Methods of critical value reduction for type-2 fuzzy variables and their applications

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:235

Article

Qin, Rui¹  Liu, Yan-Kui¹  Liu, Zhi-Qiang² 

[1] Hebei Univ, Coll Math & Comp Sci, Baoding 071002, Hebei, Peoples R China

[2] City Univ Hong Kong, Sch Creat Media, Hong Kong, Hong Kong, Peoples R China

关键词: Fuzzy possibility theory;    Type-2 fuzzy variable;    Critical value;    Reduction methods;    Data envelopment analysis;    Parametric programming;   

DOI  :  10.1016/j.cam.2010.08.031

来源: Elsevier

【 摘 要 】

A type-2 fuzzy variable is a map from a fuzzy possibility space to the real number space; it is an appropriate tool for describing type-2 fuzziness. This paper first presents three kinds of critical values (CVs) for a regular fuzzy variable (RFV), and proposes three novel methods of reduction for a type-2 fuzzy variable. Secondly, this paper applies the reduction methods to data envelopment analysis (DEA) models with type-2 fuzzy inputs and outputs, and develops a new class of generalized credibility DEA models. According to the properties of generalized credibility, when the inputs and outputs are mutually independent type-2 triangular fuzzy variables, we can turn the proposed fuzzy DEA model into its equivalent parametric programming problem, in which the parameters can be used to characterize the degree of uncertainty about type-2 fuzziness. For any given parameters, the parametric programming model becomes a linear programming one that can be solved using standard optimization solvers. Finally, one numerical example is provided to illustrate the modeling idea and the efficiency of the proposed DEA model. (C) 2010 Elsevier By. All rights reserved.

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