L-Fuzzy Sets and Isomorphic Lattices: Are All the “New” Results Really New? †

Abstract

We review several generalizations of the concept of fuzzy sets with two- or three-dimensional lattices of truth values and study their relationship. It turns out that, in the two-dimensional case, several of the lattices of truth values considered here are pairwise isomorphic, and so are the corresponding families of fuzzy sets. Therefore, each result for one of these types of fuzzy sets can be directly rewritten for each (isomorphic) type of fuzzy set. Finally we also discuss some questionable notations, in particular, those of “intuitionistic” and “Pythagorean” fuzzy sets.

Keywords

• fuzzy set
• interval-valued fuzzy set
• “intuitionistic” fuzzy set
• “pythagorean” fuzzy set
• isomorphic lattices
• truth values