A Survey on Fuzzy Association Rule Mining Methodologies
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paper_title: Knowledge Discovery in Databases: an Overview

paper_content:

After a decade of fundamental interdisciplinary research in machine learning, the spadework in this field has been done; the 1990s should see the widespread exploitation of knowledge discovery as an aid to assembling knowledge bases. The contributors to the AAAI Press book Knowledge Discovery in Databases were excited at the potential benefits of this research. The editors hope that some of this excitement will communicate itself to "AI Magazine readers of this article.
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paper_title: Algorithms for association rule mining — a general survey and comparison

paper_content:

ABSTRACT Today there are several eAE ient algorithms that ope with the popular and omputationally expensive task of asso iation rule mining. A tually, these algorithms are more or less des ribed on their own. In this paper we explain the fundamentals of asso iation rule mining and moreover derive a general framework. Based on this we des ribe today's approa hes in ontext by pointing out ommon aspe ts and di eren es. After that we thoroughly investigate their strengths and weaknesses and arry out several runtime experiments. It turns out that the runtime behavior of the algorithms is mu h more similar as to be expe ted.
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paper_title: Fuzzy association rule mining algorithm for fast and efficient performance on very large datasets

paper_content:

Fuzzy association rules use fuzzy logic to convert numerical attributes to fuzzy attributes, like “Income = High”, thus maintaining the integrity of information conveyed by such numerical attributes. On the other hand, crisp association rules use sharp partitioning to transform numerical attributes to binary ones like “Income = [100K and above]”, and can potentially introduce loss of information due to these sharp ranges. Fuzzy Apriori and its different variations are the only popular fuzzy association rule mining (ARM) algorithms available today. Like the crisp version of Apriori, fuzzy Apriori is a very slow and inefficient algorithm for very large datasets (in the order of millions of transactions). Hence, we have come up with a new fuzzy ARM algorithm meant for fast and efficient performance on very large datasets. As compared to fuzzy Apriori, our algorithm is 8-19 times faster for the very large standard real-life dataset we have used for testing with various mining workloads, both typical and extreme ones. A novel combination of features like two-phased multiple-partition tidlist-style processing, byte-vector representation of tidlists, and fast compression of tidlists contribute a lot to the efficiency in performance. In addition, unlike most two-phased ARM algorithms, the second phase is totally different from the first one in the method of processing (individual itemset processing as opposed to simultaneous itemset processing at each k-level), and is also many times faster. Our algorithm also includes an effective preprocessing technique for converting a crisp dataset to a fuzzy dataset.
---
paper_title: Mining Fuzzy Association Rules: An Overview

paper_content:

The main aim of this paper is to present a revision of the most relevant results about the use of Fuzzy Sets in Data Mining, specifically in relation with the discovery of Association Rules. Fuzzy Sets Theory has been shown to be a very useful tool in Data Mining in order to represent the so-called Association Rules in a natural and human-understandable way.
---
paper_title: Mining Fuzzy Multiple-Level Association Rules from Quantitative Data

paper_content:

Machine-learning and data-mining techniques have been developed to turn data into useful task-oriented knowledge. Most algorithms for mining association rules identify relationships among transactions using binary values and find rules at a single-concept level. Transactions with quantitative values and items with hierarchical relationships are, however, commonly seen in real-world applications. This paper proposes a fuzzy multiple-level mining algorithm for extracting knowledge implicit in transactions stored as quantitative values. The proposed algorithm adopts a top-down progressively deepening approach to finding large itemsets. It integrates fuzzy-set concepts, data-mining technologies and multiple-level taxonomy to find fuzzy association rules from transaction data sets. Each item uses only the linguistic term with the maximum cardinality in later mining processes, thus making the number of fuzzy regions to be processed the same as the number of original items. The algorithm therefore focuses on the most important linguistic terms for reduced time complexity.
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paper_title: Discovery of Multiple-Level Association Rules from Large Databases *

paper_content:

Previous studies on mining association rules find rules at single concept level, however, mining association rules at multiple concept levels may lead to the discovery of more specific and concrete knowledge from data. In this study, a top-down progressive deepening method is developed for mining multiplelevel association rules from large transaction databases by extension of some existing association rule mining techniques. A group of variant algorithms are proposed based on the ways of sharing intermediate results, with the relative performance tested on different kinds of data. Relaxation of the rule conditions for finding “level-crossing” association rules is also discussed in the paper.
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paper_title: ARMOR: Association Rule Mining based on ORacle

paper_content:

