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2014 The Construction of Type-2 Fuzzy Reasoning Relations for Type-2 Fuzzy Logic Systems
Shan Zhao, Hongxing Li
J. Appl. Math. 2014: 1-13 (2014). DOI: 10.1155/2014/459508


Type-2 fuzzy reasoning relations are the type-2 fuzzy relations obtained from a group of type-2 fuzzy reasonings by using extended t-(co)norm, which are essential for implementing type-2 fuzzy logic systems. In this paper an algorithm is provided for constructing type-2 fuzzy reasoning relations of SISO type-2 fuzzy logic systems. First, we give some properties of extended t-(co)norm and simplify the expression of type-2 fuzzy reasoning relations in accordance with different input subdomains under certain conditions. And then different techniques are discussed to solve the simplified expressions on the input subdomains by using the related methods on solving fuzzy relation equations. Besides, it is pointed out that the computation amount level of the proposed algorithm is the same as that of polynomials and the possibility of applying the proposed algorithm in the construction of type-2 fuzzy reasoning relations is illustrated on several examples. Finally, the calculation of an arbitrary extended continuous t-norm can be obtained as the special case of the proposed algorithm.


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Shan Zhao. Hongxing Li. "The Construction of Type-2 Fuzzy Reasoning Relations for Type-2 Fuzzy Logic Systems." J. Appl. Math. 2014 1 - 13, 2014.


Published: 2014
First available in Project Euclid: 2 March 2015

zbMATH: 1404.03025
MathSciNet: MR3182371
Digital Object Identifier: 10.1155/2014/459508

Rights: Copyright © 2014 Hindawi


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