On the transitivity of containment and equivalence in fuzzy power set theory
type: Item
instance of: scholarly article
title: On the transitivity of containment and equivalence in fuzzy power set theory
zbMATH Open document ID: 0609.03018
DOI: 10.1016/0022-247X(86)90224-6
author: Richard Willmott
published in: Journal of Mathematical Analysis and Applications
publication date: 1986-01-01T00:00:00Z
review text: For fuzzy sets it is natural to consider a fuzzified inclusion relation as done e.g. by \textit{S. Gottwald} [Fuzzy Sets Syst. 2, 125--151 (1979; Zbl 0408.03042)] and \textit{W. Bandler} and \textit{L. Kohout} [ibid. 4, 13--30 (1980; Zbl 0433.03013)] and also a fuzzified equality. In each case a many-valued implication operator is involved. For both types of relations and a series of implication operators of Bandler and Kohout [loc. cit.] a generalized transitivity property is proven which in a more general setting also is given by \textit{S. Gottwald} [Elektron. Informationsverarb. Kybernetik 22, 67--91 (1986; Zbl 0607.03016)] for at least each continuous t-norm. Additionally, other fuzzified inclusion relations are defined by some mean value procedures. For such inclusion relations it is proven that the generalized transitivity not always holds true.
Mathematics Subject Classification ID: 03E72
Mathematics Subject Classification ID: 03E20
zbMATH DE Number: 3985204
zbMATH Keywords: fuzzified inclusion relation
zbMATH Keywords: fuzzified equality
zbMATH Keywords: many-valued implication operator
zbMATH Keywords: generalized transitivity property
zbMATH Keywords: mean value procedures
reviewed by: Siegfried J. Gottwald
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3985204