Fuzzy sets in approximate reasoning, part 1: inference with possibility distributions
Fuzzy Sets and Systems - Special memorial volume on foundations of fuzzy reasoning
Fuzzy sets in approximate reasoning, part 2: logical approaches
Fuzzy Sets and Systems - Special memorial volume on foundations of fuzzy reasoning
On fuzzy implication operators
Fuzzy Sets and Systems
Gradual inference rules in approximate reasoning
Information Sciences: an International Journal
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
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
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
On the characterizations of (S,N)-implications
Fuzzy Sets and Systems
A survey on fuzzy relational equations, part I: classification and solvability
Fuzzy Optimization and Decision Making
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
Construction of strong equality index from implication operators
Fuzzy Sets and Systems
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To obtain a demanded fuzzy implication in fuzzy systems, a number of desired properties have been proposed, among which the first place antitonicity, the second place isotonicity and the boundary conditions are the most important ones. The three classes of fuzzy implications derived from the implication in binary logic, S-, R- and QL-implications all satisfy the second place isotonicity and the boundary conditions. However, not all the QL-implications satisfy the first place antitonicity as S- and R-implications do. In this paper we study the QL-implications satisfying the first place antitonicity. First we establish the relationship between the first place antitonicity and other required properties of QL-implications. Second we work on the conditions under which a QL-implication generated by different combinations of a t-conorm S, a t-norm T and a strong fuzzy negation N satisfy the first place antitonicity, especially in the cases that both S and T are continuous. We further investigate the interrelationships between S- and R-implications generated by left-continuous t-norms on one hand and QL-implications satisfying the first place antitonicity on the other.