In this paper, we first focus our attention on the question of how much space remains for performance improvement over current association rule mining algorithms. Our strategy is to compare their performance against an “Oracle algorithm” that knows in advance the identities of all frequent itemsets in the database and only needs to gather their actual supports to complete the mining process. Our experimental results show that current mining algorithms do not perform uniformly well with respect to the Oracle for all database characteristics and support thresholds. In many cases there is a substantial gap between the Oracle’s performance and that of the current mining algorithms. Second, we present a new mining algorithm, called ARMOR, that is constructed by making minimal changes to the Oracle algorithm. ARMOR consistently performs within a factor of two of the Oracle on both real and synthetic datasets over practical ranges of support specifications.
---
paper_title: Fuzzy association rule mining algorithm for fast and efficient performance on very large datasets

paper_content:

Fuzzy association rules use fuzzy logic to convert numerical attributes to fuzzy attributes, like “Income = High”, thus maintaining the integrity of information conveyed by such numerical attributes. On the other hand, crisp association rules use sharp partitioning to transform numerical attributes to binary ones like “Income = [100K and above]”, and can potentially introduce loss of information due to these sharp ranges. Fuzzy Apriori and its different variations are the only popular fuzzy association rule mining (ARM) algorithms available today. Like the crisp version of Apriori, fuzzy Apriori is a very slow and inefficient algorithm for very large datasets (in the order of millions of transactions). Hence, we have come up with a new fuzzy ARM algorithm meant for fast and efficient performance on very large datasets. As compared to fuzzy Apriori, our algorithm is 8-19 times faster for the very large standard real-life dataset we have used for testing with various mining workloads, both typical and extreme ones. A novel combination of features like two-phased multiple-partition tidlist-style processing, byte-vector representation of tidlists, and fast compression of tidlists contribute a lot to the efficiency in performance. In addition, unlike most two-phased ARM algorithms, the second phase is totally different from the first one in the method of processing (individual itemset processing as opposed to simultaneous itemset processing at each k-level), and is also many times faster. Our algorithm also includes an effective preprocessing technique for converting a crisp dataset to a fuzzy dataset.
---
paper_title: Fuzzy association rules mining algorithm based on equivalence redundancy of items

paper_content:

In data mining approaches, quantitative attributes should be appropriately dealt with as well as Boolean attributes. This paper presents an essential improvement for extracting fuzzy association rules from a database. The objective of this paper is to improve the computational time of mining and to prune extracted redundant rules simultaneously for an actual data mining application. In this paper, we define the equivalence redundancy of fuzzy items and related theorems as a new concept for fuzzy data mining. Then, we propose a basic algorithm based on the Apriori algorithm for rule extraction utilizing the equivalence redundancy of the fuzzy items based on redundancy concepts of fuzzy association rules. The essential performance of the algorithm is evaluated through numerical experiments using benchmark data. From the results, the method is found to be promising in terms of computational time and redundant-rule pruning.
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paper_title: Mining top-k frequent closed patterns without minimum support

paper_content:

In this paper, we propose a new mining task: mining top-k frequent closed patterns of length no less than min_/spl lscr/, where k is the desired number of frequent closed patterns to be mined, and min_/spl lscr/ is the minimal length of each pattern. An efficient algorithm, called TFP, is developed for mining such patterns without minimum support. Two methods, closed-node-count and descendant-sum are proposed to effectively raise support threshold and prune FP-tree both during and after the construction of FP-tree. During the mining process, a novel top-down and bottom-up combined FP-tree mining strategy is developed to speed-up support-raising and closed frequent pattern discovering. In addition, a fast hash-based closed pattern verification scheme has been employed to check efficiently if a potential closed pattern is really closed. Our performance study shows that in most cases, TFP outperforms CLOSET and CHARM, two efficient frequent closed pattern mining algorithms, even when both are running with the best tuned min-support. Furthermore, the method can be extended to generate association rules and to incorporate user-specified constraints.
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paper_title: An Efficient Algorithm for Mining Association Rules in Large Databases

paper_content:

