TRUTH SPACE APPROACH AND THE DIRECT APPROACH IN FUZZY-REASONING

There are several methods in fuzzy reasoning: Zadeh's (called here the direct method) and Baldwin's, Mizumoto's, and Tsukamoto's (these are called the indirect methods), and others. Thus, it would be natural to determine their interrelations. When the max-min composition rule is adopted, it is proved that the direct method and Baldwin's method give the same consequent under some conditions. Now, what would result whe n some composition rule other than max-min is adopted or when the fore mentioned conditions are not satisfied? This paper examines ''max- co mposition,'' which is a generalization of ''max-min composition'' and considers connections of direct versus indirect methods generally. If B'(d) and B'(i) are consequents by the direct method and Baldwin's met hod, respectively, then it is shown to hold generally that B'(d) subse t of B'(i). The conditions for B'(d) = B'(i) to hold also are given. F inally, the interrelations of Mizumoto's and Baldwin's methods are sho wn.