基于不能直接判定区间灰数大小的灰矩阵博弈的纯策略解及其风险

Pure Strategy Solution and Venture Problem of Grey Matrix Game Based on Undeterminable Directly Interval Grey Number

运用灰色系统思想和系统工程的理论,揭示了人们在灰信息条件下的博弈心理与博弈决策规则;提出了区间灰数的优势、均势和劣势的概念;证明了与某一区间灰数相对的另一区间的各种灰数势之和为1,且灰数势大小关系的集合是一个全序集。在此基础上,定义了灰数势意义下的纯策略解,且证明了这一纯策略解(或称灰势鞍点)存在的充要条件。最后,以煤价在一定范围内波动情况下的某单位冬季取暖用煤贮量的决策为例,对其灰数势意义下的纯策略解及其风险问题进行了研究。

The game psychology and decision-making rule of the players under the condition of grey information were revealed by using the grey system ideas and the systems engineering theories. The conceptions of the superiority, inferiority and equipollence position degrees of the interval grey number were defined, and it was proved that the sum of three position degrees for a certain interval grey number related to another grey number is 1, and that the relation set of the position degrees is a whole order set of the interval grey numbers. On this basis a pure strategy solution under the condition of grey number position degree was defined and the necessary and sufficient conditions for the existence of the pure strategy solution, or the grey position saddle point were derived. Taking a coal reservoir problem for a certain unit for the heating in the winter under the condition that there was a fluctuation area of the coal prices as an example, its pure strategy as solution and venture problem were studied.