Strict fuzzy orderings in a similarity-based set

U. Bodenhofer, M. Demirci. Strict fuzzy orderings in a similarity-based set. pages 297-302, 9, 2005.

  • Ulrich Bodenhofer
  • Mustafa Demirci
BuchProc. 4th Conf. of the European Society for Fuzzy Logic and Technology and 11 Recontres Francophones sur al Logique Flou et ses Applications (EUSFLAT/LFA 2005)
TypIn Konferenzband
Abstract This paper introduces and justifies a similarity-based concept of strict fuzzy orderingsand provides constructions how fuzzy orderings can be transformed into strict fuzzy orderings andvice versa. We demonstrate that there is a meaningful correspondence between fuzzy orderingsand strict fuzzy orderings. Unlike the classical case, however, we do not obtain a general oneto-one correspondence. We observe that the strongest results are achieved if the underlying tnorminduces a strong negation, which, in particular, includes nilpotent t-norms and the nilpotentminimum.