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Distributivity of strong implications over conjunctive and disjunctive uninorms. (English) Zbl 1249.03030

Summary: This paper deals with implications defined from disjunctive uninorms \(U\) by the expression \(I(x,y)=U(N(x),y)\), where \(N\) is a strong negation. The main goal is to solve the functional equation derived from the distributivity condition of these implications over conjunctive and disjunctive uninorms. Special cases are considered when the conjunctive and disjunctive uninorm are a t-norm or a t-conorm respectively. The obtained results show a lot of new solutions generalyzing those obtained in previous works when the implications are derived from t-conorms.

MSC:

03B52 Fuzzy logic; logic of vagueness
06F05 Ordered semigroups and monoids
94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
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References:

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