Modeling fuzzy data envelopment analysis by parametric programming method

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.     

A new ranking method to fuzzy data envelopment analysis

Due to its wide practical use, data envelopment analysis (DEA) has been adapted to many fields to deal with problems that have occurred in practice. One adaptation has been in the field of ranking decision-making units (DMUs). Most methods of ranking DMUs assume that all input and output data are exactly known, but in real life the data cannot be precisely measured. Thus this paper will carry out some researches to DEA under fuzzy environment. A fuzzy comparison of fuzzy variables is defined and the CCR model is extended to be a fuzzy DEA model based on credibility measure. In order to rank all the DMUs, a full ranking method will be given. Since the ranking method involves a fuzzy function, a fuzzy simulation is designed and embedded into the genetic algorithm to establish a hybrid intelligent algorithm. However, it is shown to be possible to avoid some of the need for dealing with these nonlinear problems by identifying conditions under which they can be replaced by linear problems. Finally we will provide a numerical example to illustrate the fuzzy DEA model and the ranking method.     

Evaluating ecommerce websites cognitive efficiency: An integrative framework based on data envelopment analysis

This paper presents an integrative framework to evaluate ecommerce website efficiency from the user viewpoint using Data Envelopment Analysis (DEA). This framework is inspired by concepts driven from theories of information processing and cognition and considers the website efficiency as a measure of its quality and performance. When the users interact with the website interfaces to perform a task, they are involved in a cognitive effort, sustaining a cognitive cost to search, interpret and process information, and experiencing either a sense of satisfaction or dissatisfaction for that. The amount of ambiguity and uncertainty, and the search (over-)time during navigation that they perceive determine the effort size – and, as a consequence, the cognitive cost amount – they have to bear to perform their task. On the contrary, task performing and result achievement provide the users with cognitive benefits, making interaction with the website potentially attractive, satisfying, and useful. In total, 9 variables are measured, classified in a set of 3 website macro-dimensions (user experience, site navigability and structure). The framework is implemented to compare 52 ecommerce websites that sell products in the information technology and media market. A stepwise regression is performed to assess the influence of cognitive costs and benefits that mostly affect website efficiency.     

An ACS-based framework for fuzzy data mining

Data mining is often used to find out interesting and meaningful patterns from huge databases. It may generate different kinds of knowledge such as classification rules, clusters, association rules, and among others. A lot of researches have been proposed about data mining and most of them focused on mining from binary-valued data. Fuzzy data mining was thus proposed to discover fuzzy knowledge from linguistic or quantitative data. Recently, ant colony systems (ACS) have been successfully applied to optimization problems. However, few works have been done on applying ACS to fuzzy data mining. This thesis thus attempts to propose an ACS-based framework for fuzzy data mining. In the framework, the membership functions are first encoded into binary-bits and then fed into the ACS to search for the optimal set of membership functions. The problem is then transformed into a multi-stage graph, with each route representing a possible set of membership functions. When the termination condition is reached, the best membership function set (with the highest fitness value) can then be used to mine fuzzy association rules from a database. At last, experiments are made to make a comparison with other approaches and show the performance of the proposed framework.     

An integrated fuzzy regression-data envelopment analysis algorithm for optimum oil consumption estimation with ambiguous data

This study introduces an integrated fuzzy regression (FR) data envelopment analysis (DEA) algorithm for oil consumption estimation and optimization with uncertain and ambiguous data. This is quite important as oil consumption estimations deals with several uncertainties due to social, economic factors. Furthermore, DEA is integrated with FR because there is no clear cut as to which FR approach is superior for oil consumption estimation. The standard indicators used in this paper are population, cost of crude oil, gross domestic production (GDP) and annual oil production. Fifteen popular and most cited FR models are considered in the algorithm. Each FR model has different approach and advantages. The input data is divided into train and test data. The FR models have been tuned for all their parameters according to the train data, and the best coefficients are identified. Center of Average Method for defuzzification output process is applied. For determining the rate of error of FR models estimations, the rate of defuzzified output of each model is compared with its actual rate consumption in test data. The efficiency of 15 FR models is examined by the output-oriented Data Envelopment Analysis (DEA) model without inputs by considering three types of relative error: RMSE, MAE and MAPE. The applicability and superiority of the proposed algorithm is shown for monthly oil consumption of Canada, United States, Japan and Australia from 1990 to 2005.     

