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Distributive idempotent uninorms. (English) Zbl 1074.03026

Summary: A characterization of all idempotent uninorms satisfying the distributivity property is given. The special cases of left-continuous and right-continuous idempotent uninorms are presented separately, and it is also proved that all idempotent uninorms are autodistributive. Moreover, all distributive pairs of idempotent uninorms (pairs \(U_{1}, U_{2}\) such that \(U_{1}\) is distributive over \(U_{2}\) and \(U_{2}\) is distributive over \(U_{1}\)) are also characterized.

MSC:

03E72 Theory of fuzzy sets, etc.
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