Interval-valued fuzzy backward reasoning

The importance and efficiency of backward reasoning in nonfuzzy reasoning has been stressed for a long time, especially in the case of expert systems and decision-support systems. The extension of this reasoning method to fuzzy theory, however, has never been considered. In this paper, the authors propose a definition of fuzzy backward reasoning based on the generalized modus ponens and show the necessity of considering interval-valued fuzzy backward reasoning. Then, the authors propose solving methods for fuzzy backward reasoning in the case of a rule with one or several conditions as well as in the case of several rules