Answer to D. Dubois, S. Gottwald, P. Hajek, J. Kacprzyk and H. Prade's paper "Terminological difficulties in fuzzy set theory - the case of "Intuitionistic Fuzzy Sets"

This note points out a terminological clash between Atanassov's “intuitionistic fuzzy sets” and what is currently understood as intuitionistic logic. They differ both by their motivations and their underlying mathematical structure. Furthermore, Atanassov's construct is isomorphic to interval-valued fuzzy sets and other similar notions, even if their interpretive settings and motivation are quite different, the latter capturing the idea of ill-known membership grade, while the former starts from the idea of evaluating degrees of membership and non-membership independently. This paper is a plea for a clarification of terminology, based on mathematical resemblances and the comparison of motivations between “intuitionistic fuzzy sets” and other theories .