Evaluation of groups using cooperative game with fuzzy data envelopment analysis

Sharifeh Soofizadeh; Reza Fallahnejad; Sharifeh Soofizadeh; Reza Fallahnejad

doi:10.3934/math.2023435

AIMS Mathematics

2023, Volume 8, Issue 4: 8661-8679. doi: 10.3934/math.2023435

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Evaluation of groups using cooperative game with fuzzy data envelopment analysis

Sharifeh Soofizadeh ,
Reza Fallahnejad ^,

Department of Mathematics, Khorramabad branch, Islamic Azad University, Khorramabad, Iran

Received: 10 October 2022 Revised: 01 January 2023 Accepted: 16 January 2023 Published: 06 February 2023
MSC : 91A12, 90C08, 90C70

Data Envelopment Analysis (DEA) is a prominent technique for evaluating the performance and ranking of a set of decision-making units (DMUs) that transform multiple inputs into multiple outputs. However, one of the challenges of the primary DEA models is facing imprecise data in real practical problems. To address this issue, fuzzy DEA have been proposed, which have been successfully applied in many real fields. On the other hand, in some real-world DEA applications, the primary objective of performance evaluation is the ranking of a group that consists of several DMUs that are typically under the control of a centralized management. In this paper, we try to use the theory of cooperative games and Shapley value method as a fair method to solve such games in order to rank groups in DEA. In this way, the resulting rank for groups is based on the average marginal shares of groups in different coalitions that are formed based on the theory of cooperative games. We applied the proposed method to rank groups of airlines considering fuzzy data. To the best of authors' knowledge, so far, no method has been presented in DEA literature for ranking groups in fuzzy environment and using game theory techniques.
- data envelopment analysis,
- ranking functions,
- fuzzy sets,
- cooperative game,
- shapley value
Citation: Sharifeh Soofizadeh, Reza Fallahnejad. Evaluation of groups using cooperative game with fuzzy data envelopment analysis[J]. AIMS Mathematics, 2023, 8(4): 8661-8679. doi: 10.3934/math.2023435

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Abstract

Data Envelopment Analysis (DEA) is a prominent technique for evaluating the performance and ranking of a set of decision-making units (DMUs) that transform multiple inputs into multiple outputs. However, one of the challenges of the primary DEA models is facing imprecise data in real practical problems. To address this issue, fuzzy DEA have been proposed, which have been successfully applied in many real fields. On the other hand, in some real-world DEA applications, the primary objective of performance evaluation is the ranking of a group that consists of several DMUs that are typically under the control of a centralized management. In this paper, we try to use the theory of cooperative games and Shapley value method as a fair method to solve such games in order to rank groups in DEA. In this way, the resulting rank for groups is based on the average marginal shares of groups in different coalitions that are formed based on the theory of cooperative games. We applied the proposed method to rank groups of airlines considering fuzzy data. To the best of authors' knowledge, so far, no method has been presented in DEA literature for ranking groups in fuzzy environment and using game theory techniques.

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