Fuzzy Implication Revisited: a New Type of Fuzzy Implication Explains

1. Formulation of the problem 1:1: It is necessary to represent implication in expert systems Our knowledge of complex systems is often incomplete, and therefore, we have to rely on the expert's statements, These statements are usually formulated not in mathematical terms, but in words of natural languages. Fuzzy logic is a methodology for formalizing such statements. Since a large part of expert knowledge consists of if{then statements, it is therefore important to formalize implication (i.e., if{then statements) in fuzzy logic. 1:2: How implication is represented now : two general ideas There has been a lot of research on representing &, _, and : in fuzzy logic. So, let us assume that we already have operations f & ; f _ : 0; 1] 0; 1] ! 0; 1] and f : : 0; 1] ! 0; 1] that correspond to &, _, and :. In this situation, there are two basic ways to describe an implication operation f !