The theoretical methods of constructing fuzzy inference relations

Xiao-Ning Wang

Xue-Hai Yuan

pp. 157-169

in: Bing-yuan Cao, Cheng-yi Zhang, Tai-fu Li (eds), Fuzzy information and Engineering I, Berlin, Springer, 2009

Abstract

In this paper, a theoretical method of selecting fuzzy implication operators for the fuzzy inference sentence as "if x is A, then y is B" is presented. By applying representation theorems, thirty-two fuzzy implication operators are obtained. It is shown that the thirty-two fuzzy implication operators are generalizations of classical inference rule A→B, A ^c →B, A→B ^c and A ^c →B ^c respectively and can be divided four classes. By discussion, it is found that thirty fuzzy implication operators among 420 fuzzy implication operators presented by Li can be derived by applying representation theorems and two new fuzzy implication operators are obtained by the use of our methods.