Efficiencya Assessment and Target Setting Using a Fully Fuzzy DEA Approach (original) (raw)

Data Envelopment Analysis with Fuzzy Parameters

Optimizing, Innovating, and Capitalizing on Information Systems for Operations

Data envelopment analysis (DEA) is a methodology for measuring the relative efficiencies of a set of decision making units (DMUs) that use multiple inputs to produce multiple outputs. In the conventional DEA, all the data assume the form of specific numerical values. However, the observed values of the input and output data in real-life problems are sometimes imprecise or vague. Previous methods have not considered the preferences of the decision makers (DMs) in the evaluation process. This paper proposes an interactive evaluation process for measuring the relative efficiencies of a set of DMUs in fuzzy DEA with consideration of the DMs’ preferences. The authors construct a linear programming (LP) model with fuzzy parameters and calculate the fuzzy efficiency of the DMUs for different a levels. Then, the DM identifies his or her most preferred fuzzy goal for each DMU under consideration. A modified Yager index is used to develop a ranking order of the DMUs. This study allows the DMs...

Fuzzy data envelopment analysis in the presence of undesirable outputs with ideal points

Complex & Intelligent Systems

Data envelopment analysis (DEA) is a prominent technique for evaluating relative efficiency of a set of entities called decision making units (DMUs) with homogeneous structures. In order to implement a comprehensive assessment, undesirable factors should be included in the efficiency analysis. The present study endeavors to propose a novel approach for solving DEA model in the presence of undesirable outputs in which all input/output data are represented by triangular fuzzy numbers. To this end, two virtual fuzzy DMUs called fuzzy ideal DMU (FIDMU) and fuzzy anti-ideal DMU (FADMU) are introduced into proposed fuzzy DEA framework. Then, a lexicographic approach is used to find the best and the worst fuzzy efficiencies of FIDMU and FADMU, respectively. Moreover, the resulting fuzzy efficiencies are used to measure the best and worst fuzzy relative efficiencies of DMUs to construct a fuzzy relative closeness index. To address the overall assessment, a new approach is proposed for ranki...

Efficiency measurement in fuzzy additive data envelopment analysis

International Journal of Industrial and Systems Engineering, 2012

Performance evaluation in conventional data envelopment analysis (DEA) requires crisp numerical values. However, the observed values of the input and output data in real-world problems are often imprecise or vague. These imprecise and vague data can be represented by linguistic terms characterised by fuzzy numbers in DEA to reflect the decision-makers' intuition and subjective judgements. This paper extends the conventional DEA models to a fuzzy framework by proposing a new fuzzy additive DEA model for evaluating the efficiency of a set of decision-making units (DMUs) with fuzzy inputs and outputs. The contribution of this paper is threefold: (1) we consider ambiguous, uncertain and imprecise input and output data in DEA, (2) we propose a new fuzzy additive DEA model derived from the-level

A taxonomy and review of the fuzzy data envelopment analysis literature: Two decades in the making

European Journal of Operational Research, 2011

Data envelopment analysis (DEA) is a methodology for measuring the relative efficiencies of a set of decision making units (DMUs) that use multiple inputs to produce multiple outputs. Crisp input and output data are fundamentally indispensable in conventional DEA. However, the observed values of the input and output data in real-world problems are sometimes imprecise or vague. Many researchers have proposed various fuzzy methods for dealing with the imprecise and ambiguous data in DEA. In this study, we provide a taxonomy and review of the fuzzy DEA methods. We present a classification scheme with four primary categories, namely, the tolerance approach, the a-level based approach, the fuzzy ranking approach and the possibility approach. We discuss each classification scheme and group the fuzzy DEA papers published in the literature over the past 20 years. To the best of our knowledge, this paper appears to be the only review and complete source of references on fuzzy DEA.

