Fuzzy Sets

Abstract

The basic concept of a fuzzy set is introduced in the next section. t-norms and t-conorms are used throughout fuzzy set theory and fuzzy logic and they are studied in the third section. t-norms (t-conorms) are used to compute the intersection (union) of fuzzy sets. Once we have intersection and union of fuzzy sets, we can study the algebra of fuzzy sets in section four. In Section 2.4 we notice that all the laws of crisp set theory (presented in Section 2.2) do not necessarily hold for fuzzy sets. Mixed fuzzy logic is introduced in Section 2.5 to show one method of getting fuzzy sets to obey all the basic laws of crisp set theory. a-cuts, or a way to represent a fuzzy set as a collection of nested crisp sets, is then discussed in section six. To initiate a calculus of continuous fuzzy subsets of the real numbers, determining the distance between these fuzzy sets comprises the final section of this chapter.