Abstract: This paper focuses on the problem of the cooperative game with payoffs of intuitionistic fuzzy sets(IFS)and its fuzzy nucleolus. Firstly, the score function and accurate function of IFS are defined and given their the approach for ranking of IFS. The cooperative game model and its related definitions are given. The concept of the fuzzy nucleolus in fuzzy cooperative game is put forward. Secondly, according to the new ranking approach, the intuitionistic fuzzy nucleolus can be obtained by solving the bi-objective nonlinear programming model. Finally, an example is given to explain the feasibility and availability of this method.

Key words: fuzzy cooperative game, intuitionistic fuzzy sets, the core, the nucleolus

摘要： 本文主要研究支付值为直觉模糊集的合作对策问题及其模糊核仁解.首先定义了直觉模糊集的得分函数和精确函数,并给出其排序方法,得到基于直觉模糊集的合作对策模型和适合这种模型的相应定义,同时提出了直觉模糊核仁解的概念;其次运用新的排序方法将求核仁解的问题转化为求解双目标非线性规划问题;最后通过实例分析验证了该方法的可行性和有效性。

关键词: 模糊合作对策, 直觉模糊集, 核心, 核仁解