Operations on Fuzzy/Intuitionistic Fuzzy Sets and Application in Decision Making

This chapter defines various types of fuzzy operations. Among the well‐known operations, which are performed on fuzzy sets are fuzzy union, fuzzy intersection, fuzzy complement, fuzzy algebraic sum, and algebraic product. Fuzzy aggregation operators are discussed where different objects are combined into a single object of a same set. These include weighted averaging operator, ordered weighting operator, hybrid averaging operator, fuzzy generalized ordered weighted averaging operator, fuzzy induced generalized aggregation operator, fuzzy quasi arithmetic weighted averaging operator, fuzzy induced generalized averaging operator, Choquet ordered aggregation operator and induced Choquet ordered aggregation operator. Different types of intuitionistic fuzzy aggregation operators similar to fuzzy aggregation operators are explained with examples. These are generalized intuitionistic fuzzy aggregation operator, generalized intuitionistic fuzzy ordered aggregation operator, generalized intuitionistic fuzzy hybrid operator, intuitionistic fuzzy ordered weighted geometric operator, Choquet ordered aggregation operator and induced Choquet ordered aggregation operator.