On the relationship between some extensions of fuzzy set theory

  • Authors:

  • Glad Deschrijver;Etienne E. Kerre

  • Affiliations:

  • Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281, S9, B-9000 Gent, Belgium;Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281, S9, B-9000 Gent, Belgium

  • Venue:
  • Fuzzy Sets and Systems - Theme: Basic notions
  • Year:
  • 2003

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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).