Transcription of Chapter 3 Fuzzy Membership Functions (Repaired)
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Chapter 3 Fuzzy Membership Functions (Repaired)
Debasis Samanta, Indian institute of technology kharagpur 1 Chapter 3 Fuzzy Membership Function Formulation and Parameterization The Membership function of a Fuzzy set is a generalization of the indicator function in classical sets. In Fuzzy logic, it represents the degree of truth as an extension of valuation. Degrees of truth are often confused with probabilities, although they are conceptually distinct, because Fuzzy truth represents Membership in vaguely defined sets, not likelihood of some event or condition. Membership Functions were introduced by Zadeh in the first paper on Fuzzy sets (1965). Figure : Membership Functions in Fuzzy vs. crisp sets Formal Definition of Membership function Let us consider Fuzzy set A, A = {(x, A(x))| x X} where A(x) is called the Membership function for the Fuzzy set A.
©Debasis Samanta, Indian Institute of Technology Kharagpur 10 References 1. Leszek Rutkowski., Flexible Neuro-Fuzzy Systems: Structures, Learning and Performance Evaluation, Technical University of Czestochowa, Poland, Kluwer Academic Publishers New York, Chapter 2:ELEMENTS OF THE THEORY OF FUZZY SETS. 2.
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