Affiliations: [a] Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran
| [b] Department of Mathematics, Zahedan Branch, Islamic Azad University, Zahedan, Iran
| [c] Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
| [d] Department of Mathematics, South Tehran Branch, Islamic Azad University, Tehran, Iran
Correspondence:
[*]
Corresponding author. Masoud Sanei, Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran. E-mail: masoudsanei49@yahoo.com.
Abstract: In this paper, crisp two-stage data envelopment analysis (TSDEA) models are expanded for decision-making problems where inputs, intermediate data, and outputs are expressed with fuzzy numbers. Considering the merits of credibility theory, we propose the use of this theory in the efficiency measurement of fuzzy serially-connected two-stage systems. For determined credibility levels, we transform the fuzzy model into a linear programming problem and then obtain the credibility function and membership function for fuzzy efficiency of two-stage decision-making units (DMUs). We also explore the sensitivity and stability analysis of two-stage DMUs based on the proposed methodology. As a result, the projection of inefficient fuzzy two-stage DMUs and the stability radius of efficient fuzzy two-stage DMUs, i.e. the region in which efficiency status is preserved, are also determined. We also provide an illustrative example to better explain the method and demonstrate its performance in comparison with other developed methods for fuzzy TSDEA.
Keywords: Two-stage data envelopment analysis, fuzzy input- intermediate -output data, credibility measure, sensitivity and stability analysis