Mining for a.ssociation rules between items in a large database of sales transactions has been described as an important database mining problem. In this paper we present an efficient algorithm for mining association rules that is fundamentally different from known algorithms. Compared to previous algorithms, our algorithm not only reduces the I/O overhead significantly but also has lower CPU overhead for most cases. We have performed extensive experiments and compared the performance of our algorithm with one of the best existing algorithms. It was found that for large databases, the CPU overhead was reduced by as much as a factor of four and I/O was reduced by almost an order of magnitude. Hence this algorithm is especially suitable for very large size databases.
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paper_title: Fuzzy Cluster Analysis: Methods for Classification, Data Analysis and Image Recognition

paper_content:

Introduction. Basic Concepts. Classical Fuzzy Clustering Algorithms. Linear and Ellipsoidal Prototypes Shell Prototypes. Polygonal Object Boundaries. Cluster Estimation Models. Cluster Validity. Rule Generation with Clustering. Appendix. Bibliography.
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paper_title: An ACS-based framework for fuzzy data mining

paper_content:

Data mining is often used to find out interesting and meaningful patterns from huge databases. It may generate different kinds of knowledge such as classification rules, clusters, association rules, and among others. A lot of researches have been proposed about data mining and most of them focused on mining from binary-valued data. Fuzzy data mining was thus proposed to discover fuzzy knowledge from linguistic or quantitative data. Recently, ant colony systems (ACS) have been successfully applied to optimization problems. However, few works have been done on applying ACS to fuzzy data mining. This thesis thus attempts to propose an ACS-based framework for fuzzy data mining. In the framework, the membership functions are first encoded into binary-bits and then fed into the ACS to search for the optimal set of membership functions. The problem is then transformed into a multi-stage graph, with each route representing a possible set of membership functions. When the termination condition is reached, the best membership function set (with the highest fitness value) can then be used to mine fuzzy association rules from a database. At last, experiments are made to make a comparison with other approaches and show the performance of the proposed framework.
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paper_title: Mining generalized fuzzy association rules via determining minimum supports

paper_content:

Summary from only given. Association rule mining is based on the assumption that users can specify the minimum-support for mining their databases. It has been identified that setting the minimum support is a difficult task to users. This can hamper the widespread applications of these algorithms. This paper proposes a method for computing minimum supports for each item. It therefore will run the fuzzy multi-level mining algorithm for extracting knowledge implicit in quantitative transactions, immediately. More specifically, our algorithms automatically generate actual minimum-supports according to users' mining requirements. In order to address this need, the new approach can express tow profits includes computing the minimum support for each item regarding to characteristic for each item in database and making a system automation. We considered an algorithm that can cover the multiple level association rules under multiple item supports. We experimentally examine the algorithms using a dataset, and demonstrate that our algorithm fittingly approximates actual minimum-supports from the commonly-used requirements.
---
paper_title: Concise representations for approximate association rules

paper_content:

The quality of association rule mining has drawn more and more attention recently. One problem with the quality of the discovered association rules is the huge size of the extracted rule set. Often for a dataset, a huge number of rules can be extracted, but many of them can be redundant to other rules and thus useless in practice. Mining non-redundant rules is a promising approach to solve this problem. In this paper, we firstly propose a definition for redundancy; then we propose a concise representation called reliable basis for representing non-redundant association rules for both exact rules and approximate rules. We prove that the redundancy elimination based on the reliable basis does not reduce the belief to the extracted rules. We also prove that all association rules can be deduced from the reliable basis. Therefore the reliable basis is a lossless representation of association rules. Experimental results show that the reliable basis significantly reduces the number of extracted rules.
---
paper_title: A fuzzy relative of the isodata process and its use in detecting compact well-separated clusters

paper_content:

Abstract Two fuzzy versions of the k-means optimal, least squared error partitioning problem are formulated for finite subsets X of a general inner product space. In both cases, the extremizing solutions are shown to be fixed points of a certain operator T on the class of fuzzy, k-partitions of X, and simple iteration of T provides an algorithm which has the descent property relative to the least squared error criterion function. In the first case, the range of T consists largely of ordinary (i.e. non-fuzzy) partitions of X and the associated iteration scheme is essentially the well known ISODATA process of Ball and Hall. However, in the second case, the range of T consists mainly of fuzzy partitions and the associated algorithm is new; when X consists of k compact well separated (CWS) clusters, Xi , this algorithm generates a limiting partition with membership functions which closely approximate the characteristic functions of the clusters Xi . However, when X is not the union of k CWS clusters, the limi...
---
paper_title: Mining Fuzzy Multiple-level Association Rules under Multiple Minimum Supports

paper_content:

