On the relationship between some extensions of fuzzy set theory

Abstract

Since Zadeh introduced fuzzy sets in 1965, a lot of new theories treating imprecision and uncertainty have been introduced. Some of these theories are extensions of fuzzy set theory, others try to handle imprecision and uncertainty in a different (better?) way. Kerre (Computational Intelligence in Theory and Practice, Physica-Verlag, Heidelberg, 2001, pp. 55–72) has given a summary of the links that exist between fuzzy sets and other mathematical models such as flou sets (Gentilhomme), two-fold fuzzy sets (Dubois and Prade) and L-fuzzy sets (Goguen). In this paper, we establish the relationships between intuitionistic fuzzy sets (Atanassov, VII ITKR's Session, Sofia, June 1983 (Deposed in Central Sci.—Techn. Library of Bulg. Acad. of Sci., 1697/84) (in Bulgarian)), L-fuzzy sets (J. Math. Anal. Appl. 18 (1967) 145), interval-valued fuzzy sets (Sambuc, Ph.D. Thesis, University of Marseille, France, 1975), interval-valued intuitionistic fuzzy sets (Intuitionistic fuzzy set, Physica-Verlag, Heidelberg, New York, 1999).