On the representation of intuitionistic fuzzy t-norms and t-conorms
Glad Deschrijver, Chris Cornelis, Etienne E. Kerre · 2002
Abstract—Intuitionistic fuzzy sets form an extension of fuzzy sets: while fuzzy sets give a degree to which an element belongs to a set, intuitionistic fuzzy sets give both a membership degree and a nonmembership degree. The only constraint on those two degrees is that their sum must be smaller than or equal to 1. In fuzzy set theory, an important class of triangular norms and conorms is the class of continuous Archimedean nilpotent triangular norms and conorms. It has been shown that for such-norms there exists a permutation of [0,1] such that is the-transform of the Łukasiewicz-norm. In this paper we introduce the notion of intuitionistic fuzzy-norm and-conorm, and investigate under which conditions a similar representation theorem can be obtained. Index Terms—Archimedean property, intuitionistic fuzzy set, intuitionistic fuzzy triangular norm and conorm, nilpotency, representation theorem,-transform. I.