Development of Bi-Objective Fuzzy Data Envelopment Analysis Model to Measure the Efficiencies of Decision-Making Units

Mathematics

The proposed bi-objective fuzzy data envelopment analysis (BOFDEA) model is a new approach to assess the performance efficiency of decision-making units (DMUs) in uncertain environments using α-cuts. The model is based on fuzzy data envelopment analysis (FDEA) and considers two objectives, and a solution method and ranking system are provided. Generally, the efficiency score obtained for a DMU using the α-cut approach is an interval. Intervals are partially ordered sets, due to which ranking intervals is a challenging task. The proposed BOFDEA model with α-cuts provides the efficiency of DMUs in the crisp form, not in the form of intervals. Due to this, ranking DMUs with the proposed method’s help becomes very easy and less computationally. The proposed model has been validated through numerical examples, and a real-world application in the education sector has been shown to demonstrate its practicality.

Ranking units in Data Envelopment Analysis with fuzzy data

Data Envelopment Analysis (DEA) is a widely applied approach for measuring the relative efficiencies of a set of Decision Making Units (DMUs), which use multiple inputs to produce multiple outputs. In real world problems the data available may be imprecise. With fuzzy inputs and fuzzy outputs, the optimality conditions for the crisp DEA Models need to be clarified and generalized. The corresponding fuzzy linear programming problem is usually solved using some ranking methods for fuzzy sets. The methods of solving fuzzy DEA problems can be categorized into four distinct approaches: tolerance approach, defuzzification approach, α-level based approach, and fuzzy ranking approach In this paper, we introduce a new α-level based approach and a numerical method for ranking DMUs with fuzzy data.

Evaluating the Efficiency and Classifying the Fuzzy Data: A Dea Based Approach

International Journal of Industrial Mathematics, 2014

Data envelopment analysis (DEA) has been proven as an efficient technique to evaluate the performance of homogeneous decision making units (DMUs) where multiple inputs and outputs exist. In the conventional applications of DEA, the data are considered as specific numerical values with explicit designation of being an input or output. However, the observed values of the data are sometimes imprecise (i.e. input and output variables cannot be measured precisely) and data are sometimes flexible (measures with unknown status of being input or output are referred to as flexible measures in the literature). In the current paper a number of methods are proposed to evaluate the relative efficiency and to identify the status of fuzzy flexible measures. Indeed, the modified fuzzy DEA models are suggested to accommodate flexible measures. In order to obtain correct results, alternative optimal solutions are considered to deal with the fuzzy flexible measures. Numerical examples are used to illu...

Measure of efficiency in DEA with fuzzy input-output levels: a methodology for assessing, ranking and imposing of weights restrictions

Applied Mathematics and Computation, 2004

In this paper, a fuzzy comparison of fuzzy numbers is defined and a slack-based measure (SBM model) in data envelopment analysis (DEA) is extended to be a fuzzy DEA model, using it. Proposed measure is employed for evaluation and ranking of all decision making units, using a fuzzy concept called fuzzy profit. Also, it is shown that the introduced model is convenient for using weights restrictions. Furthermore, we compare the results of proposed model with Guo and TanakaÕs results [Fuzzy Sets Syst. 119 (2001) 149] by representing a numerical example introduced by them.

Cost Efficiency Measures with Trapezoidal Fuzzy Numbers in Data Envelopment Analysis Based on Ranking Functions

International Journal of Fuzzy System Applications, 2012

Cost efficiency (CE) evaluates the ability to produce current outputs at minimal cost, given its input prices. In ordinary CE model, the input prices are assumed to be definite. In recent years, various attempts have been made to measuring CE when the input prices are as trapezoidal fuzzy numbers. The main contribution of this paper is to provide a new approach for generalizing the CE of decision making units in data envelopment analysis when the input prices are trapezoidal fuzzy numbers, where concepts of fuzzy linear programming problems and CE, are directly used. Here, the author used the linear ranking functions to compare fuzzy numbers. The proposed method is illustrated with two application examples and proves to be persuasive and acceptable in real world systems.