Fuzzy Zero-Sum Game Multi-Objective Programming Model Based on Hybrid Variable Expert Integration Weights

Abstract:

Existing studies on fuzzy zero-sum games fail to account for variations in environmental complexity and overlook the specific process of construction payoff matrices. To address these limitations， a multi-objective programming model for solving T-spherical fuzzy zero-sum game based on hybrid variable experts integration weights is proposed in this paper， which is able to help players choose the optimal competition strategy when the total amount of resources remains relatively constant and all parties in the game pursue the maximization of their own interests. First， a novel dynamic expert integration weight calculation model， considering objective individual and subjective evaluation information simultaneously， is devised. The expert weights obtained by the above model can vary with subjective evaluation information provided by experts， which are closer to the actual practices. Then， in virtue of the weighted average method， a multi-objective programming framework for T-spherical fuzzy zero-sum game is formulated to determine the optimal mixed strategies for players， which can present the specific feasibility and divergence degree of each competitive strategy and be less impacted by the number of strategies. Finally， an illustrative example and several comparative analyses validate the reasonability and effectiveness of the proposed model. The results demonstrate that the proposed model offer higher decision-making efficiency， lower computational complexity， and reduced sensitivity to the number of alternatives. Additionally， the hybrid solution， expressed as probabilities， can effectively reflect the differences between alternatives. When the optimal strategy fails， alternative suggestions can be provided， helping to avoid redundant decision-making and minimizing resource wastage.