基于混合变动专家权重的模糊零和博弈多目标规划模型

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

摘要:

针对现有模糊零和博弈难以适应环境复杂度变化及忽视收益矩阵构造的不足，提出了一种基于混合动态专家集成权重确定模型的T阶球形模糊零和博弈多目标求解方法，以帮助博弈方在资源总量保持相对恒定且局中各方追求自身利益最大化的情境下选择最优竞争策略。首先，提出了一种同时考虑客观个体和主观评价信息的混合变动专家集成权重计算模型，该机制下得到的专家权重会随专家的主观评价信息而变化，更接近实际情况。其次，利用加权平均法搭建了T阶球形模糊零和博弈多目标规划模型，该方法不受策略数量的影响，且求得的最优混合策略能反映博弈各方竞争策略的具体可行性和分歧程度。最后，通过实例计算和对比分析，验证了所提出方法的实用性和优越性。结果表明，所提出的模型具有决策效率高、计算复杂度低、受方案数量影响小的特点，且得到的概率形式的混合解可以有效地反映策略间的差异程度，当最优策略失效时可提供替代建议，有助于避免重复决策，浪费决策资源。

关键词:零和博弈;T阶球形模糊集;专家可信度量表;Hausdorff距离;混合变动专家集成权重

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.

Key words:zero-sum game;T-spherical fuzzy set;expert credibility scale;Hausdorff distance;hybrid variable expert integration weights