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 \(E=\bigcup_{n\geq 1}[0,1]^n\).


03E72 Theory of fuzzy sets, etc.
Full Text: DOI


[1] DOI: 10.1016/0022-247X(83)90216-0 · Zbl 0522.03012 · doi:10.1016/0022-247X(83)90216-0
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[3] DOI: 10.1142/S0218488597000312 · Zbl 1232.03015 · doi:10.1142/S0218488597000312
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[7] DOI: 10.1073/pnas.28.12.535 · Zbl 0063.03886 · doi:10.1073/pnas.28.12.535
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[10] DOI: 10.1109/21.87068 · Zbl 0637.90057 · doi:10.1109/21.87068
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