On fuzzy implications derived from multiplicative generator pair of overlap functions

Abstract

Fuzzy implications are widely used in approximate reasoning. Since there is no fuzzy implication satisfying all algebraic properties, it is necessary to construct fuzzy implications for different applications. One of the main construction methods of fuzzy implications is based on the generator of aggregation functions. Meanwhile, overlap functions are a class of extensively used aggregation functions. Moreover, one of classes of multiplicative generator pairs of overlap functions has only a few weaker conditions in its definition. Therefore, for approximate reasoning, this article introduces a novel class of fuzzy implications called MO-implications based on a class of multiplicative generator pairs of overlap functions. Furthermore, we study the basic properties of MO-implications and some classical tautologies related to MO-implications. The results show that (1) MO-implications are a novel class of fuzzy implications, which are distinct from some other classes of overlap functions-related fuzzy implications; (2) MO-implications always satisfy some useful algebraic properties, such as left neutrality property and consequent boundary; (3) Some classical tautologies related to MO-implications hold in many cases, including T-conditionality law, O-conditionality law and contraction law, such that MO-implications can be used in approximate reasoning.