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

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...

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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 235; no. 5; pp. 1454 - 1481
Main Authors: Qin, Rui, Liu, Yan-Kui, Liu, Zhi-Qiang
Format: Journal Article
Language:English
Published: Kidlington Elsevier B.V 2011
Elsevier
Subjects:
Calculus of variations and optimal control
Critical value
Data envelopment analysis
Exact sciences and technology
Fuzzy
Fuzzy logic
Fuzzy possibility theory
Fuzzy set theory
Mathematical analysis
Mathematical models
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming, optimization and calculus of variations
Numerical methods in optimization and calculus of variations
Parametric programming
Programming
Reduction
Reduction methods
Sciences and techniques of general use
Type-2 fuzzy variable
Critical value
Reduction methods
Type-2 fuzzy variable
Fuzzy possibility theory
Parametric programming
Data envelopment analysis
Data analysis
Optimization method
Linear programming
Linear model
Reduction method
Numerical analysis
Applied mathematics
Variational calculus
Mathematical programming
ISSN:0377-0427, 1879-1778
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Summary: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.
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content type line 23
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2010.08.031