Finding association rules in transaction databases is most commonly seen in data mining. In real applications, different items may have different support criteria to judge their importance, taxonomic relationships among items may appear, and data may have quantitative values. This paper thus proposes a fuzzy multiple-level mining algorithm for extracting knowledge implicit in quantitative transactions with multiple minimum supports of items. Items may have different minimum supports and the maximum-itemset minimum-taxonomy support constraint is adopted to discover the large itemsets. Under the constraint, the characteristic of downward-closure is kept, such that the original Apriori algorithm can be easily extended to find fuzzy large itemsets. The proposed algorithm adopts a top-down progressively deepening approach to derive large itemsets. It can also discover cross-level fuzzy association rules under the maximum-itemset minimum-taxonomy support constraint. An example is also given to demonstrate that the proposed mining algorithm can derive the multiple-level association rules under multiple item supports in a simple and effective way.
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paper_title: Multi-level fuzzy mining with multiple minimum supports

paper_content:

Finding association rules in transaction databases is most commonly seen in data mining. In real applications, different items may have different support criteria to judge their importance, taxonomic relationships among items may appear, and data may have quantitative values. This paper thus proposes a fuzzy multiple-level mining algorithm for extracting knowledge implicit in quantitative transactions with multiple minimum supports of items. Items may have different minimum supports and the maximum-itemset minimum-taxonomy support constraint is adopted to discover the large itemsets. Under the constraint, the characteristic of downward-closure is kept, such that the original apriori algorithm can be easily extended to find fuzzy large itemsets. The proposed algorithm adopts a top-down progressively deepening approach to derive large itemsets. It can also discover cross-level fuzzy association rules under the maximum-itemset minimum-taxonomy support constraint. An example is also given to demonstrate that the proposed mining algorithm can derive the multiple-level association rules under multiple item supports in a simple and effective way.
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paper_title: Fuzzy versus quantitative association rules: a fair data-driven comparison

paper_content:

As opposed to quantitative association rule mining, fuzzy association rule mining is said to prevent the overestimation of boundary cases, as can be shown by small examples. Rule mining, however, becomes interesting in large databases, where the problem of boundary cases is less apparent and can be further suppressed by using sensible partitioning methods. A data-driven approach is used to investigate if there is a significant difference between quantitative and fuzzy association rules in large databases. The influence of the choice of a particular triangular norm in this respect is also examined.
---
paper_title: Fuzzy association rules: general model and applications

paper_content:

The theory of fuzzy sets has been recognized as a suitable tool to model several kinds of patterns that can hold in data. In this paper, we are concerned with the development of a general model to discover association rules among items in a (crisp) set of fuzzy transactions. This general model can be particularized in several ways; each particular instance corresponds to a certain kind of pattern and/or repository of data. We describe some applications of this scheme, paying special attention to the discovery of fuzzy association rules in relational databases.
---
paper_title: An implementation of the FP-growth algorithm

paper_content:

The FP-growth algorithm is currently one of the fastest approaches to frequent item set mining. In this paper I describe a C implementation of this algorithm, which contains two variants of the core operation of computing a projection of an FP-tree (the fundamental data structure of the FP-growth algorithm). In addition, projected FP-trees are (optionally) pruned by removing items that have become infrequent due to the projection (an approach that has been called FP-Bonsai). I report experimental results comparing this implementation of the FP-growth algorithm with three other frequent item set mining algorithms I implemented (Apriori, Eclat, and Relim).
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paper_title: Mining Positive and Negative Fuzzy Association Rules

paper_content:

While traditional algorithms concern positive associations between binary or quantitative attributes of databases, this paper focuses on mining both positive and negative fuzzy association rules. We show how, by a deliberate choice of fuzzy logic connectives, significantly increased expressivity is available at little extra cost. In particular, rule quality measures for negative rules can be computed without additional scans of the database.
---
paper_title: Fuzzy association rules mining algorithm based on output specification and redundancy of rules

paper_content:

