Coimplication and its application to fuzzy expert systems

In two-valued logic or classical logic, an evaluation takes each of a given set of propositions into one of the extreme truth values 0 or 1, subject to certain consistency rules. In fuzzy logic or multiple-valued logic, the truth value of a formula can assume any value in the interval [0, 1] and is used to indicate the degree of truth represented by the formula. Many of the present expert systems use two-valued logic and probability. Since much of the information in the knowledge base of a typical expert system is imprecise and vague, it is well known that we cannot handle those kinds of uncertainties using those tools. In a fuzzy conditional inference of the fuzzy expert systems, the problem is that, given values, for A → B and A′, we have to find a consistent value for B′ through the modus ponens. In this paper we propose to use the equivalence relation for modus ponens of the inference in fuzzy expert systems instead of fuzzy implication and introduce the concept of coimplication as a new approach to approximate reasoning of expert systems using the new concept of modus ponens.