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

Shan Zhao | Zendy; Hongxing Li | Zendy

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

Author(s) -

Shan Zhao,

Hongxing Li

Publication year - 2014

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2014/459508

Subject(s) - mathematics , fuzzy logic , fuzzy number , fuzzy classification , fuzzy set operations , defuzzification , type (biology) , algebra over a field , type 2 fuzzy sets and systems , neuro fuzzy , fuzzy mathematics , fuzzy subalgebra , algorithm , fuzzy set , computer science , fuzzy control system , artificial intelligence , pure mathematics , ecology , biology

Type-2 fuzzy reasoning relations are the type-2 fuzzy relations obtained from a group of type-2 fuzzy reasoningsby using extended t-(co)norm, which are essential for implementing type-2 fuzzy logic systems. In this paper analgorithm 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 inaccordance with different input subdomains under certain conditions. And then different techniques are discussedto solve the simplified expressions on the input subdomains by using the related methods on solving fuzzy relationequations. Besides, it is pointed out that the computation amount level of the proposed algorithm is the same as thatof polynomials and the possibility of applying the proposed algorithm in the construction of type-2 fuzzy reasoningrelations is illustrated on several examples. Finally, the calculation of an arbitrary extended continuous t-norm can beobtained as the special case of the proposed algorithm

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