A new ranking method to fuzzy data envelopment analysis

Due to its wide practical use, data envelopment analysis (DEA) has been adapted to many fields to deal with problems that have occurred in practice. One adaptation has been in the field of ranking decision-making units (DMUs). Most methods of ranking DMUs assume that all input and output data are exactly known, but in real life the data cannot be precisely measured. Thus this paper will carry out some researches to DEA under fuzzy environment. A fuzzy comparison of fuzzy variables is defined and the CCR model is extended to be a fuzzy DEA model based on credibility measure. In order to rank all the DMUs, a full ranking method will be given. Since the ranking method involves a fuzzy function, a fuzzy simulation is designed and embedded into the genetic algorithm to establish a hybrid intelligent algorithm. However, it is shown to be possible to avoid some of the need for dealing with these nonlinear problems by identifying conditions under which they can be replaced by linear problems. Finally we will provide a numerical example to illustrate the fuzzy DEA model and the ranking method.

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