In data mining approach, the quantitative attributes should be appropriately dealt with as well as the Boolean attributes. This paper presents a fast algorithm for extracting fuzzy association rules from database. The objective of the algorithm is to improve the computational time of mining for actual applications. In this paper, we propose a basic algorithm based on the Apriori algorithm for rule extraction utilizing output fields specifications and redundancy of the extracted rules. The performance of the algorithm is evaluated through numerical experiments using benchmark data. From the results, the method is found to be promising in terms of computational time and redundant rule pruning.
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paper_title: FUZZY ASSOCIATION RULES : A TWO-SIDED APPROACH ∗

paper_content:

We bring to the surface the fundamental two-sidedness of knowledge in the framework of association rules, until now only slumberingly present in the measures of support and confidence. We identify the set of positive as well as the set of negative examples which are not necessarily complementary. Taking this into account we introduce new quality measures comprising the existing ones. Finally, we carefully examine the generalization of our findings to fuzzy association rules. Keyword: fuzzy association rule, support, opposition, positive example, negative example
---
paper_title: Fuzzy association rule mining algorithm for fast and efficient performance on very large datasets

paper_content:

Fuzzy association rules use fuzzy logic to convert numerical attributes to fuzzy attributes, like “Income = High”, thus maintaining the integrity of information conveyed by such numerical attributes. On the other hand, crisp association rules use sharp partitioning to transform numerical attributes to binary ones like “Income = [100K and above]”, and can potentially introduce loss of information due to these sharp ranges. Fuzzy Apriori and its different variations are the only popular fuzzy association rule mining (ARM) algorithms available today. Like the crisp version of Apriori, fuzzy Apriori is a very slow and inefficient algorithm for very large datasets (in the order of millions of transactions). Hence, we have come up with a new fuzzy ARM algorithm meant for fast and efficient performance on very large datasets. As compared to fuzzy Apriori, our algorithm is 8-19 times faster for the very large standard real-life dataset we have used for testing with various mining workloads, both typical and extreme ones. A novel combination of features like two-phased multiple-partition tidlist-style processing, byte-vector representation of tidlists, and fast compression of tidlists contribute a lot to the efficiency in performance. In addition, unlike most two-phased ARM algorithms, the second phase is totally different from the first one in the method of processing (individual itemset processing as opposed to simultaneous itemset processing at each k-level), and is also many times faster. Our algorithm also includes an effective preprocessing technique for converting a crisp dataset to a fuzzy dataset.
---
paper_title: Fuzzy association rules mining algorithm based on equivalence redundancy of items

paper_content:

In data mining approaches, quantitative attributes should be appropriately dealt with as well as Boolean attributes. This paper presents an essential improvement for extracting fuzzy association rules from a database. The objective of this paper is to improve the computational time of mining and to prune extracted redundant rules simultaneously for an actual data mining application. In this paper, we define the equivalence redundancy of fuzzy items and related theorems as a new concept for fuzzy data mining. Then, we propose a basic algorithm based on the Apriori algorithm for rule extraction utilizing the equivalence redundancy of the fuzzy items based on redundancy concepts of fuzzy association rules. The essential performance of the algorithm is evaluated through numerical experiments using benchmark data. From the results, the method is found to be promising in terms of computational time and redundant-rule pruning.
---
paper_title: Mining generalized fuzzy association rules via determining minimum supports

paper_content:

Summary from only given. Association rule mining is based on the assumption that users can specify the minimum-support for mining their databases. It has been identified that setting the minimum support is a difficult task to users. This can hamper the widespread applications of these algorithms. This paper proposes a method for computing minimum supports for each item. It therefore will run the fuzzy multi-level mining algorithm for extracting knowledge implicit in quantitative transactions, immediately. More specifically, our algorithms automatically generate actual minimum-supports according to users' mining requirements. In order to address this need, the new approach can express tow profits includes computing the minimum support for each item regarding to characteristic for each item in database and making a system automation. We considered an algorithm that can cover the multiple level association rules under multiple item supports. We experimentally examine the algorithms using a dataset, and demonstrate that our algorithm fittingly approximates actual minimum-supports from the commonly-used requirements.
---
paper_title: Fuzzy association rules mining algorithm based on output specification and redundancy of rules

paper_content:

