Notions and Concepts of Fuzzy Sets: An Introduction
Witold Pedrycz, Petr Ekel, Roberta Parreiras · 2010
This chapter introduces the essential concepts of fuzzy sets. It focuses on the fundamental idea of partial membership, which is conveniently quantified through membership functions and membership degrees. The chapter presents the underlying rationale and then move on to a detailed description of fuzzy sets by discussing the most commonly encountered classes of membership functions and relating these classes to the semantics of fuzzy sets. It elaborates on the basic operations on fuzzy sets (intersection, union, complement, negation) and covers early fuzzy set operations and continuing with their generalization, interpretations, formal requirements, and realizations. Analyses of the fundamental properties and characteristics of operations with fuzzy sets are discussed. The chapter explains the concepts of fuzzy relations and their main properties, which are of direct relevance in the context of decision-making. It presents the relationships between fuzzy sets and sets by stressing that sets are subsumed as particular cases of sets. Controlled Vocabulary Terms fuzzy set theory; geometric codes; linguistics