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Journal of Applied Mathematics
Volume 2014, Article ID 459508, 13 pages
Research Article

The Construction of Type-2 Fuzzy Reasoning Relations for Type-2 Fuzzy Logic Systems

School of Control Science and Engineering, Dalian University of Technology, Dalian 116024, China

Received 24 November 2013; Accepted 7 January 2014; Published 9 March 2014

Academic Editor: Chong Lin

Copyright © 2014 Shan Zhao and Hongxing Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.