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225637

The theoretical methods of constructing fuzzy inference relations

Xiao-Ning WangXue-Hai Yuan

pp. 157-169

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 AB, A c B, AB class="EmphasisTypeItalic ">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.

Publication details

Published in:

Cao Bing-yuan, Zhang Cheng-yi, Li Tai-fu (2009) Fuzzy information and Engineering I. Dordrecht, Springer.

Pages: 157-169

DOI: 10.1007/978-3-540-88914-4_21

Full citation:

Wang Xiao-Ning, Yuan Xue-Hai (2009) „The theoretical methods of constructing fuzzy inference relations“, In: B. Cao, C. Zhang & T.-f. Li (eds.), Fuzzy information and Engineering I, Dordrecht, Springer, 157–169.