Ranking efficient decision-making units in data envelopment analysis using fuzzy concept

This paper introduces a new mathematical method for improving the discrimination power of data envelopment analysis and to completely rank the efficient decision-making units (DMUs). Fuzzy concept is utilised. For this purpose, first all DMUs are evaluated with the CCR model. Thereafter, the resulted weights for each output are considered as fuzzy sets and are then converted to fuzzy numbers. The introduced model is a multi-objective linear model, endpoints of which are the highest and lowest of the weighted values. An added advantage of the model is its ability to handle the infeasibility situation sometimes faced by previously introduced models.     

An extended multiple criteria data envelopment analysis model

Several researchers have adapted the data envelopment analysis (DEA) models to deal with two inter-related problems: weak discriminating power and unrealistic weight distribution. The former problem arises as an application of DEA in the situations where decision-makers seek to reach a complete ranking of units, and the latter problem refers to the situations in which basic DEA model simply rates units 100% efficient on account of irrational input and/or output weights and insufficient number of degrees of freedom. Improving discrimination power and yielding more reasonable dispersion of input and output weights simultaneously remain a challenge for DEA and multiple criteria DEA (MCDEA) models. This paper puts emphasis on weight restrictions to boost discriminating power as well as to generate true weight dispersion of MCDEA when a priori information about the weights is not available. To this end, we modify a very recent MCDEA models in the literature by determining an optimum lower bound for input and output weights. The contribution of this paper is sevenfold: first, we show that a larger amount for the lower bound on weights often leads to improving discriminating power and reaching realistic weights in MCDEA models due to imposing more weight restrictions; second, the procedure for sensitivity analysis is designed to define stability for the weights of each evaluation criterion; third, we extend a weighted MCDEA model to three evaluation criteria based on the maximum lower bound for input and output weights; fourth, we develop a super-efficiency model for efficient units under the proposed MCDEA model in this paper; fifth, we extend an epsilon-based minsum BCC-DEA model to proceed our research objectives under variable returns to scale (VRS); sixth, we present a simulation study to statistically analyze weight dispersion and rankings between five different methods in terms of non-parametric tests; and seventh, we demonstrate the applicability of the proposed models with an application to European Union member countries.     

An integrated data envelopment analysis and free disposal hull framework for cost-efficiency measurement using rough sets

Traditional cost-efficiency analysis methods require exact and precise values for inputs, outputs and input prices. However, this is not the case in many real-life applications. This study proposes a rough cost-efficiency approach to the problem of ranking efficient decision making units (DMUs). Based on rough set theory, a nonparametric methodology for cost-efficiency analysis is developed. The merits of this methodology include computational ease and the capacity to incorporate data uncertainty. Furthermore, it applies to both convex data envelopment analysis (DEA) and non-convex free disposal hull (FDH) technologies under different returns-to-scale assumptions. A numerical example and a real-life case study in the Japanese banking industry demonstrate the applicability of the proposed framework. In particular, the rankings of the DMUs resulting from the proposed models are compared with those obtained using the maximum technical efficiency loss index.     

Personnel selection using analytic network process and fuzzy data envelopment analysis approaches

This paper develops a decision support tool using an integrated analytic network process (ANP) and fuzzy data envelopment analysis (DEA) approach to effectively deal with the personnel selection problem drawn from an electric and machinery company in Taiwan. The current personnel selection procedure is a separate two-stage method. The administration practice shows that the separation between stages 1 and 2 reduces the administration quality and may incur both the top manager’s displeasure and the decision-makers’ depression. An illustrative example by a simulated application demonstrates the implementation of the proposed approach. This example demonstrates how this approach can avoid the main drawback of the current method, and more importantly, can deal with the personnel selection problem more convincingly and persuasively. This study supports the applications of ANP and fuzzy DEA as decision support tools in personnel selection.     

