外文翻译—模糊数据包络分析（dea）模型和排序方法.doc
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外文翻译—模糊数据包络分析（dea）模型和排序方法,fuzzy data envelopment analysis (dea)model and ranking method meilin wen ，huaishu li ba department of system engineering of engineering technology, beijing univ...
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Fuzzy data envelopment analysis (DEA)Model and ranking method
Meilin Wen ，Huaishu Li b
a Department of System Engineering of Engineering Technology, Beijing University of Aeronautics and Astronautics, Beijing, 100083, China b Department of Computer Technology and Science, Beijing Jiaotong University, Beijing 100044, China
Abstract
Data Envelopment Analysis (DEA) is a very effective method to eva luate the relative efficiency of decision-making units (DMUs). Since the data of production processes cannot be precisely measured in some cases, the uncertain theory has played an important role in DEA. This paper attempts to extend the traditional DEA models to a fuzzy framework, thus producing a fuzzy DEA model based on credibility measure. Following is a method of ranking all the DMUs. In order to solve the fuzzy model, we have designed the hybrid algorithm combined with fuzzy simulation and genetic algorithm. When the inputs and outputs are all trapezoidal or triangular fuzzy variables, the model can be transformed to linear programming. Finally, a numerical example is presented to illustrate the fuzzy DEA model and the method of ranking all the DMUs.
Keywords:Data envelopment analysis,Efficiency,Credibility measure
Ranking method,Fuzzy programming
1. Introduction
Data envelopment analysis (DEA), which initially proposed by Charnes et al. [5], is a nonparametric method for eva luating the relative efficiency of decision -making units (DMUs) on the basis of multiple inputs and outputs. Since DEA was proposed in 1978, it has been got comprehensive attention both in theory and application. Now DEA becomes the important analysis tool and research way in management science, operational research, system engineering, decision analysis and so on. Based on the original DEA model [5], various theoretical extensions have been developed [3,4,25,28,8]. More DEA papers can refer to Seiford [26] in which 500 references are documented.
Often decision makers are interested in a complete ranking beyond the dichotomized classification. The researches on ranking have come up. By now many papers on ranking have been published over the last decade within the DEA context. The cross-efficiency ranking method was first developed by Sexton et al. [27]. By eva luating DMUs through both self and peer pressure, one can attain a more balanced view of the decision-making units. Andersen & Petersen [2] developed the super-efficiency approach, in which the efficient units can receive a score greater than one, through the unit's exclusion
from the column being scored in the linear program. However, each unit is eva luated by its own weights as opposed to the cross-efficiency concept in which all units are compared using the same sets of weights. In the benchmarking ranking method [29], a DMU is highly ranked if it is chosen as a useful target for many other DMUs. This is of substantial use when looking to benchmark industries. For a review of ranking methods see [1].
Most methods of ranking DMUs assume that all inputs and outputs data are exactly known. But in more general cases, the data for eva luation are often collected from investigation to decide the natural language such as good, medium and bad rather than a specific case. That is, the inputs and outputs are fuzzy. We can find several fuzzy approaches to the assessment of efficiency in the DEA literature. Cooper et al. [6,7] were the first, to the best of our knowledge, to study how to deal with imprecise data such as bounded data, ordinal data and ratio bounded data in DEA. Kao and Liu [11] develop a method to find the membership functions of the fuzzy efficiency scores when some observations are fuzzy numbers. Entani et al. [9] propose an interval efficiency obtained from the pessimistic and the optimistic viewpoints. Since Zadeh [32,33] initiated the possibility measure, many researchers have introduced it into DEA [10,12]. Although possibility measure has been widely used, it has no self-duality property. However, a self-dual measure is absolutely needed in both theory and practice. In order to define a self-dual measure, Liu and Liu [20] presented the concept of credibility measure in 2002. An axiomatic foundation of credibility theory was given by Liu [22] in 2004. In this paper, the credibility measure is employed to the fuzzy DEA models.
This paper is organized as follows: some basic concept and results on credibility measure will be introduced in Section 2; n Section 3, we will give some introduction about CCR model; Section 4 will give the fuzzy DEA model and the ranking method; In order to solve the fuzzy DEA model, a hybrid algorithm is designed in Section 5. Section 6 will predigest the fuzzy model when the inputs and outputs are all trapezoidal fuzzy variables. Finally, a numerical example will be given to illustrate the fuzzy DEA model and the method of ranking al..
