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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.

MSC:

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

Citations:

Zbl 0839.90002
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References:

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