A call for crispness in fuzzy set theory
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
Fuzzy if-Then Rules in Computational Intelligence: Theory and Applications
Fuzzy if-Then Rules in Computational Intelligence: Theory and Applications
R0 implication: characteristics and applications
Fuzzy Sets and Systems - Mathematics
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
On contra-symmetry and MPT conditionality in fuzzy logic
International Journal of Intelligent Systems
Soft Computing - A Fusion of Foundations, Methodologies and Applications
Information Sciences: an International Journal
Rule reduction for efficient inferencing in similarity based reasoning
International Journal of Approximate Reasoning
Fuzzy Implications
Discovering a cover set of ARsi with hierarchy from quantitative databases
Information Sciences: an International Journal
A Survey on Fuzzy Implication Functions
IEEE Transactions on Fuzzy Systems
Intersections between some families of (U,N)- and RU-implications
Fuzzy Sets and Systems
On fuzzy implications determined by aggregation operators
Information Sciences: an International Journal
Construction of strong equality index from implication operators
Fuzzy Sets and Systems
On the vertical threshold generation method of fuzzy implication and its properties
Fuzzy Sets and Systems
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A fuzzy implication, commonly defined as a two-place operation on the unit interval, is an extension of the classical binary implication. It plays important roles in both mathematical and applied sides of fuzzy set theory. Besides the basic axioms, there are many potential fuzzy implication axioms, among which eight are widely used in the literature. Different fuzzy implications satisfying different subgroups of these eight axioms can be found. However, certain interrelationships exist between these eight axioms. But the results remain incomplete. This paper aims to lay bare the interrelationships between these eight axioms. The result is instrumental to propose a classification of fuzzy implications.