Modeling fuzzy data envelopment analysis by parametric programming method

作     者：Qin, Rui Liu, Yankui Liu, Zhi-Qiang 

作者机构：Hebei Univ Coll Math & Comp Sci Baoding 071002 Peoples R China City Univ Hong Kong Sch Creat Media Hong Kong Hong Kong Peoples R China 

出 版 物：《EXPERT SYSTEMS WITH APPLICATIONS》 (专家系统及其应用)

年 卷 期：2011年第38卷第7期

页      面：8648-8663页

核心收录：

学科分类：1201[管理学-管理科学与工程(可授管理学、工学学位)] 0808[工学-电气工程] 08[工学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：National Natural Science Foundation of China Natural Science Foundation of Hebei Province [A2011201007] City UHK SRG [7001794, 7001679] 

主　　题：Data envelopment analysis Type-2 fuzzy variable Reduction methods Parametric programming 

摘      要：Data envelopment analysis (DEA) is a methodology for measuring the relative efficiency of decision making units (DMUs) consuming the same types of inputs and producing the same types of outputs. This paper studies the DEA models with type-2 data variations. In order to deal with the existed type-2 fuzziness, we propose the mean reduction methods for type-2 fuzzy variables. Based on the mean reductions of the type-2 fuzzy inputs and outputs, we formulate a new class of fuzzy generalized expectation DEA models. When the inputs and outputs are mutually independent type-2 triangular fuzzy variables, we discuss the equivalent parametric forms for the constraints and the generalized expectation objective, where the parameters characterize the degree of uncertainty of the type-2 fuzzy coefficients so that the information cannot be lost via our reduction method. For any given parameters, the proposed model becomes nonlinear programming, which can be solved by standard optimization solvers. To illustrate the modeling idea and the efficiency of the proposed DEA model, we provide one numerical example. (C) 2011 Elsevier Ltd. All rights reserved.