Fuzzy preference structures without incomparability. (English) Zbl 0858.90001

Summary: We establish important relationships between the basic properties of the components of a fuzzy preference structure without incomparability. This study is carried out for the fuzzy preference structures introduced recently by the authors [J. Fuzzy Math. 3, No. 2, 373-381 (1995; Zbl 0839.90002)]. A set of remarkable theorems gives detailed insight in the relationships between the sup-\({\mathcal T}\) transitivity of the fuzzy preference and indifference relations and the sup-\({\mathcal T}\) transitivity of the fuzzy large preference relation. Several paths of thought, involving \(t\)-norms with or without zero-divisors, are explored and, where required, illustrative counterexamples confirm the falsity of certain implications. Finally, we introduce the \(({\mathcal T},{\mathcal N})\)-Ferrers property of a binary fuzzy relation and show that the fuzzy preference and fuzzy large preference relations share certain types of this Ferrers property.


91B06 Decision theory
03E72 Theory of fuzzy sets, etc.


Zbl 0839.90002
Full Text: DOI


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