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 cross-efficiencies 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. © 2014 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Sirvent, I., & León, T. (2014). Cross-efficiency in fuzzy data envelopment analysis (FDEA): Some proposals. Studies in Fuzziness and Soft Computing, 309, 101–116. https://doi.org/10.1007/978-3-642-41372-8_5
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