In data mining approach, the quantitative attributes should be appropriately dealt with as well as the Boolean attributes. This paper presents a fast algorithm for extracting fuzzy association rules from database. The objective of the algorithm is to improve the computational time of mining for actual applications. In this paper, we propose a basic algorithm based on the Apriori algorithm for rule extraction utilizing output fields specifications and redundancy of the extracted rules. The performance of the algorithm is evaluated through numerical experiments using benchmark data. From the results, the method is found to be promising in terms of computational time and redundant rule pruning.
---
paper_title: Mining Fuzzy Association Rules: An Overview

paper_content:

The main aim of this paper is to present a revision of the most relevant results about the use of Fuzzy Sets in Data Mining, specifically in relation with the discovery of Association Rules. Fuzzy Sets Theory has been shown to be a very useful tool in Data Mining in order to represent the so-called Association Rules in a natural and human-understandable way.
---
paper_title: Fuzzy association rule mining algorithm for fast and efficient performance on very large datasets

paper_content:

Fuzzy association rules use fuzzy logic to convert numerical attributes to fuzzy attributes, like “Income = High”, thus maintaining the integrity of information conveyed by such numerical attributes. On the other hand, crisp association rules use sharp partitioning to transform numerical attributes to binary ones like “Income = [100K and above]”, and can potentially introduce loss of information due to these sharp ranges. Fuzzy Apriori and its different variations are the only popular fuzzy association rule mining (ARM) algorithms available today. Like the crisp version of Apriori, fuzzy Apriori is a very slow and inefficient algorithm for very large datasets (in the order of millions of transactions). Hence, we have come up with a new fuzzy ARM algorithm meant for fast and efficient performance on very large datasets. As compared to fuzzy Apriori, our algorithm is 8-19 times faster for the very large standard real-life dataset we have used for testing with various mining workloads, both typical and extreme ones. A novel combination of features like two-phased multiple-partition tidlist-style processing, byte-vector representation of tidlists, and fast compression of tidlists contribute a lot to the efficiency in performance. In addition, unlike most two-phased ARM algorithms, the second phase is totally different from the first one in the method of processing (individual itemset processing as opposed to simultaneous itemset processing at each k-level), and is also many times faster. Our algorithm also includes an effective preprocessing technique for converting a crisp dataset to a fuzzy dataset.
---
paper_title: Fuzzy association rules mining algorithm based on equivalence redundancy of items

paper_content:

In data mining approaches, quantitative attributes should be appropriately dealt with as well as Boolean attributes. This paper presents an essential improvement for extracting fuzzy association rules from a database. The objective of this paper is to improve the computational time of mining and to prune extracted redundant rules simultaneously for an actual data mining application. In this paper, we define the equivalence redundancy of fuzzy items and related theorems as a new concept for fuzzy data mining. Then, we propose a basic algorithm based on the Apriori algorithm for rule extraction utilizing the equivalence redundancy of the fuzzy items based on redundancy concepts of fuzzy association rules. The essential performance of the algorithm is evaluated through numerical experiments using benchmark data. From the results, the method is found to be promising in terms of computational time and redundant-rule pruning.
---
paper_title: Fuzzy Cluster Analysis: Methods for Classification, Data Analysis and Image Recognition

paper_content:

Introduction. Basic Concepts. Classical Fuzzy Clustering Algorithms. Linear and Ellipsoidal Prototypes Shell Prototypes. Polygonal Object Boundaries. Cluster Estimation Models. Cluster Validity. Rule Generation with Clustering. Appendix. Bibliography.
---
paper_title: Mining generalized fuzzy association rules via determining minimum supports

paper_content:

Summary from only given. Association rule mining is based on the assumption that users can specify the minimum-support for mining their databases. It has been identified that setting the minimum support is a difficult task to users. This can hamper the widespread applications of these algorithms. This paper proposes a method for computing minimum supports for each item. It therefore will run the fuzzy multi-level mining algorithm for extracting knowledge implicit in quantitative transactions, immediately. More specifically, our algorithms automatically generate actual minimum-supports according to users' mining requirements. In order to address this need, the new approach can express tow profits includes computing the minimum support for each item regarding to characteristic for each item in database and making a system automation. We considered an algorithm that can cover the multiple level association rules under multiple item supports. We experimentally examine the algorithms using a dataset, and demonstrate that our algorithm fittingly approximates actual minimum-supports from the commonly-used requirements.
---
paper_title: Concise representations for approximate association rules

paper_content:

