Theoretical methods of constructing fuzzy inference relations |
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Authors: | Xue-hai Yuan Hong-xing Li Xiao-ning Wang |
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Affiliation: | 1. School of Electronic and Information Engineering, Dalian University of Technology, Dalian, 116024, China 2. School of Mathematics, Liaoning Normal University, Dalian, 116029, China
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Abstract: | In this paper, a theoretical method is presented to select fuzzy implication operators for the fuzzy inference sentence “if x is A, then y is B”. By applying representation theorems, thirty-two fuzzy implication operators are obtained. It is shown that the obtained 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 into four classes. By discussion, it is found that thirty of them among 420 fuzzy implication operators presented by Li can be derived by applying representation theorems and another two new ones are obtained by the use of our methods. |
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