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Distributivity and conditional distributivity of a uninorm and a continuous t-conorm

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2 Author(s)
Ruiz, D. ; Univ. de les Illes Baleares, Palma de Mallorca ; Torrens, J.

The open problem recalled by Klement in the Linz2000 closing session, related to distributivity and conditional distributivity of a uninorm and a continuous t-conorm, is solved for the most usual known classes of uninorms. From the obtained results, it is deduced that distributivity and conditional distributivity are equivalent for these cases. It is remarkable that solutions appear involving not only strict t-conorms but also ordinal sums of the maximum with a strict t-conorm. Conversely, the distributivity of a t-conorm over a uninorm is also studied leading only to already known solutions. Moreover, the dual case of distributivity and conditional distributivity involving uninorms and continuous t-norms is also solved, proving again the equivalence of both kinds of distributivities

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Fuzzy Systems, IEEE Transactions on  (Volume:14 ,  Issue: 2 )