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

Rui Qin; Yan-Kui Liu; Zhi-Qiang Liu

doi:10.1016/j.cam.2010.08.031

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

Rui Qin
, Yan-Kui Liu
, Zhi-Qiang Liu

School of Creative Media

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

124 Citations (Scopus)

Abstract

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. © 2010 Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	1454-1481
Journal	Journal of Computational and Applied Mathematics
Volume	235
Issue number	5
DOIs	https://doi.org/10.1016/j.cam.2010.08.031
Publication status	Published - 1 Jan 2011

Bibliographical note

Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

Funding

This work was supported by the National Natural Science Foundation of China (No. 60974134), the Natural Science Foundation of Hebei Province (A2008000563), and the Program for One Hundred Excellent and Innovative Talents in Colleges and Universities of Hebei Province.

Research Keywords

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

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abstract = "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. {\textcopyright} 2010 Elsevier B.V. All rights reserved.",

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N2 - 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. © 2010 Elsevier B.V. All rights reserved.

AB - 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. © 2010 Elsevier B.V. All rights reserved.

KW - Critical value

KW - Data envelopment analysis

KW - Fuzzy possibility theory

KW - Parametric programming

KW - Reduction methods

KW - Type-2 fuzzy variable

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DO - 10.1016/j.cam.2010.08.031

M3 - RGC 21 - Publication in refereed journal

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JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

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ER -

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

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Bibliographical note

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Research Keywords

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