Efficiency ranking of decision making units in data envelopment analysis by using TOPSIS-DEA method

Data envelopment analysis methods classify the decision making units into two groups: efficient and inefficient ones. Therefore, the fully ranking all DMUs is demanded by most of the decision makers. However, data envelopment analysis and multiple criteria decision making units are developed independently and designed for different purposes. However, there are some applications in problem solving such as ranking, where these two methods are combined. Combination of multiple criteria decision making methods with data envelopment analysis is a new idea for elimination of disadvantages when applied independently. In this paper, first the new combined method is proposed named TOPSIS-DEA for ranking efficient units which not only includes the benefits of both data envelopment analysis and multiple criteria decision making methods, but also solves the issues that appear in former methods. Then properties and advantages of the suggested method are discussed and compared with super efficiency method, MAJ method, statistical-based model (CCA), statistical-based model (DR/DEA), cross-efficiency—aggressive, cross-efficiency—benevolent, Liang et al.’s model, through several illustrative examples. Finally, the proposed methods are validated.     

基于分段策略评分的冲突主体偏好排序方法及其应用

冲突中各利益主体的偏好信息对冲突局势的演变和纠纷调解具有重要影响。现有的冲突偏好排序方法主要基于决策者对冲突局势或状态、策略权重和声明信息的主观判断和理解,缺乏科学的数据来源支撑。为准确获取冲突主体的偏好信息,本文提出了一种基于调查法的分段策略冲突偏好排序方法。首先,根据决策者类别将冲突策略集合进行分段,并通过问卷、调研等方法获取每个冲突主体对所有分段策略的重要度评分信息。在此基础上,计算决策者对各个冲突状态的综合偏好评分,进而得到状态偏好的排序结果。最后以医患纠纷为例,对比分析了传统策略权重法和分段策略评分法的偏好排序和稳定性分析结果,进一步验证了所提方法的有效性。     

A new method for ranking fuzzy numbers and its application to group decision making

In this paper, a new method for comparing fuzzy numbers based on a fuzzy probabilistic preference relation is introduced. The ranking order of fuzzy numbers with the weighted confidence level is derived from the pairwise comparison matrix based on 0.5-transitivity of the fuzzy probabilistic preference relation. The main difference between the proposed method and existing ones is that the comparison result between two fuzzy numbers is expressed as a fuzzy set instead of a crisp one. As such, the ranking order of n fuzzy numbers provides more information on the uncertainty level of the comparison. Illustrated by comparative examples, the proposed method overcomes certain unreasonable (due to the violation of the inequality properties) and indiscriminative problems exhibited by some existing methods. More importantly, the proposed method is able to provide decision makers with the probability of making errors when a crisp ranking order is obtained. The proposed method is also able to provide a probability-based explanation for conflicts among the comparison results provided by some existing methods using a proper ranking order, which ensures that ties of alternatives can be broken.     

Ranking decision making units by imposing a minimum weight restriction in the data envelopment analysis

It has been widely recognized that data envelopment analysis (DEA) lacks discrimination power to distinguish between DEA efficient units. This paper proposes a new methodology for ranking decision making units (DMUs). The new methodology ranks DMUs by imposing an appropriate minimum weight restriction on all inputs and outputs, which is decided by a decision maker (DM) or an assessor in terms of the solutions to a series of linear programming (LP) models that are specially constructed to determine a maximin weight for each DEA efficient unit. The DM can decide how many DMUs to be retained as DEA efficient in final efficiency ranking according to the requirement of real applications, which provides flexibility for DEA ranking. Three numerical examples are investigated using the proposed ranking methodology to illustrate its power in discriminating between DMUs, particularly DEA efficient units.     

