Transcription of Chapter 1 Fuzzy set - IITKGP
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Chapter 1 Fuzzy set - IITKGP
Debasis Samanta, Indian Institute of Technology Kharagpur 1 Chapter 1 Introduction to Fuzzy Set In this Chapter , the concept of Fuzzy sets and the operations on the Fuzzy set are discussed. The concepts are the generalizations of crisp sets. Classical sets are also called crisp sets so as to distinguish them from Fuzzy sets. In fact, the Crisp sets can be taken as special cases of Fuzzy sets. Let A be a crisp set defined over the Universe X. Then for any element x in X, either x is a member of A or not. In Fuzzy set theory, this property is generalized. Therefore, in a Fuzzy set, it is not necessary that x is a full Member of the set or not a member. It can be a partial member of the sets. Figure 1: Crisp vs.
In fuzzy logic everything is a matter of degree. Any logical system can be fuzzified In fuzzy logic, knowledge is interpreted as a collection of elastic or, equivalently , fuzzy constraint on a collection of variables Inference is viewed as a process of propagation of elastic constraints. Fuzzy Sets Fuzzy Set Theory was formalized by Professor ...
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