A new class of fuzzy implications, axioms of fuzzy implication revisited
Fuzzy Sets and Systems
On a class of distributive fuzzy implications
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems - Special issue on aggregation operators
Contrapositive symmetry of distributive fuzzy implications
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Information Sciences: an International Journal
Distributivity of residual implications over conjunctive and disjunctive uninorms
Fuzzy Sets and Systems
Fuzzy Implications
On the distributivity of fuzzy implications over nilpotent or strict triangular conorms
IEEE Transactions on Fuzzy Systems
On the distributivity of fuzzy implications over representable uninorms
Fuzzy Sets and Systems
Distributive equations of implications based on nilpotent triangular norms
International Journal of Approximate Reasoning
On the distributivity of fuzzy implications over continuous archimedean triangular norms
ICAISC'10 Proceedings of the 10th international conference on Artificial intelligence and soft computing: Part I
WILF'11 Proceedings of the 9th international conference on Fuzzy logic and applications
Combinatorial rule explosion eliminated by a fuzzy rule configuration
IEEE Transactions on Fuzzy Systems
Comments on “Combinatorial rule explosion eliminated by a fuzzy rule configuration” [and reply]
IEEE Transactions on Fuzzy Systems
IEEE Transactions on Fuzzy Systems
Comment on “Combinatorial rule explosion eliminated by a fuzzy rule configuration” [and reply]
IEEE Transactions on Fuzzy Systems
IEEE Transactions on Fuzzy Systems
On the law [p∧q→r]=[(p→r)V(q→r)] in fuzzy logic
IEEE Transactions on Fuzzy Systems
On the distributivity of implication operators over T and S norms
IEEE Transactions on Fuzzy Systems
Distributive Equations of Implications Based on Continuous Triangular Norms (I)
IEEE Transactions on Fuzzy Systems
International Journal of Approximate Reasoning
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Recently, we have examined the solutions of the following distributivity functional equation I(x,S"1(y,z))=S"2(I(x,y),I(x,z)), when S"1, S"2 are continuous, Archimedean t-conorms and I is an unknown function. In particular, between these solutions, we have shown that implication functions are among its solutions. In this paper we continue these investigations for the following distributivity equations I(T(x,y),z)=S(I(x,z),I(y,z)), I(S(x,y),z)=T(I(x,z),I(y,z)), when T is a continuous, Archimedean t-norm and S is a continuous, Archimedean t-conorm. The first equation has been investigated by Trillas and Alsina in 2002 [31], while the second equation has been investigated by Balasubramaniam and Rao in 2004 [12], for different classes of fuzzy implications, like R-implications, S-implications and QL-implications. Obtained results are not only theoretical but it can also be useful for the practical problems, since such equations have an important role to play in efficient inferencing in approximate reasoning, especially in fuzzy control systems.