基于Z球型犹豫模糊语言的矩阵博弈方法  

Matrix Game Method Based on Z-Spherical Hesitant Fuzzy Linguistic

作　　者：陈黄山 杨志辉 

机构地区：[1]东华理工大学理学院,江西 南昌 收稿日期:2024年6月17日 [2]录用日期:2024年7月11日 [3]发布日期:2024年7月19日

出　　处：《应用数学进展》2024年第7期3281-3300,共20页Advances in Applied Mathematics

摘　　要：本文从决策者和自然方的角度提出一种用于解决多属性决策问题的矩阵博弈方法。首先结合Z-number和球型犹豫模糊集,定义Z球型犹豫模糊集。其次提出有利于决策问题中信息聚合的Z球型犹豫模糊Einstein有序加权平均算子。然后,考虑到矩阵博弈中信息表达问题包含了决策者判断的模糊性、随机性和犹豫性,将Z球型犹豫模糊集运用到矩阵博弈,表示决策者的支付值,同时为了获得具有决策者偏好的最优策略,建立了两个具有多目标函数的非线性数学规划模型,并应用加权平均法将其转化为经典的线性规划模型。随后,依据最优策略下决策者期望支付的相对相似度对备选方案择优排序。最后,将本文所提方法应用于鄱阳湖国家级自然保护区制定经济战略时方案重要性排序中,并与文献方法对比分析,验证该方法的有效性、灵活性和优越性。In this paper, a matrix game method for solving multiple attribute decision making problems is proposed from the perspective of decision maker and natural party. Firstly, the Z-spherical hesitant fuzzy set is defined by combining Z-number and spherical hesitant fuzzy set. Secondly, a Z-spherical hesitant fuzzy Einstein ordered weighted average operator is proposed, which is beneficial to information aggregation in decision-making problems. Then, considering that the information expression problem in the matrix game contains the fuzziness, randomness and hesitation of the decision maker’s judgment, the Z-sphere hesitant fuzzy set is applied to the matrix game to represent the payoff value of the decision maker. At the same time, in order to obtain the optimal strategy with the decision maker’s preference, a Z-sphere hesitant fuzzy non-linear programming model is constructed. Subsequently, the alternatives are ranked according to the relative similarity of the expected payment of the decision maker under the optimal strategy. Finally, the proposed method is applied to the plan importance ranking of Poyang Lake National Nature Reserve, and compared with the literature method, the effectiveness, flexibility and superiority of the method are verified.

关 键 词：矩阵博弈 Z球型犹豫模糊集 Z球型犹豫模糊非性规划模型 相对相似度 

分 类 号：G63[文化科学—教育学]