A distance-based measure of super efficiency in data envelopment analysis: an application to gas companies

Conventional data envelopment analysis (DEA) assists decision makers in distinguishing between efficient and inefficient decision making units (DMUs) in a homogeneous group. Standard DEA models can not provide more information about efficient units. Super-efficiency DEA models can be used in ranking the performance of efficient DMUs and overcome this obstacle. Because of the possible infeasibility, the use of super efficiency models has been restricted. This research proposes a methodology to determine a distance-based measure of super-efficiency. The proposed methodology overcomes the infeasibility problem of the existing ranking methodologies. The applicability of the proposed model is illustrated in the context of the analysis of gas companies?? performance.     

A fuzzy closeness approach to fuzzy multi-attribute decision making

The aim of this paper is to develop a new fuzzy closeness (FC) methodology for multi-attribute decision making (MADM) in fuzzy environments, which is an important research field in decision science and operations research. The TOPSIS method based on an aggregating function representing “closeness to the ideal solution” is one of the well-known MADM methods. However, while the highest ranked alternative by the TOPSIS method is the best in terms of its ranking index, this does not mean that it is always the closest to the ideal solution. Furthermore, the TOPSIS method presumes crisp data while fuzziness is inherent in decision data and decision making processes, so that fuzzy ratings using linguistic variables are better suited for assessing decision alternatives. In this paper, a new FC method for MADM under fuzzy environments is developed by introducing a multi-attribute ranking index based on the particular measure of closeness to the ideal solution, which is developed from the fuzzy weighted Minkowski distance used as an aggregating function in a compromise programming method. The FC method of compromise ranking determines a compromise solution, providing a maximum “group utility” for the “majority” and a minimum individual regret for the “opponent”. A real example of a personnel selection problem is examined to demonstrate the implementation process of the method proposed in this paper.     

Interactive Utility Assessment in Multicriteria Decision Analysis Using Implicit Trade-off Information

This paper introduces a methodology for the assessment of a decision-maker's utility function, based on interactions requiring relatively easy responses of the implicit trade-off type, i.e. similar to responses required in STEM or goal programming methods. The estimation of the value-function model to represent preferences is useful in ranking or pruning elements of the decision space. Inputs required from the decision-maker are, however, less demanding than the pairwise comparisons (or similar preference statements) typically required by value-function models. The methodology thus appears to be appropriate for relatively large numbers of criteria. An algorithm for implementing the proposed methodology for finite action spaces is developed and applied to examples involving up to 15 criteria.     

Dominance,potential optimality and alternative ranking in imprecise multi-attribute decision making

In this paper, we introduce a methodology based on an additive multiattribute utility function that does not call for precise estimations of the inputs, such as utilities, attribute weights and performances of decision alternatives. The information about such inputs is assumed to be in the form of ranges, which constitute model constraints and give rise to nonlinear programming problems. This has significant drawbacks for outputting the sets of non-dominated and potentially optimal alternatives for such problems, and we, therefore, propose their transformation into equivalent linear programming problems. The set of non-dominated and potentially optimal alternatives is a non-ranked set and can be very large, which makes the choice of the most preferred alternative very difficult. The above problem is solved by proposing several methods for alternative ranking. An application to the disposal of surplus weapons-grade plutonium is considered, showing the advantages of this approach.     

A Fuzzy Multi-Criteria Outranking Approach in Support of Business Angels’ Decision Analysis Process for the Assessment of Companies as Investment Opportunities

In this paper, a multi-criteria method is presented for the evaluation and ranking of a selected set of companies as investment opportunities in aid of the relevant decision analysis process of business angels. The multi-criteria methodology is based on the PROMETHEE method, which is further extended to deal with fuzzy input data in order to address the data imprecision and uncertainty of the decision process. The paper concludes by suggesting a web-based system implementation of the proposed methodology, which will significantly enhance modern business angels networks.     

