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.
Obviously, Ferrari and Rolls Royce have membership value of 1 whereas BMW, which is less expensive, has a Membership value of 0.7 and Honda 0.4. The Fuzzy set is similar to the super set of the Boolean logic with extra membership functions in between “true” and “false”. As its name suggests, it is the logic underlying modes of reasoning
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