Fuzzy Efficiency Decomposition in Two–Stage Systems: A New Slack-Based Measure Approach

Subject Areas : International Journal of Mathematical Modelling & Computations

Manoochehr Ziyae Berentin ¹ , Ghasem Tohidi ² , Shabnam Razavyan ^{3 *} , Mahnaz Barkhordari Ahmadi ⁴

1 - Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran.
2 - Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran.
3 - Department of Mathematics, South Tehran Branch, Islamic Azad University, Tehran, Iran.
4 - Department of Mathematics, Bandarabbas Branch, Islamic Azad University, Bandarabbas, Iran.

Received: 2024-09-30 Accepted : 2024-12-01 Published : 2024-12-25

Keywords: Data envelopment analysis, Efficiency, Two stage system, Triangular fuzzy number, Slack Based Measure.,

Abstract :

Data envelopment analysis (DEA) is a non-parametric tool for evaluating the relative efficiency of comparable entities referred to as Decision Making Units (DMUs). Conventional DEA models treat systems as black box and do not consider their internal structure. Network data envelopment analysis (NDEA) is a prominent method for assessing the efficiency of network systems based on radial and non-radial approaches. The special case of network systems are two-stage systems. Many real practices have two-stage structure where is divided into two processes. Conventional NDEA calculates the efficiency of these systems in presence of crisp data. But in real life applications, the observed values of data are often uncertain. In this paper, for the first time, a new non-radial approach (based on slack based measure) is introduced, which evaluates the efficiency of two-stage systems in the presence of triangular fuzzy numbers(TFNs) using cut technique and optimistic and pessimistic procedures. The properties of the suggested models will also be examined. Finally, a numerical example will be provided to illustrate the proposed models.