The quality of association rule mining has drawn more and more attention recently. One problem with the quality of the discovered association rules is the huge size of the extracted rule set. Often for a dataset, a huge number of rules can be extracted, but many of them can be redundant to other rules and thus useless in practice. Mining non-redundant rules is a promising approach to solve this problem. In this paper, we firstly propose a definition for redundancy; then we propose a concise representation called reliable basis for representing non-redundant association rules for both exact rules and approximate rules. We prove that the redundancy elimination based on the reliable basis does not reduce the belief to the extracted rules. We also prove that all association rules can be deduced from the reliable basis. Therefore the reliable basis is a lossless representation of association rules. Experimental results show that the reliable basis significantly reduces the number of extracted rules.
---
paper_title: A fuzzy relative of the isodata process and its use in detecting compact well-separated clusters

paper_content:

Abstract Two fuzzy versions of the k-means optimal, least squared error partitioning problem are formulated for finite subsets X of a general inner product space. In both cases, the extremizing solutions are shown to be fixed points of a certain operator T on the class of fuzzy, k-partitions of X, and simple iteration of T provides an algorithm which has the descent property relative to the least squared error criterion function. In the first case, the range of T consists largely of ordinary (i.e. non-fuzzy) partitions of X and the associated iteration scheme is essentially the well known ISODATA process of Ball and Hall. However, in the second case, the range of T consists mainly of fuzzy partitions and the associated algorithm is new; when X consists of k compact well separated (CWS) clusters, Xi , this algorithm generates a limiting partition with membership functions which closely approximate the characteristic functions of the clusters Xi . However, when X is not the union of k CWS clusters, the limi...
---
paper_title: Fuzzy association rules: general model and applications

paper_content:

The theory of fuzzy sets has been recognized as a suitable tool to model several kinds of patterns that can hold in data. In this paper, we are concerned with the development of a general model to discover association rules among items in a (crisp) set of fuzzy transactions. This general model can be particularized in several ways; each particular instance corresponds to a certain kind of pattern and/or repository of data. We describe some applications of this scheme, paying special attention to the discovery of fuzzy association rules in relational databases.
---
paper_title: Fuzzy association rules mining algorithm based on output specification and redundancy of rules

paper_content:

In data mining approach, the quantitative attributes should be appropriately dealt with as well as the Boolean attributes. This paper presents a fast algorithm for extracting fuzzy association rules from database. The objective of the algorithm is to improve the computational time of mining for actual applications. In this paper, we propose a basic algorithm based on the Apriori algorithm for rule extraction utilizing output fields specifications and redundancy of the extracted rules. The performance of the algorithm is evaluated through numerical experiments using benchmark data. From the results, the method is found to be promising in terms of computational time and redundant rule pruning.
---

Title: A Survey on Fuzzy Association Rule Mining Methodologies

Section 1: INTRODUCTION
Description 1: Introduce the concept of rule mining, its importance in data mining, and provide background on association rule mining.

Section 2: CLASSIFICATION OF ASSOCIATION RULE MINING ALGORITHMS
Description 2: Discuss the basic classification of association rule mining algorithms, differentiating between BFS and DFS algorithms, and their sub-classes.

Section 3: CLASSICAL ASSOCIATION RULE MINING AND FUZZY ASSOCIATION RULE MINING
Description 3: Explain the limitations of classical association rule mining and introduce the concept of fuzzy association rule mining with its advantages.

Section 4: FUZZY ASSOCIATION RULE MINING ALGORITHMS
Description 4: Detail various fuzzy association rule mining algorithms, discussing specific methodologies and research contributions in this field.

Section 5: COMPARATIVE ANALYSIS
Description 5: Provide a comparative analysis of the surveyed fuzzy association rule mining methodologies based on parameters like strategy, complexity, execution time, and accuracy.

Section 6: Conclusion And Future Work
Description 6: Summarize the findings, highlight the limitations observed in current methodologies, and suggest directions for future research in fuzzy association rule mining.