A Fuzzy Approach to Support Evaluation of Fuzzy Cross Efficiency

Abstract

Cross-efficiency evaluation effectively distinguishes a set of decision-making units (DMUs) via self- and peer-evaluations. In constant returns to scale, this evaluation technique is usually applied for data envelopment analysis (DEA) models because negative efficiencies will not occur in this case. For situations of variable returns to scale, the negative cross-efficiencies may occur in this evaluation method. In the real world, the observations could be uncertain and difficult to measure precisely. The existing fuzzy cross-evaluation methods are restricted to production technologies with constant returns to scale. Generally, symmetry is a fundamental characteristic of binary relations used when modeling optimization problems. Additionally, the notion of symmetry appeared in many studies about uncertain theories employed in DEA problems, and this approach can be considered an engineering tool for supporting decision-making. This paper proposes a fuzzy cross-efficiency evaluation model with fuzzy observations under variable returns to scale. Since all possible weights of all DMUs are considered, a choice of weights is not required. Most importantly, negative cross-efficiencies are not produced. An example shows that this paper’s fuzzy cross-efficiency evaluation method has discriminative power in ranking the DMUs when observations are fuzzy numbers.

Input/Output Variables Selection in Data Envelopment Analysis: A Shannon Entropy Approach

“…Notably, the main limitation of the study is that the proposed DEASE approach is not capable to be used under data uncertainty. Accordingly, for future research, the DEASE approach can be proposed under uncertain data, including fuzzy [76][77][78][79][80][81][82][83][84][85][86][87][88][89][90], stochastic [91][92][93][94][95][96][97][98][99][100][101][102], and interval [103][104][105][106][107][108][109][110][111][112][113] data. Additionally, the DEASE approach can be combined with machine learning approaches for the prediction of input and output data, and consequently, evaluation of the future performance of DMUs [114][115][116][117][118][119][120][121][122]…”

Fuzzy Order Acceptance and Scheduling on Identical Parallel Machines

“…In general, symmetry is a fundamental property of optimization models used to represent binary relations such as the FOASIPM problem [3]. In addition, there are many classifications of Fuzzy Linear Programming (FLP).…”