or having reinforcement effects are considered.
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paper_title: Fuzzy logic = computing with words

paper_content:

As its name suggests, computing with words (CW) is a methodology in which words are used in place of numbers for computing and reasoning. The point of this note is that fuzzy logic plays a pivotal role in CW and vice-versa. Thus, as an approximation, fuzzy logic may be equated to CW. There are two major imperatives for computing with words. First, computing with words is a necessity when the available information is too imprecise to justify the use of numbers, and second, when there is a tolerance for imprecision which can be exploited to achieve tractability, robustness, low solution cost, and better rapport with reality. Exploitation of the tolerance for imprecision is an issue of central importance in CW. In CW, a word is viewed as a label of a granule; that is, a fuzzy set of points drawn together by similarity, with the fuzzy set playing the role of a fuzzy constraint on a variable. The premises are assumed to be expressed as propositions in a natural language. In coming years, computing with words is likely to evolve into a basic methodology in its own right with wide-ranging ramifications on both basic and applied levels.
---
paper_title: Logical Preference Representation and Combinatorial Vote

paper_content:

We introduce the notion of combinatorial vote, where a group of agents (or voters) is supposed to express preferences and come to a common decision concerning a set of non-independent variables to assign. We study two key issues pertaining to combinatorial vote, namely preference representation and the automated choice of an optimal decision. For each of these issues, we briefly review the state of the art, we try to define the main problems to be solved and identify their computational complexity.
---
paper_title: Linguistic Truth-Valued Lattice Implication Algebra and Its Properties

paper_content:

The subject of this work is to establish a mathematical framework that provides the basis and tool for automated reasoning and uncertainty reasoning based on linguistic information. This paper focuses on a flexible and realistic approach, i.e., the use of linguistic terms, specially, the symbolic approach acts by direct computation on linguistic terms. An algebra model with linguistic terms, which is based on a logical algebraic structure, i.e., lattice implication algebra, is constructed and applied to represent imprecise information and deal with both comparable and incomparable linguistic terms (i.e., non-ordered linguistic terms). Some properties and its substructures of this algebraic model are discussed.
---
paper_title: Linguistic Values Based Intelligent Information Processing: Theory, Methods and Applications

paper_content:

This book focuses on systematic and intelligent information processing theories and methods based on linguistic values. The main contents include topics such as the 2-tuple model of linguistic values, 2-tuple linguistic aggregation operator hedge algebras, complete hedge algebras and linguistic value reasoning, reasoning with linguistic quantifiers, linguistic reasoning based on a random set, the fuzzy number model of linguistic values, linguistic value aggregation based on the fuzzy number model, extraction of linguistic proposition from a database and handling of linguistic information on the Internet, linguistic truth value lattice implication algebras, linguistic truth value resolution automatic reasoning, linguistic truth value reasoning based on lattice implication algebra, and related applications in decision-making and forecast.
---
paper_title: Linguistic truth-valued lattice-valued propositional logic system ℓP(X) based on linguistic truth-valued lattice implication algebra

paper_content:

In the semantics of natural language, quantification may have received more attention than any other subject, and syllogistic reasoning is one of the main topics in many-valued logic studies on inference. Particularly, lattice-valued logic, a kind of important non-classical logic, can be applied to describe and treat incomparability by the incomparable elements in its truth-valued set. In this paper, we first focus on some properties of linguistic truth-valued lattice implication algebra. Secondly, we introduce some concepts of linguistic truth-valued lattice-valued propositional logic system @?P(X), whose truth-valued domain is a linguistic truth-valued lattice implication algebra. Then we investigate the semantic problem of @?P(X). Finally, we further probe into the syntax of linguistic truth-valued lattice-valued propositional logic system @?P(X), and prove the soundness theorem, deduction theorem and consistency theorem.
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paper_title: A lattice-valued linguistic-based decision making method

paper_content:

The subject of this work is to establish a mathematical framework that provides the basis and tool for synthesis and evaluation analysis in decision making, especially from the logic point of view. This paper focuses on a flexible and realistic approach, i.e., the use of linguistic assessment in decision making, specially, the symbolic approach acts by direct computation on linguistic values. A lattice-valued linguistic algebra model, which is based on a logical algebraic structure, i.e., lattice implication algebra, is applied to represent imprecise information and deal with both comparable and incomparable linguistic values (i.e., non-ordered linguistic values). Within this framework, some known weighted aggregation functions are analyzed and extended to deal with these kinds of lattice-value linguistic information.
---
paper_title: Some Views on Information Fusion and Logic Based Approaches in Decision Making under Uncertainty

paper_content:

Decision making under uncertainty is a key issue in information fusion and logic based reasoning approaches. The aim of this paper is to show noteworthy theoretical and applicational issues in the area of decision making under uncertainty that have been already done and raise new open research related to these topics pointing out promising and challenging research gaps that should be addressed in the coming future in order to improve the resolution of decision making problems under uncertainty. Keyword: decision making, uncertainty, information fusion, logics, uncertain information processing, computing with words Categories: I.1, I.2, M.4, F.4.1
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paper_title: Situation Assessment in Disaster Management

paper_content:

