Gradation of being fuzzy function

Demirci M.

FUZZY SETS AND SYSTEMS, vol.119, no.3, pp.383-392, 2001 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 119 Issue: 3
  • Publication Date: 2001
  • Doi Number: 10.1016/s0165-0114(99)00166-9
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.383-392
  • Keywords: fuzzy relation, fuzzy function, fuzzy equality, degree of being fuzzy function (FREL)
  • Akdeniz University Affiliated: Yes


For crisp sets X and Y, considering two fuzzy equalities Ex, Er on X and Y, respectively, the concept of fuzzy function and several types of it were studied in M. Demirci, Fuzzy Sets and Systems 106 (1999) 239-246. In this paper, for a fuzzy relation f on X x Y, considering the fuzzy equalities Ex on X and Er an Y the degree of f of being fuzzy function, being surjective, being injective and being bijective is defined. Then setting the connections between several types of degree of being fuzzy function and various types of fuzzy function the essential properties of these degrees are investigated. (C) 2001 Elsevier Science B.V. All rights reserved.