Optimization of Backward Fuzzy Reasoning Based on Rule Knowledge

In [14], we have presented a fuzzy forward reasoning methodology for rule-based systems using the functional representation of rules (fuzzy implications). In this paper, we extend methodology for selecting relevant fuzzy implications from [14] in backward reasoning. The proposed methodology takes full advantage of the functional representation of fuzzy implications and the algebraic properties of the family of all fuzzy implications. It allows to compare two fuzzy implications. If the truth value of the conclusion and the truth value of the implication are given, we can easily optimize the truth value of the implication premise. This methodology can be useful for the design of an inference engine based on the rule knowledge for a given rule-based system.