鉴于实际对策问题中, 灰信息是普 遍存在的, 但经典合作对策中未能考虑对策过程中出 现的灰色不确定性, 使得对策模型缺乏柔性. 基于合 作对策理论和灰集相关理论的思想, 文章建立了一种新 的包含有区间灰数的合作对策模型— 灰色合作对策, 研究了其核仁解. 首先定义了灰色集的核函数和灰度函数, 在此基础上给出其排序方法, 得到适合此模型的相应定义, 同时提出了灰色核仁解的概念; 其次运用新的排序方法, 将求核仁解的问题转化为求解非线性规划问题; 最后进一步探讨了灰色合作对策核仁的存在唯一性, 以及核仁与其他解之间的关系. 从而解决了灰色合作对策的解的结构问题.

The grey information is universal in the actual game. But the classical cooperative game failed to consider the grey uncertainty in the process of the game, which makes the game model lacks flexibility. A new cooperative game model contains interval grey numbers-grey cooperative game is established based on the idea of cooperative game theory and the related theory of grey sets in this paper. And the nucleolus solution is studied. Firstly, the concepts of kernel function and degree of greyness function of grey sets are proposed. Based on these concepts, the ranking method is presented. Then the corresponding definitions for this model are get. The concept of grey nucleolus solution is put forward at the same time. Secondly, the problem of nucleolus solution can be converted to solving nonlinear programming problem by using the new ranking method. Finally, the existence and uniqueness of nucleolus of grey cooperative game are further discussed, as well as the relationship between the nucleolus and other solution. Thus, the problem of the solution structure of grey cooperative game is solved.