Theoretical methods of constructing fuzzy inference relations

Xue-hai Yuan (), Hong-xing Li and Xiao-ning Wang
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Xue-hai Yuan: Dalian University of Technology
Hong-xing Li: Dalian University of Technology
Xiao-ning Wang: Liaoning Normal University

Fuzzy Information and Engineering, 2009, vol. 1, issue 4, 385-399

Abstract: 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.

Keywords: Fuzzy set; Cut set; Representation theorem; Fuzzy inference; Implication operator (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1007/s12543-009-0030-0

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