Inverted Fuzzy Implications in Backward Reasoning

Abstract

Fuzzy inference systems generate inference results based on fuzzy IF-THEN rules. Fuzzy implications are mostly used as a way of interpretation of the IF-THEN rules with fuzzy antecedent and fuzzy consequent. From over eight decades a number of different fuzzy implications have been described, e.g. [6-10]. This leads to the following question: how to choose the proper function among basic fuzzy implications. In our paper, we propose a new method for choosing implication. Our method allows to compare two fuzzy implications. If the truth value of the consequent and the truth value of the implication are given, by means of inverse fuzzy implications we can easily optimize the truth value of the implication antecedent. In other words, we can choose the fuzzy implication, which has the highest or the lowest truth value of the implication antecedent or which has higher or lower truth value than another implication.