## Fuzzy efficiency measures in data envelopment analysis.(English)Zbl 0965.90025

Summary: The existing data envelopment analysis (DEA) models for measuring the relative efficiencies of a set of decision making units (DMUs) using various inputs to produce various outputs are limited to crisp data. To deal with imprecise data, the notion of fuzziness has been introduced. This paper develops a procedure to measure the efficiencies of DMUs with fuzzy observations. The basic idea is to transform a fuzzy DEA model to a family of conventional crisp DEA models by applying the $$\alpha$$-cut approach. A pair of parametric programs is formulated to describe that family of crisp DEA models, via which the membership functions of the efficiency measures are derived. Since the efficiency measures are expressed by membership functions rather than by crisp values, more information is provided for management. By extending to fuzzy environment, the DEA approach is made more powerful for applications.

### MSC:

 90B50 Management decision making, including multiple objectives 03E72 Theory of fuzzy sets, etc. 90C51 Interior-point methods
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### References:

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