Invited ReviewA taxonomy and review of the fuzzy data envelopment analysis literature: Two decades in the making
Introduction
Data envelopment analysis (DEA) was first proposed by Charnes et al. (1978), and is a non-parametric method of efficiency analysis for comparing units relative to their best peers (efficient frontier). Mathematically, DEA is a linear programming-based methodology for evaluating the relative efficiency of a set of decision making units (DMUs) with multi-inputs and multi-outputs. DEA evaluates the efficiency of each DMU relative to an estimated production possibility frontier determined by all DMUs. The advantage of using DEA is that it does not require any assumption on the shape of the frontier surface and it makes no assumptions concerning the internal operations of a DMU. Since the original DEA study by Charnes et al. (1978), there has been a continuous growth in the field. As a result, a considerable amount of published research and bibliographies have appeared in the DEA literature, including those of Seiford, 1996, Gattoufi et al., 2004, Emrouznejad et al., 2008, Cook and Seiford, 2009.
The conventional DEA methods require accurate measurement of both the inputs and outputs. However, the observed values of the input and output data in real-world problems are sometimes imprecise or vague. Imprecise evaluations may be the result of unquantifiable, incomplete and non obtainable information. Some researchers have proposed various fuzzy methods for dealing with this impreciseness and ambiguity in DEA. Since the original study by Sengupta, 1992a, Sengupta, 1992b, there has been a continuous interest and increased development in fuzzy DEA literature. In this study, we review the fuzzy DEA methods and present a taxonomy by classifying the fuzzy DEA papers published over the past two decades into four primary categories, namely, the tolerance approach, the α-level based approach, the fuzzy ranking approach, and the possibility approach; and a secondary category to group the pioneering papers that do not fall into the four primary classifications. This study appears to be the only review and complete source of references on fuzzy DEA since its inception two decades ago. This paper is organized into five sections. In Section 2, we present the fundamentals of DEA. In Section 3, we review the fuzzy DEA principles. In Section 4, we present a summary development of the fuzzy DEA followed by a detailed description of the fuzzy DEA methods in the literature. Conclusions and future research directions are drawn in Section 5.
Section snippets
The fundamentals of DEA
There are basically two main types of DEA models: a constant returns-to-scale (CRS) or CCR model that initially introduced by Charnes et al. (1978) and a variable returns-to-scale (VRS) or BCC model that later developed by Banker et al. (1984). The BCC model is one of the extensions of the CCR model where the efficient frontiers set is represented by a convex curve passing through all efficient DMUs.
DEA can be either input- or output-orientated. In the first case, the DEA method defines the
The fuzzy DEA principles
The observed values in real-world problems are often imprecise or vague. Imprecise or vague data may be the result of unquantifiable, incomplete and non obtainable information. Imprecise or vague data is often expressed with bounded intervals, ordinal (rank order) data or fuzzy numbers. In recent years, many researchers have formulated fuzzy DEA models to deal with situations where some of the input and output data are imprecise or vague.
The fuzzy DEA methods
The applications of fuzzy set theory in DEA are usually categorized into four groups (Lertworasirikul et al., 2003a, Lertworasirikul et al., 2003b, Lertworasirikul, 2002, Karsak, 2008): (1) The tolerance approach. (2) The α-level based approach. (3) The fuzzy ranking approach. (4) The possibility approach.
In this section, we provide a mathematical description of each approach followed by a brief review of the most widely cited literature relevant to each of the four approaches. In addition to
Conclusions, limitations and directions for future research
There are relatively a large number of papers in the fuzzy DEA literature. Fuzzy sets theory has been used widely to model uncertainty in DEA. Although other models such as probabilistic/stochastic DEA and statistical preference (e.g., bootstrapping) are also used to model uncertainty in DEA, in this paper we focus on the fuzzy sets DEA papers published in the English-language academic journals. The applications of fuzzy sets theory in DEA are usually categorized into four groups: the tolerance
Acknowledgement
The authors thank the anonymous reviewers and Professor Robert G. Dyson, the editor of EJOR, for their insightful comments and suggestions.
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