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t-operators. (English) Zbl 1087.03515

Summary: This paper examines a class of operators, introduced by T. Calvo, A. Fraile, and G. Mayor in 1986, called t-operators. Introduced in order to be applied to fuzzy preorders, their properties make them also appropriate in other fields such as aggregation problems and expert systems. We characterize these operators as a special combination of a t-norm and a t-conorm on \([0,1]\) in a similar way to the uninorms of J. C. Fodor, R. R. Yager, and A. Rybalov. We study duality and self duality on t-operators with respect to a strong negation \(N\). We also give a classification of continuous t-operators in terms of ordinal sums. Finally, we obtain from some t-operators (those that are idempotent) a special kind of extended aggregation functions by extending them to \(E=\bigcup_{n\geq 1}[0,1]^n\).

MSC:

03E72 Theory of fuzzy sets, etc.
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