Personnel selection using analytic network process and fuzzy data envelopment analysis approaches

This paper develops a decision support tool using an integrated analytic network process (ANP) and fuzzy data envelopment analysis (DEA) approach to effectively deal with the personnel selection problem drawn from an electric and machinery company in Taiwan. The current personnel selection procedure is a separate two-stage method. The administration practice shows that the separation between stages 1 and 2 reduces the administration quality and may incur both the top manager’s displeasure and the decision-makers’ depression. An illustrative example by a simulated application demonstrates the implementation of the proposed approach. This example demonstrates how this approach can avoid the main drawback of the current method, and more importantly, can deal with the personnel selection problem more convincingly and persuasively. This study supports the applications of ANP and fuzzy DEA as decision support tools in personnel selection.     

Some properties of Pareto efficiency under the framework of data envelopment analysis

Data envelopment analysis (DEA) has been widely applied to measure the Pareto efficiency of multiple-input and multiple-output decision making units (DMUs). In this paper it is shown that under linear production frontiers DMU efficiency is a weighted arithmetic mean of the efficiencies of the outputs; whereas under loglinear production frontiers DMU efficiency is a weighted geometric mean of the output efficiencies. Furthermore, DMU efficiency can be decomposed with respect to input factors as well, and some results are derived. As a consequence, a modified DEA model is devised, whereby the efficiency of each output (or input) in addition to DMU efficiency is able to be measured in one linear programming solution.     

An interactive application of data envelopment analysis in microcomputers

This article describes a general-purpose microcomputer code for data envelopment analysis (DEA) that incorporates four different DEA models in the form of a user-friendly, menu-driven structure.Research financially supported by Dean's Professorship, College of Business, the Ohio State University.     

An acceptance system decision rule with data envelopment analysis

This paper further discusses the suggestion proposed by Troutt et al. [1] that data envelopment analysis (DEA) can be used to develop an acceptance boundary. It is shown that the linear programming model with an arbitrary objective function developed by Troutt et al. [1] can, in fact, be directly obtained from their assumptions. We develop a DEA-type linear programming model to determine not only whether a new case is accepted, but also the location of the new case with respect to the samples proviously classified. A numerical example is provided.     

Sensitivity analysis of the additive model in data envelopment analysis while inputs and outputs are fuzzy data

Data envelopment analysis (DEA) requires input and output data to be precisely known. This is not always the case in real applications. Sensitivity analysis of the additive model in DEA is studied in this paper while inputs and outputs are symmetric triangular fuzzy numbers. Sufficient conditions for simultaneous change of all outputs and inputs of an efficient decision-making unit (DMU) which preserves efficiency are established. Two kinds of changes on inputs and outputs are considered. For the first state, changes are exerted on the core and margin of symmetric triangular fuzzy numbers so that the value of inputs increase and the value of outputs decrease. In the second state, a non-negative symmetric triangular fuzzy number is subtracted from outputs to decrease outputs and it is added to inputs to increase inputs. A numerical illustration is provided.     

Slacks-based measures of efficiency in imprecise data envelopment analysis: An approach based on data envelopment analysis with double frontiers

Data envelopment analysis (DEA) is a mathematical approach for evaluating the efficiency of decision-making units (DMUs) that convert multiple inputs into multiple outputs. Traditional DEA models assume that all input and output data are known exactly. In many situations, however, some inputs and/or outputs take imprecise data. In this paper, we present optimistic and pessimistic perspectives for obtaining an efficiency evaluation for the DMU under consideration with imprecise data. Additionally, slacks-based measures of efficiency are used for direct assessment of efficiency in the presence of imprecise data with slack values. Finally, the geometric average of the two efficiency values is used to determine the DMU with the best performance. A ranking approach based on degree of preference is used for ranking the efficiency intervals of the DMUs. Two numerical examples are used to show the application of the proposed DEA approach.     