Selecting IS personnel use fuzzy GDSS based on metric distance method

In this paper we propose a new approach to rank fuzzy numbers by metric distance. For showing our method is a good ranking method, we give two examples to compare with other methods. The paper also developes a computer-based group decision support system, FMCGDSS, to increase the recruiting productivity and to easily compare our method with other fuzzy number ranking methods. The FMCGDSS includes three ranking methods: intuition ranking, Lee and Li's fuzzy mean/spread and our metric distance method to help manager make better decision under fuzzy circumstance. The result indicates that the new method is coincident with the intuition ranking and the Lee and Li's fuzzy mean/spread method on each type weight.     

面向直觉模糊集排序能力提升的记分函数设计研究

直觉模糊集记分函数的排序能力是影响直觉模糊型多准则决策绩效的重要因素。本文以直觉模糊集记分函数的特性分析为切入点,较为系统地分析了现有各类记分函数的有界性、符合直觉性、排序能力、连续性等四类特征;其次,基于现有记分函数特征匹配状况,提出了新的直觉模糊集记分函数的分段函数并加以证明;最后,系统比较了现有记分函数与本文提出的记分函数在排序能力和区分度方面的差异,验证了本方法的优越性和合理性。     

基于AHP的群决策排名问题

针对排名结果是由分差大的那部分评委主导,分差小的评委的决策意见往往被湮没的问题给出基于AHP的群决策排名方法.详细介绍了多属性群决策专家权重确定的方法、属性权重确定的方法和信息集结的方法.     

Multicriteria approaches for ranking of efficient units in DEA models

Data envelopment analysis models usually split decision making units into two basic groups, efficient and inefficient. Efficiency score of inefficient units allows their ranking but efficient units cannot be ranked directly because of their maximum efficiency. That is why there are formulated several models for ranking of efficient units. The paper presents two original models for ranking of efficient units in data envelopment analysis—they are based on multiple criteria decision making techniques—goal programming and analytic hierarchy process. The first model uses goal programming methodology and minimizes either the sum of undesirable deviations or maximal undesirable deviation from the efficient frontier. The second approach is analytic hierarchy process model for ranking of efficient units. The two presented models are compared with several super-efficiency models and other approaches for ranking decision making units in DEA models including definitions based on distances from optimistic and pessimistic envelopes and cross efficiency evaluation models. The results of the analysis by all presented models are illustrated on a real data set—evaluation of 194 bank branches of one of the Czech commercial banks.     

模糊环境下的一种多准则决策方法

本文利用模糊集理论以及层次分析法（AHP）原理，建立了一种在模糊环境下对方案进行择优或排序的多准则决策方法。     

Regularized estimation for preference disaggregation in multiple criteria decision making

Disaggregation methods have been extensively used in multiple criteria decision making to infer preferential information from reference examples, using linear programming techniques. This paper proposes simple extensions of existing formulations, based on the concept of regularization which has been introduced within the context of the statistical learning theory. The properties of the resulting new formulations are analyzed for both ranking and classification problems and experimental results are presented demonstrating the improved performance of the proposed formulations over the ones traditionally used in preference disaggregation analysis.     

Rough approximation of a preference relation by dominance relations

An original methodology for using rough sets to preference modeling in multi-criteria decision problems is presented. This methodology operates on a pairwise comparison table (PCT), including pairs of actions described by graded preference relations on particular criteria and by a comprehensive preference relation. It builds up a rough approximation of a preference relation by graded dominance relations. Decision rules derived from the rough approximation of a preference relation can be used to obtain a recommendation in multi-criteria choice and ranking problems. The methodology is illustrated by an example of multi-criteria programming of water supply systems.     

A Fuzzy Multi-criteria Outranking Approach in Support of Business Angels’ Decision-Analysis Process for the Assessment of Companies as Investment Opportunities

In this paper, a multi-criteria method is presented for the evaluation and ranking of a selected set of companies as investment opportunities in aid of the relevant decision-analysis process of business angels. The multi-criteria methodology is based on the PROMETHEE method, which is further extended to deal with fuzzy input data in order to address the data imprecision and uncertainty of the decision process. The paper concludes by suggesting a web-based system implementation of the proposed methodology, which will significantly enhance modern business angels networks.     

