多冲突环境下混合模糊双矩阵对策的集结

Integration of mixed fuzzy bimatrix games in multi-conflict conditions

针对策略集模糊与具有模糊支付值的多冲突环境,建立了混合模糊双矩阵对策的综合集结模型。基于局中人的约束条件,构造局中人面向多冲突环境的可行策略串集合,建立新的结局空间;在假定模糊支付值为三角模糊数的情形下,基于模糊数的运算,构造局中人在新结局空间上的合成结局模糊支付值,建立多冲突环境下的混合模糊双矩阵对策综合集结模型,将集结模型清晰化并求解。最后,给出军事想定实例,说明了模型的实用性及有效性。

Aiming at the uncertain multi-conflict conditions with fuzzy strategy sets and fuzzy payoffs,the synthetic aggregation model of mixed fuzzy bimatrix games was established.Based on the constraints,the feasible strategy string sets of the players for multi-conflict conditions were constructed,and a new outcome space was established;by the operations of fuzzy numbers,the synthetic outcome fuzzy payoffs were obtained while fuzzy payoffs were triangular fuzzy numbers,and then the synthetic aggregation model of mixed fuzzy bimatrix games in multi-conflict conditions was established.The aggregation model can be used for solution by transforming it into a clear bimatrix game.Finally,a military example was provided for illustrating the practicality and affectivity of the model.