Efficiency measurement in fuzzy additive data envelopment analysis

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 a-level approach and (3) we demonstrate the practical aspects of our model with two numerical examples and show its comparability with five different fuzzy DEA methods in the literature. Copyright © 2011 Inderscience Enterprises Ltd.

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

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. © 2011 Elsevier B.V. All rights reserved.

An overall profit Malmquist productivity index with fuzzy and interval data

Although crisp data are fundamentally indispensable for determining the profit Malmquist productivity index (MPI), the observed values in real-world problems are often imprecise or vague. These imprecise or vague data can be suitably characterized with fuzzy and interval methods. In this paper, we reformulate the conventional profit MPI problem as an imprecise data envelopment analysis (DEA) problem, and propose two novel methods for measuring the overall profit MPI when the inputs, outputs, and price vectors are fuzzy or vary in intervals. We develop a fuzzy version of the conventional MPI model by using a ranking method, and solve the model with a commercial off-the-shelf DEA software package. In addition, we define an interval for the overall profit MPI of each decision-making unit (DMU) and divide the DMUs into six groups according to the intervals obtained for their overall profit efficiency and MPIs. We also present two numerical examples to demonstrate the applicability of the two proposed models and exhibit the efficacy of the procedures and algorithms. © 2011 Elsevier Ltd.

Aggregating preference ranking with fuzzy Data Envelopment Analysis

Selecting the best alternative in a group decision making is a subject of many recent studies. The most popular method proposed for ranking the alternatives is based on the distance of each alternative to the ideal alternative. The ideal alternative may never exist; hence the ranking results are biased to the ideal point. The main aim in this study is to calculate a fuzzy ideal point that is more realistic to the crisp ideal point. On the other hand, recently Data Envelopment Analysis (DEA) is used to find the optimum weights for ranking the alternatives. This paper proposes a four stage approach based on DEA in the Fuzzy environment to aggregate preference rankings. An application of preferential voting system shows how the new model can be applied to rank a set of alternatives. Other two examples indicate the priority of the proposed method compared to the some other suggested methods.