Axioms of the System Behavior in FLC Using Uninormas

Abstract

Based on the idea of experiences in engineering applications, an axiom system was set up which has to be satisfied by approximate reasoning in fuzzy systems. Investigations about conditions under which the Mamdani inference mechanism satisfies this axiom system can be found in different sources. In this article a generalization of axioms was given, and a modified firing level in fuzzy rule base, satisfying the previously mentioned axiom system. The introduced degree of coincidence by the low level of covering over of rule premise and rule input has measurable influence on rule output, and on the other hand, make weaker the low level of coincidence, and make stronger the high level of coincidence between fuzzy sets. The question arises to what extent and under what conditions the approximate reasoning based on similarity measures satisfies the basic axioms in fuzzy inference mechanism.