An inequality approach for evaluating decision making units with a fuzzy output¹

Article type: Research Article

Authors: Meng, Xiao-Li^{a; b} | Shi, Fu-Gui^{a; b; *} | Yao, Jen-Chih^{c; d}

Affiliations: [a] School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, P.R. China | [b] Beijing Key Laboratory on MCAACI, Beijing Institute of Technology, Beijing, P.R. China | [c] Center for General Education, China Medical University, Taichung, Taiwan | [d] Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung, Taiwan

Correspondence: [*] Corresponding author. Fu-Gui Shi. E-mail: fuguishi@bit.edu.cn.

Note: [1] The work is supported by the National Natural Science Foundation of China (11371002) and Specialized Research Fund for the Doctoral Program of Higher Education (20131101110048).

Abstract: In this paper, a fuzzy evaluation approach is developed to evaluate the efficiency of decision making units (DMUs) with a fuzzy output. In the approach, the production possibility set is spanned by all the DMUs except the DMU under evaluation, and expressed in terms of fuzzy inequalities. In addition, the line segment joining the origin to the evaluated DMU is employed in the proposed approach, and its mathematical expression is expressed by fuzzy inequality. Fuzzy efficiency of the evaluated DMU is dependent upon the number of solutions of fuzzy inequalities, and the fuzzy inequalities consist of inequalities of the production possibility set and the line segment. Moreover, the partially ordered set and maximal element are introduced to distinguish the weak efficiency and efficiency. Finally, the use of the fuzzy approach is illustrated by means of an example.

Keywords: Fuzzy evaluation, inequality approach, data envelopment analysis, decision making unit, maximal element

DOI: 10.3233/JIFS-17267

Journal: Journal of Intelligent & Fuzzy Systems, vol. 34, no. 1, pp. 459-465, 2018