Geodesic
Distributivity of strong implications over conjunctive and disjunctive uninorms
Kybernetika, Tome 42 (2006) no. 3, pp. 319-336 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 03B52, 06F05, 94D05
Keywords: $t$-norm; $t$-conorm; uninorm; implication operator; S-implication; R-implication; distributivity 
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Ruiz-Aguilera, Daniel; Torrens, Joan. Distributivity of strong implications over conjunctive and disjunctive uninorms. Kybernetika, Tome 42 (2006) no. 3, pp. 319-336. http://geodesic.mathdoc.fr/item/KYB_2006_42_3_a5/

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