基于结构元方法的模糊矩阵博弈求解

Solution of matrix fuzzy game based on structuring element theory

在博弈论中,要求模糊数的序不仅要有好的分辨能力,还要满足经济人理性的假说.为此,提出了元序概念,并证明该序为全序.利用结构元相关定理,证明了m×n阶模糊矩阵必存在一m×n阶实数矩阵与其对应,且二者有相同的纳什均衡解.进而,利用结构元方法简化了模糊博弈矩阵的求解.最后,通过一个实际例子,表明了该方法的有效性.

Not only is it necessary to have a good ability to distinguish something for compared order of fuzzy number in game theory, but also meet the rational hypothesis of economic man. Therefore, in this paper, the concept of element-order is advanced, and we prove that it is the whole order, by using the relevent structured element theorem, we proved that for arbitrary fuzzy dual matrix, there have to be a real dual-matrix corresponding to it and, both have the same Nash equilibrium solution, the solving of original problem is simplified by using method of structured element. Finally, take an example to illustrate effectivity.