Strict fuzzy orderings in a similarity-based set

Authors Ulrich Bodenhofer
Mustafa Demirci
Title Strict fuzzy orderings in a similarity-based set
Booktitle Proc. 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)
Type in proceedings
Address Barcelona, Spain
ISBN 84-7653-872-3
Month September
Year 2005
Pages 297-302
SCCH ID# 504

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.