Fuzzy cross-efficiency evaluation: a possibility approach

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• 作者：José L. Ruiz ; Inmaculada Sirvent
• 关键词：Fuzzy cross ; efficiency evaluation ; Fuzzy data envelopment analysis ; Possibility theory
• 刊名：Fuzzy Optimization and Decision Making
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：16
• 期：1
• 页码：111-126
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematical Logic and Foundations; Probability Theory and Stochastic Processes; Optimization; Calculus of Variations and Optimal Control; Optimization; Artificial Intelligence (incl. Robotics); Opera
• 出版者：Springer US
• ISSN：1573-2908
• 卷排序：16

文摘

Cross-efficiency evaluation is an extension of data envelopment analysis (DEA) aimed at ranking decision making units (DMUs) involved in a production process regarding their efficiency. As has been done with other enhancements and extensions of DEA, in this paper we propose a fuzzy approach to the cross-efficiency evaluation. Specifically, we develop a fuzzy cross-efficiency evaluation based on the possibility approach by Lertworasirikul et al. (Fuzzy Sets Syst 139:379–394, 2003a) to fuzzy DEA. Thus, a methodology for ranking DMUs is presented that may be used when data are imprecise, in particular for fuzzy inputs and outputs being normal and convex. We prove some results that allow us to define “consistent” cross-efficiencies. The ranking of DMUs for a given possibility level results from an ordering of cross-efficiency scores, which are real numbers. As in the crisp case, we also develop benevolent and aggressive fuzzy formulations in order to deal with the alternate optima for the weights.