Meilin Wen ，Huaishu Li b
a Department of System Engineering of Engineering Technology, Beijing University of Aeronautics and Astronautics, Beijing, 100083, China b Department of Computer Technology and Science, Beijing Jiaotong University, Beijing 100044, China
Abstract
Data Envelopment Analysis (DEA) is a very effective method to eva luate the relative efficiency of decision-making units (DMUs). Since the data of production processes cannot be precisely measured in some cases, the uncertain theory has played an important role in DEA. This paper attempts to extend the traditional DEA models to a fuzzy framework, thus producing a fuzzy DEA model based on credibility measure. Following is a method of ranking all the DMUs. In order to solve the fuzzy model, we have designed the hybrid algorithm combined with fuzzy simulation and genetic algorithm. When the inputs and outputs are all trapezoidal or triangular fuzzy variables, the model can be transformed to linear programming. Finally, a numerical example is presented to illustrate the fuzzy DEA model and the method of ranking all the DMUs.
Keywords:Data envelopment analysis,Efficiency,Credibility measure
Ranking method,Fuzzy programming
1. Introduction
Data envelopment analysis (DEA), which initially proposed by Charnes et al. [5], is a nonparametric method for eva luating the relative efficiency of decision -making units (DMUs) on the basis of multiple inputs and outputs. Since DEA was proposed in 1978, it has been got comprehensive attention both in theory and application. Now DEA becomes the important analysis tool and research way in management science, operational research, system engineering, decision analysis and so on. Based on the original DEA model [5], various theoretical extensions have been developed [3,4,25,28,8]. More DEA papers can refer to Seiford [26] in which 500 references are documented.
Often decision makers are interested in a complete ranking beyond the dichotomized classification. The researches on ranking have come up. By now many papers on ranking have been published over the last decade within the DEA context. The cross-efficiency ranking method was first developed by Sexton et al. [27]. By eva luating DMUs through both self and peer pressure, one can attain a more balanced view of the decision-making units. Andersen & Petersen [2] developed the super-efficiency approach, in which the efficient units can receive a score greater than one, through the unit's exclusion
from the column being scored in the linear program. However, each unit is eva luated by its own weights as opposed to the cross-efficiency concept in which all units are compared using the same sets of weights. In the benchmarking ranking method [29], a DMU is highly ranked if it is chosen as a useful target for many other DMUs. This is of substantial use when looking to benchmark industries. For a review of ranking methods see [1].
Most methods of ranking DMUs assume that all inputs and outputs data are exactly known. But in more general cases, the data for eva luation are often collected from investigation to decide the natural language such as good, medium and bad rather than a specific case. That is, the inputs and outputs are fuzzy. We can find several fuzzy approaches to the assessment of efficiency in the DEA literature. Cooper et al. [6,7] were the first, to the best of our knowledge, to study how to deal with imprecise data such as bounded data, ordinal data and ratio bounded data in DEA. Kao and Liu [11] develop a method to find the membership functions of the fuzzy efficiency scores when some observations are fuzzy numbers. Entani et al. [9] propose an interval efficiency obtained from the pessimistic and the optimistic viewpoints. Since Zadeh [32,33] initiated the possibility measure, many researchers have introduced it into DEA [10,12]. Although possibility measure has been widely used, it has no self-duality property. However, a self-dual measure is absolutely needed in both theory and practice. In order to define a self-dual measure, Liu and Liu [20] presented the concept of credibility measure in 2002. An axiomatic foundation of credibility theory was given by Liu [22] in 2004. In this paper, the credibility measure is employed to the fuzzy DEA models.
This paper is organized as follows: some basic concept and results on credibility measure will be introduced in Section 2; n Section 3, we will give some introduction about CCR model; Section 4 will give the fuzzy DEA model and the ranking method; In order to solve the fuzzy DEA model, a hybrid algorithm is designed in Section 5. Section 6 will predigest the fuzzy model when the inputs and outputs are all trapezoidal fuzzy variables. Finally, a numerical example will be given to illustrate the fuzzy DEA model and the method of ranking al..
