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
Automorphisms, negations and implication operators
Fuzzy Sets and Systems - Implication operators
On some new classes of implication operators and their role in approximate reasoning
Information Sciences—Informatics and Computer Science: An International Journal
Information Sciences: an International Journal
Distributivity of residual implications over conjunctive and disjunctive uninorms
Fuzzy Sets and Systems
On the characterizations of (S,N)-implications
Fuzzy Sets and Systems
On the distributivity of fuzzy implications over nilpotent or strict triangular conorms
IEEE Transactions on Fuzzy Systems
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
On the law [p∧q→r]=[(p→r)V(q→r)] in fuzzy logic
IEEE Transactions on Fuzzy Systems
On the distributivity of fuzzy implications over representable uninorms
Fuzzy Sets and Systems
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
A generalization of Yager's f-generated implications
International Journal of Approximate Reasoning
International Journal of Approximate Reasoning
Information Sciences: an International Journal
| Hi-index | 0.20 |
Recently, we have examined the solutions of the following distributive functional equation I(x,S"1(y,z))=S"2(I(x,y),I(x,z)), when S"1, S"2 are either both strict or nilpotent t-conorms and I is an unknown function. In particular, between these solutions, we have presented functions which are fuzzy implications. In this paper we continue these investigations for the situation when S"1, S"2 are continuous and Archimedean t-conorms, i.e., we consider in detail the situation when S"1 is a strict t-conorm and S"2 is a nilpotent t-conorm and vice versa. Towards this end, we firstly present solutions of two functional equations related to the additive Cauchy functional equation. Using obtained results we show that the above distributive equation does not hold when S"1, S"2 are continuous and Archimedean t-conorms and I is a continuous fuzzy implication. Further, we present the solutions I which are non-continuous fuzzy implications. Obtained results are not only theoretical but also 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.