A new generalized intuitionistic fuzzy set

Abstract

A generalized intuitionistic fuzzy set (GIFSB) is proposed. It is shown that Atanassov’s intuitionistic fuzzy set, intuitionistic fuzzy sets of root type and intuitionistic fuzzy sets of second type are special cases of this new one. Some important notions, basic algebraic properties of GIFSB, three operators and their relationship are discussed. The algebraic properties include being closed under union, being closed under intersection, being closed under a necessity measure, being closed under a possibility measure and de Morgan type identities.