Z-number fuzzy cognitive maps for environmental pollution efficiency evaluation based on a bargaining game

Wenting Xue, Zijin Lin, Weihua Su and Chonghui Zhang

Journal of the Operational Research Society, 2025, vol. 76, issue 12, 2431-2451

Abstract: The existing methods for environmental pollution efficiency evaluation usually fail to capture the influence of pollution diffusion among adjacent regions, leading to inaccuracies of the evaluation results. The Z-number is a powerful technique for describing both the extent of pollution diffusion and the reliability of the evaluation. In the paper, we propose Z-number Fuzzy Cognitive Maps Based on a Bargaining Game (Z-FCM-BG) method to investigate the impact of the pollution diffusion on the alternatives. According to the operations of Z-numbers, fuzzy cognitive maps under the Z-number framework are employed to address the complex causal relationships. While traditional FCMs highlight the overall characteristics and behavior of the system, they often overlook the value of concepts. The Z-FCM-BG method incorporates Nash Product Equilibrium (NPE) and the logic of the bargaining game. The average of NPEs for each pair of alternatives with causal relationships serves as a fitness function when solving the Z-FCM-BG model by the multi-objective particle swarm optimization algorithm. A case study is presented on environmental pollution efficiency evaluation for 11 provinces and municipalities in the Yangtze River Economic Belt. Finally, the comparative analysis is conducted to validate the effectiveness and rationality of the proposed method.

Date: 2025
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DOI: 10.1080/01605682.2025.2476064

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