We present a framework for decision-making in relation to disaster management with a focus on situation assessment during disaster management monitoring. The use of causality reasoning based on the temporal evolution of a scenario provides a natural way to chain meaningful events and possible states of the system. There are usually different ways to analyse a problem and different strategies to follow as a solution and it is also often the case that information originating in different sources can be inconsistent or unreliable. Therefore we allow the specification of possibly conflicting situations as they are typical elements in disaster management. A decision procedure to decide on those conflicting situations is presented which not only provides a framework for the assistance of one decision-maker but also how to handle opinions from a hierarchy of decision-makers.
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paper_title: Hard and soft constraints for reasoning about qualitative conditional preferences

paper_content:

Many real life optimization problems are defined in terms of both hard and soft constraints, and qualitative conditional preferences. However, there is as yet no single framework for combined reasoning about these three kinds of information. In this paper we study how to exploit classical and soft constraint solvers for handling qualitative preference statements such as those captured by the CP-nets model. In particular, we show how hard constraints are sufficient to model the optimal outcomes of a possibly cyclic CP-net, and how soft constraints can faithfully approximate the semantics of acyclic conditional preference statements whilst improving the computational efficiency of reasoning about these statements.
---
paper_title: Semiring-based constraint logic programming: syntax and semantics

paper_content:

We extend the Constraint Logic Programming (CLP) formalism in order to handle semiring-based constraints. This allows us to perform in the same language both constraint solving and optimization. In fact, constraints based on semirings are able to model both classical constraint solving and more sophisticated features like uncertainty, probability, fuzziness, and optimization. We then provide this class of languages with three equivalent semantics: model-theoretic, fix-point, and proof-theoretic, in the style of classical CLP programs.
---
paper_title: Probabilistic Borda rule voting

paper_content:

An alternative voting system, referred to as probabilistic Borda rule, is developed and analyzed. The winning alternative under this system is chosen by lottery where the weights are determined from each alternative’s Borda score relative to all Borda points possible. Advantages of the lottery include the elimination of strategic voting on the set of alternatives under consideration and breaking the tyranny of majority coalitions. Disadvantages include an increased incentive for strategic introduction of new alternatives to alter the lottery weights, and the possible selection of a Condorcet loser. Normative axiomatic properties of the system are also considered. It is shown this system satisfies the axiomatic properties of the standard Borda procedure in a probabilistic fashion.
---
paper_title: Logical Preference Representation and Combinatorial Vote

paper_content:

We introduce the notion of combinatorial vote, where a group of agents (or voters) is supposed to express preferences and come to a common decision concerning a set of non-independent variables to assign. We study two key issues pertaining to combinatorial vote, namely preference representation and the automated choice of an optimal decision. For each of these issues, we briefly review the state of the art, we try to define the main problems to be solved and identify their computational complexity.
---
paper_title: Linguistic Values Based Intelligent Information Processing: Theory, Methods and Applications

paper_content:

This book focuses on systematic and intelligent information processing theories and methods based on linguistic values. The main contents include topics such as the 2-tuple model of linguistic values, 2-tuple linguistic aggregation operator hedge algebras, complete hedge algebras and linguistic value reasoning, reasoning with linguistic quantifiers, linguistic reasoning based on a random set, the fuzzy number model of linguistic values, linguistic value aggregation based on the fuzzy number model, extraction of linguistic proposition from a database and handling of linguistic information on the Internet, linguistic truth value lattice implication algebras, linguistic truth value resolution automatic reasoning, linguistic truth value reasoning based on lattice implication algebra, and related applications in decision-making and forecast.
---

Title: Ordering Based Decision Making - A Survey
Section 1: Introduction
Description 1: Briefly introduce decision making and its importance, especially related to ordering based decision making, and outline the challenges and methods in dealing with complex decision-making scenarios.

Section 2: Representation of Ordinal Qualitative Information
Description 2: Discuss various methods of representing ordinal qualitative information, including fuzzy sets, symbolic approaches, and hedge algebra, highlighting their strengths and weaknesses.

Section 3: Preference Based Decision Making
Description 3: Review methods for decision making based on preferences, including utility functions, preference relations, and preference orderings, and discuss their application in real-world problems.

Section 4: Decision Making Based on Preference Relations
Description 4: Detail different types of preference relations, including multiplicative, fuzzy, and linguistic preference relations, and their use in decision making.

Section 5: Decision Making with Preference Ordering
Description 5: Explore approaches that involve ranking alternatives based on preference orderings, focusing on methods used in social choice and other applications.

Section 6: Logic Based Decision Making
Description 6: Examine how logic is used to model decision making problems, including both syntactic and semantic representations, and review logic-based reasoning approaches.

Section 7: Conclusions and Perspectives
Description 7: Summarize the strengths and weaknesses of the reviewed methods, and discuss future research directions and potential solutions for improving ordering based decision making methods.