Efficiency score in the presence of flexible factors, integer and fuzzy integer data

Subject Areas : International Journal of Industrial Mathematics

Zahra Moazenzadeh ¹ , Saber Saati ² , reza farzipoor saen ³ , Reza Kazemi Matin ⁴ , sevan sohraiee ⁵

1 - Mathematics Department, Tehran-North Branch, Islamic Azad University, Tehran, Iran
2 - Dep. of Mathematics, North Tehran Branch, Islamic Azad University, Tehran, IRAN
3 - Faculty of Business, Sohar University, Sohar, Oman
4 - Islamic Azad University of karaj
5 - استادیار

Received: 2024-04-28 Accepted : 2024-09-07 Published : 2024-09-21

Keywords: : Data Envelopment Analysis, Efficiency, Slack-Based Efficiency Measure Model, Flexible Factor, Fuzzy Integer Data, Integer Data.,

Abstract :

In traditional Data Envelopment Analysis (DEA) approaches, inputs and outputs are usually considered as exact and real values. The relative efficiency of the Decision Making Units (DMUs) is evaluated and it is known that the factors are inputs and/or outputs. However, there are some conditions under which the efficiency of DMUs should be calculated while the data are integer and ambiguous. Therefore, various integer DEA models have been proposed to determine the performance of DMUs when integer data and fuzzy factors are available. In addition, there are cases where the efficiency of DMUs should be determined when integer data and flexible factors are available. Therefore, some integer DEA methods have been proposed to calculate the performance of DMUs and specify the role of flexible measures when some of the data are integer and flexible factors are available. However, there are some situations where there are integer data, fuzzy integer measures and flexible factors. Therefore, this paper sheds light on the nature of the model to determine the efficiency of DMUs when there are integer inputs and/or outputs, flexible factors and fuzzy integer measures, and determines the role of factors with uncertain inputs or outputs. In fact, slacks are addressed and a slack-based efficiency measure (SBM) is defined to compute the performance of DMUs in the presence of flexible factors, integer data and fuzzy integer measures. The proposed approaches are demonstrated and illustrated using an example.

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