On the implication operator in fuzzy logic
Information Sciences: an International Journal
On fuzzy implication operators
Fuzzy Sets and Systems
Fuzzy implication operators and generalized fuzzy method of cases
Fuzzy Sets and Systems
Fuzzy sets and fuzzy logic: theory and applications
Fuzzy sets and fuzzy logic: theory and applications
Contrapositive symmetry of fuzzy implications
Fuzzy Sets and Systems
On global requirements for implication operators in fuzzy modus ponens
Fuzzy Sets and Systems - Special issue on fuzzy modeling and dynamics
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
Discovering a cover set of ARsi with hierarchy from quantitative databases
Information Sciences—Informatics and Computer Science: An International Journal - Special issue: Dealing with uncertainty in data mining and information extraction
Information Sciences: an International Journal
Unified forms of fully implicational restriction methods for fuzzy reasoning
Information Sciences: an International Journal
Issues on adjointness in multiple-valued logics
Information Sciences: an International Journal
A normal form which preserves tautologies and contradictions in a class of fuzzy logics
Journal of Algorithms
Some results of weighted quasi-arithmetic mean of continuous triangular norms
Information Sciences: an International Journal
Fuzzy Relational Calculus and Its Application to Image Processing
WILF '09 Proceedings of the 8th International Workshop on Fuzzy Logic and Applications
Xor-Implications and E-Implications: Classes of Fuzzy Implications Based on Fuzzy Xor
Electronic Notes in Theoretical Computer Science (ENTCS)
QL-implications: Some properties and intersections
Fuzzy Sets and Systems
On interval fuzzy S-implications
Information Sciences: an International Journal
Solutions to the functional equation I(x,y)=I(x,I(x,y)) for a continuous D-operation
Information Sciences: an International Journal
Interval valued QL-implications
WoLLIC'07 Proceedings of the 14th international conference on Logic, language, information and computation
A characterization of residual implications derived from left-continuous uninorms
Information Sciences: an International Journal
On a new class of fuzzy implications: h-Implications and generalizations
Information Sciences: an International Journal
Solutions of equation I(x, y) = I(x, I(x, y)) for implications derived from uninorms
WILF'11 Proceedings of the 9th international conference on Fuzzy logic and applications
Information Sciences: an International Journal
Fuzzy implications derived from additive generators of continuous Archimedean t-norms
International Journal of Intelligent Systems
Threshold generation method of construction of a new implication from two given ones
Fuzzy Sets and Systems
A new class of fuzzy implications derived from generalized h-generators
Fuzzy Sets and Systems
Aggregating fuzzy implications
Information Sciences: an International Journal
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Iterative boolean-like laws in fuzzy logic have been studied by Alsina and Trillas [C. Alsina, E. Trillas, On iterative boolean-like laws of fuzzy sets, in: Proc. 4th Conf. Fuzzy Logic and Technology, Barcelona, Spain, 2005, pp. 389-394] for functional equations with boolean background in which only fuzzy conjunctions, fuzzy disjunctions and fuzzy negations are contained. In this paper we study an iterative boolean-like law with fuzzy implications, more precisely we derive characterizations of some classes of fuzzy implications satisfying I(x,y)=I(x,I(x,y)), for all (x,y)@?[0,1]^2. Our discussion mainly focuses on the three important classes of implications: S-implications, R-implications and QL-implications. We prove the sufficient and necessary conditions for an S-implication generated by any t-conorm and any fuzzy negation, an R-implication generated by a left-continuous t-norm, a QL-implication generated by a continuous t-conorm, a continuous t-norm and a strong fuzzy negation to satisfy I(x,y)=I(x,I(x,y)), for all (x,y)@?[0,1]^2.