An integrated model-based interactive approach to FMAGDM with incomplete preference information

Incomplete fuzzy preference relations, incomplete multiplicative preference relations, and incomplete linguistic preference relations are very useful to express decision makers’ incomplete preferences over attributes or alternatives in the process of decision making under fuzzy environments. The aim of this paper is to investigate fuzzy multiple attribute group decision making problems where the attribute values are represented in intuitionistic fuzzy numbers and the information on attribute weights is provided by decision makers by means of one or some of the different preference structures, including weak ranking, strict ranking, difference ranking, multiple ranking, interval numbers, incomplete fuzzy preference relations, incomplete multiplicative preference relations, and incomplete linguistic preference relations. We transform all individual intuitionistic fuzzy decision matrices into the interval decision matrices and construct their expected decision matrices, and then aggregate all these expected decision matrices into a collective one. We establish an integrated model by unifying the collective decision matrix and all the given different structures of incomplete weight preference information, and develop an integrated model-based approach to interacting with the decision makers so as to adjust all the inconsistent incomplete fuzzy preference relations, inconsistent incomplete linguistic preference relations and inconsistent incomplete multiplicative preference relations into the ones with acceptable consistency. The developed approach can derive the attribute weights and the ranking of the alternatives directly from the integrated model, and thus it has the following prominent characteristics: (1) it does not need to construct the complete fuzzy preference relations, complete linguistic preference relations and complete multiplicative preference relations from the incomplete fuzzy preference relations, incomplete linguistic preference relations and incomplete multiplicative preference relations, respectively; (2) it does not need to unify the different structures of incomplete preferences, and thus can simplify the calculation and avoid distorting the given preference information; and (3) it can sufficiently reflect and adjust the subjective desirability of decision makers in the process of interaction. A practical example is also provided to illustrate the developed approach.     

A ranking method based on a full-inefficient frontier

Since in evaluating by traditional data envelopment analysis (DEA) models many decision making units (DMUs) are classified as efficient, a large number of methods for fully ranking both efficient and inefficient DMUs have been proposed. In this paper a ranking method is suggested which basically differs from previous methods but its models are similar to traditional DEA models such as BCC, additive model, etc. In this ranking method, DMUs are compared against an full-inefficient frontier, which will be defined in this paper. Based on this point of view many models can be designed, and we mention a radial and a slacks-based one out of them. This method can be used to rank all DMUs to get analytic information about the system, and also to rank only efficient DMUs to discriminate between them.     

Extension of the LINMAP for multiattribute decision making under Atanassov’s intuitionistic fuzzy environment

The aim of this article is further extending the linear programming techniques for multidimensional analysis of preference (LINMAP) to develop a new methodology for solving multiattribute decision making (MADM) problems under Atanassov’s intuitionistic fuzzy (IF) environments. The LINMAP only can deal with MADM problems in crisp environments. However, fuzziness is inherent in decision data and decision making processes. In this methodology, Atanassov’s IF sets are used to describe fuzziness in decision information and decision making processes by means of an Atanassov’s IF decision matrix. A Euclidean distance is proposed to measure the difference between Atanassov’s IF sets. Consistency and inconsistency indices are defined on the basis of preferences between alternatives given by the decision maker. Each alternative is assessed on the basis of its distance to an Atanassov’s IF positive ideal solution (IFPIS) which is unknown a prior. The Atanassov’s IFPIS and the weights of attributes are then estimated using a new linear programming model based upon the consistency and inconsistency indices defined. Finally, the distance of each alternative to the Atanassov’s IFPIS can be calculated to determine the ranking order of all alternatives. A numerical example is examined to demonstrate the implementation process of this methodology. Also it has been proved that the methodology proposed in this article can deal with MADM problems under not only Atanassov’s IF environments but also both fuzzy and crisp environments.