The Defuzzification by the Median and Centroid Rules

H.-M. Lee, T.-Y. Lee, S.-Y. Lee (Taiwan), and J.-J. Chen (USA)


Median rule; Centroid; Defuzzification


2. Fuzzy set theoryThe purpose of this article is to point out that the defuzzification by the median rule is not the same as by the classical centroid for the trapezoid or the triangular fuzzy number unless the trapezoid or the triangular is isosceles. If we defuzzify to solve the problem by the median then the computing errors will be out of our tolerance The fuzzy set theory was introduced by Zadeh [5] to deal with problems in which a source of vagueness is present. It has been considered as a modeling language to approximate situations in which fuzzy phenomena and criteria exist. In a universe of discourse X, a fuzzy subset A of X is a set defined by a membership function fA(x) representing a mapping which maps each element x in X to a real number in the closed interval [0, 1]. Here, the value of fA(x) for the fuzzy set A is called the membership value or the grade of the membership of x in X. The membership value represents the degree of x belonging to the fuzzy set A. The greater fA(x) the stronger the grade of membership for x in A.

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