A Study of Generalized QL′-Implications

Abstract

In this paper, we introduce and study the GQL (Formula presented.) -operations. We prove that this class is a hyper class of the known class of QL (Formula presented.) -operations. Similar to QL (Formula presented.) -operations, GQL (Formula presented.) -operations are not always fuzzy implications. On the other hand, we present and prove a necessary but not sufficient condition that leads to the generation of a GQL (Formula presented.) -implication. Our study is completed by studying the satisfaction or the violation of some basic properties of fuzzy implications, such as the left neutrality property, the exchange principle, the identity principle and the left ordering property. Our study also completes the study of the aforementioned basic properties for QL (Formula presented.) -implications and leads to a new connection between QL-operations and D (Formula presented.) -operations.