Neutrosophic Sets and Systems
Abstract
This paper addresses the challenge of measuring efficiency in systems with two components using Stackelberg game theory and neutrosophic numbers to handle data uncertainty. Unlike traditional Data Envelopment Analysis (DEA) models that treat Decision Making Units (DMUs) as black boxes, we propose a new neutrosophic Network DEA (NDEA) model to compute efficiency scores for each division. By applying Stackelberg game theory, we break down the system's efficiency scores into sub-system efficiencies, providing a more detailed assessment of performance. Our proposed model represents a significant contribution to the literature by developing a two-stage Network Slack Based Measure (NSBM) model. This model addresses conflicts arising from the dual role of intermediate measures and assumes a Stackelberg-game relationship between the two stages while ensuring continuity in the flow of links between them. Additionally, the model imposes a penalty on the follower's objective to discourage deviation from the leader's objectives, thereby enhancing feasibility robustness. To handle uncertainty within the model, we further refine it into a two-stage framework that leverages Pareto efficiency concepts to establish lower and upper bounds for DMU efficiencies. To validate our approach, we utilized data from the Iranian Airline Industry. This empirical study evaluates the efficiencies of 13 Iranian airlines, illustrating how our methodology effectively captures and quantifies operational efficiencies within uncertainty.
Recommended Citation
Tatlari, Ali Asghar; Bijan Rahmani Perchkolaei; and Farhad Hosseinzadeh Lotfi. "Innovative Efficiency Measurement Using Stackelberg Games and Neutrosophic Numbers." Neutrosophic Sets and Systems 80, 1 (2025). https://digitalrepository.unm.edu/nss_journal/vol80/iss1/22
