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 and fuzzy logic: theory and applications
Fuzzy sets and fuzzy logic: theory and applications
Contrapositive symmetry of fuzzy implications
Fuzzy Sets and Systems
A first course in fuzzy logic
Automorphisms, negations and implication operators
Fuzzy Sets and Systems - Implication operators
When (S,N)-implications are (T,T1)-conditional functions?
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
On the structure of left-continuous t-norms that have a continuous contour line
Fuzzy Sets and Systems
On the characterizations of fuzzy implications satisfying I(x,y)=I(x,I(x,y))
Information Sciences: an International Journal
On the characterizations of (S,N)-implications
Fuzzy Sets and Systems
(S, N)- and R-implications: A state-of-the-art survey
Fuzzy Sets and Systems
On the first place antitonicity in QL-implications
Fuzzy Sets and Systems
Fuzzy Implications
On the law [p∧q→r]=[(p→r)V(q→r)] in fuzzy logic
IEEE Transactions on Fuzzy Systems
A Survey on Fuzzy Implication Functions
IEEE Transactions on Fuzzy Systems
On the Law of Importation in Fuzzy Logic
IEEE Transactions on Fuzzy Systems
Intersections between some families of (U,N)- and RU-implications
Fuzzy Sets and Systems
Intersection of Yager's implications with QL and D-implications
International Journal of Approximate Reasoning
Fuzzy implications derived from additive generators of continuous Archimedean t-norms
International Journal of Intelligent Systems
A generalization of Yager's f-generated implications
International Journal of Approximate Reasoning
A new class of fuzzy implications derived from generalized h-generators
Fuzzy Sets and Systems
A class of implications related to Yager's f-implications
Information Sciences: an International Journal
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In this paper, we attempt a systematic study of QL-implications. Towards this end, firstly, we investigate the conditions under which a QL-operation becomes a fuzzy implication without imposing any conditions on the underlying operations. Following this, we discuss the conditions under which this family satisfies some desirable algebraic properties. Based on the obtained results and existing characterization results, the intersections between QL-implications and the two most established families of fuzzy implications, viz., (S,N)- and R-implications are determined. It is shown that QL-implications contain the set of all R-implications obtained from left-continuous t-norms that are also (S,N)-implications. Finally, the overlaps between QL-implications and the recently proposed f- and g-implications are also studied.