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
Conjugacy Classes of Fuzzy Implications
Proceedings of the 6th International Conference on Computational Intelligence, Theory and Applications: Fuzzy Days
Automorphisms, negations and implication operators
Fuzzy Sets and Systems - Implication operators
Distributivity of residual implications over conjunctive and disjunctive uninorms
Fuzzy Sets and Systems
International Journal of Approximate Reasoning
On the representation of fuzzy rules
International Journal of Approximate Reasoning
Modus ponens and modus tollens in discrete implications
International Journal of Approximate Reasoning
On the distributivity of fuzzy implications over nilpotent or strict triangular conorms
IEEE Transactions on Fuzzy Systems
The distributive equations for idempotent uninorms and nullnorms
Fuzzy Sets and Systems
Combinatorial rule explosion eliminated by a fuzzy rule configuration
IEEE Transactions on Fuzzy Systems
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
IUKM'11 Proceedings of the 2011 international conference on Integrated uncertainty in knowledge modelling and decision making
Formalization of implication based fuzzy reasoning method
International Journal of Approximate Reasoning
Algebraic structures of interval-valued fuzzy ( S,N)-implications
International Journal of Approximate Reasoning
On fuzzy implications: An axiomatic approach
International Journal of Approximate Reasoning
Distributivity equations of implications based on continuous triangular conorms (II)
Fuzzy Sets and Systems
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In this paper, we explore the distributive equations of implications, both independently and along with other equations. In detail, we consider three classes of equations. (1) By means of the section of I, we give out the sufficient and necessary conditions of solutions for the distributive equation of implication I(x,T(y,z))=T(I(x,y),(x,z)) based on a nilpotent triangular norm T and an unknown function I, which indicates that there are no continuous solutions satisfying the boundary conditions of implications. Under the assumptions that I is continuous except the vertical section I(0,y), y@?[0,1), we get its complete characterizations. (2) We prove that there are no solutions for the functional equations I(x,T(y,z))=T(I(x,y),I(x,z)),I(x,I(y,z))=I(T(x,y),z). (3) We obtain the sufficient and necessary conditions on T and I to be solutions of the functional equations I(x,T(y,z))=T(I(x,y),I(x,z)), I(x,y)=I(N(y),N(x)).