Cross-Efficiency in Fuzzy Data Envelopment Analysis (FDEA): Some Proposals
Different techniques have been proposed in the literature to rank decision making units (DMUs) in the context of Fuzzy Data Envelopment Analysis. In our opinion, those that result from using a ranking method to order the fuzzy efficiencies obtained are su
- PDF / 526,229 Bytes
- 16 Pages / 439.37 x 666.142 pts Page_size
- 55 Downloads / 247 Views
Cross-Efficiency in Fuzzy Data Envelopment Analysis (FDEA): Some Proposals Inmaculada Sirvent and Teresa León
Abstract Different techniques have been proposed in the literature to rank decision making units (DMUs) in the context of Fuzzy Data Envelopment Analysis. In our opinion, those that result from using a ranking method to order the fuzzy efficiencies obtained are susceptible to a serious criticism: they are not based on objective criteria. Cross-efficiency evaluation was introduced as an extension of DEA aimed at ranking the DMUs. This methodology has found a significant number of applications and has been extensively investigated. In this chapter, we discuss some difficulties that arise with the definition of fuzzy cross-efficiencies and we propose a fuzzy cross-efficiency evaluation based on the FDEA model by Guo and Tanaka. Such model relies on the dual multiplier formulation of the CCR model and the fuzzy efficiency of a given DMU is defined in a ratio form in terms of the input and output weights obtained. This allows us to define the crossefficiencies in an analogous manner to that of the fuzzy efficiency. The resulting cross-efficiencies are consistent in the sense that the cross-efficiency of a given DMU, calculated with its own input and output weights, is equal to the relative efficiency of this unit. We illustrate our methodology with an example. Keywords Data envelopment analysis Cross-efficiency Ordering
Fuzzy mathematical programming
I. Sirvent Centro de Investigación Operativa, Universidad Miguel Hernández, Alicante, Spain T. León (&) Departament de Estadística e Investigación Operativa, Universitat de Valencia, Valencia, Spain e-mail: [email protected]
A. Emrouznejad and M. Tavana (eds.), Performance Measurement with Fuzzy Data Envelopment Analysis, Studies in Fuzziness and Soft Computing 309, DOI: 10.1007/978-3-642-41372-8_5, Springer-Verlag Berlin Heidelberg 2014
101
102
I. Sirvent and T. León
1 Introduction Data Envelopment Analysis (DEA), as introduced in Charnes et al. [1], is a methodology for the assessment of relative efficiency of a set of decision making units (DMUs) that use several inputs to produce several outputs. For each DMU, it provides efficiency scores in the form of a ratio of a weighted sum of the outputs to a weighted sum of the inputs. DEA results classify DMUs into two groups, those that are efficient and define the Pareto frontier and those that are inefficient. However, in many practical applications decision makers are interested in a ranking beyond this classification. Many authors claim that we should not derive an ordering of the units based on the efficiency scores since these scores are not comparable as a result of the fact that the different DMUs attach different weights to the inputs and outputs when being evaluated. Thus, different techniques have been proposed in the literature to rank DMUs in the context of DEA (see Adler et al. [2] for a review of these methods). One such method that has found a significant number of applications and h
Data Loading...
