On Relations Between Several Methods In Fuzzy Reasoning

Abstract

There are several methods in Fuzzy reasoning, proposed Zadeh, Baldwin, Tsukamoto, Mizumoto, and Yager. In this note, we investigate relations between these methos. For the purpose, we study implicfation functions in section 2,and obtain our main results in sectin 3,which are as follows : B'_<Zad>(y)=B'_<Bal>(y)=B'_<tsu>(y) (Theorem 3.1〜3.2), B'_<Miz>(y)≦B'_<Bal>(y) (Theorem 3.3), B'_<Yag>(y)≦B'_<Bal>(y) (Theorem 3.4), B'_<Miz>(y)≦B'_<Yag>(y) (Theorem 3.5), where B'_<Zad>, B'_<Bal>, B'_<Tsu>, B'_<Miz>, and B'_<Yag> are consequents by Zadeh's method, Baldwin's, Tsukamoto's, Mizumoto's and Yager's, respectively.Also we give a lisy showing the results using several kinds of "implication functions".