A framework for benchmarking service process using data envelopment analysis and decision tree

With the increase in the influence of service industry on the economy, more and more firms are becoming concern about service and service management. Unlike tangible products, since service is a delivery system, designing and controlling delivery process are important in management of services. One of the most important issues in managing service delivery process is how to find out and improve inefficient process in an organization. Once inefficient processes are found, it should be determined which process is to be improved first, since it is impossible for any firm to improve all of their inefficient processes simultaneously. Then, in order to get some ideas about improvement, selecting a benchmark process is required. The objective of this paper is to provide a systematic approach for benchmarking service process. We used the integrated form of data envelopment analysis (DEA) and decision tree (DT) as a benchmarking method instead of using DEA alone. Although DEA is a useful technique for benchmarking, it fails to give any clear directions as to which process should be improved first. The proposed approach enables firm’s manager to find inefficient service units in a firm-level and inefficient processes in a service unit-level. The proposed approach also allows the manager to select which process to improve first and which process a benchmark for referencing. As a result, it can be helpful for operating and managing firms’ processes. To show how useful the suggested service process benchmarking framework is, an illustrative example is addressed.     

Ranking alternatives in a preferential voting system using fuzzy concepts and data envelopment analysis

In this paper, a new method for aggregating the opinions of experts in a preferential voting system is proposed. The method, which uses fuzzy concept in handling crisp data, is computationally efficient and is able to completely rank the alternatives. Through this method, the number of votes for certain rank position that each alternative receives are first grouped together to form fuzzy numbers. The nearest point to a fuzzy number concept is then used to introduce an artificial ideal alternative. Data envelopment analysis is next used to find the efficiency scores of the alternatives in a pair-wise comparison with the artificial ideal alternative. Alternatives are rank based on these efficiency scores. If the alternatives are not completely ranked, a weight restriction method also based on fuzzy concept is used on the un-discriminated alternatives until they are completely ranked. Two examples are given for illustration of the method.     

Ranking alternatives in a preferential voting system using fuzzy concepts and data envelopment analysis

In this paper, a new method for aggregating the opinions of experts in a preferential voting system is proposed. The method, which uses fuzzy concept in handling crisp data, is computationally efficient and is able to completely rank the alternatives. Through this method, the number of votes for certain rank position that each alternative receives are first grouped together to form fuzzy numbers. The nearest point to a fuzzy number concept is then used to introduce an artificial ideal alternative. Data envelopment analysis is next used to find the efficiency scores of the alternatives in a pair-wise comparison with the artificial ideal alternative. Alternatives are rank based on these efficiency scores. If the alternatives are not completely ranked, a weight restriction method also based on fuzzy concept is used on the un-discriminated alternatives until they are completely ranked. Two examples are given for illustration of the method.     

An enumeration algorithm for integer‐valued data envelopment analysis

Data envelopment analysis (DEA) models assume real‐valued inputs and outputs, but on many occasions, some inputs and/or outputs can only take integer values. In these cases, using DEA models can result in misleading efficiency assessments and inaccurate performance targets. In this paper, we propose an enumeration algorithm for computing efficiency scores and performance targets of decision‐making units with integer value inputs/outputs. In the presented algorithm, we do not use any of the mixed integer linear programming (MILP) models that are used in previous studies. We show that the result of our algorithm and that of the MILP model presented in this context is the same. We also generalize our algorithm for different types of returns to scale as well as for the hybrid setting with real‐valued data.     

数据包络分析研究热点综述

数据包络分析是面向多输入多输出决策单元的有效性评估方法。在介绍数据包络分析的基本思想和模型基础之上,总结了近年来国内外的研究热点,包括两阶段DEA、效率排序DEA、随机DEA和相关扩展问题,旨在围绕以上研究热点,对DEA近年来的理论研究及其扩展模型进行梳理和分类。最后对数据包络分析进一步研究提出展望。