灰色风险型多属性群决策方法

Grey multi-attribute risk group decision-making method

对一类权重信息未知并且属性值为区间灰数的灰色风险型多属性群决策问题进行了探讨,提出了一种基于理想矩阵的相对优属度决策方法。首先,利用属性值为区间灰数这一特性,将灰色系统理论的思想和方法与经典风险决策方法相融合,构建了决策系统中各方案之间的关联度公式以及优化模型,合理地解决了属性权重未知问题。然后综合考虑决策者群体的主观偏好,通过构造理想矩阵,借助每一方案决策矩阵与理想矩阵、负理想矩阵的综合加权距离获得每个方案相对于理想方案的优属度,再由优属度的大小对方案的优劣进行排序。应用实例说明了所提出决策方法的合理性和算法的有效性。为解决灰色风险型决策问题提供了一种新思路。

The problem of grey multi-attribute risk group decision-making is studied, in which the attributive values are interval grey numbers and the attribute weights are unknown. Based on the ideal matrix, a relative superior membership degree method is presented. First, by use of the characteristic that the attributive value is a grey interval number, combining the thought and method of grey system theory with the classical risk decision-making method, the incidence degree formula among alternatives and the optimization model in decision- making system are constructed, and the problem of attribute weight unknownis rationally solved. Then, comprehensively considering the subjective preferences of decision-maker group, by means of the synthetically weighted distance between the alternative decision matrix and both the positive and the negative ideal matrix, the relative superior membership degree of each alternative corresponding to the ideal alternative is obtained. The alternatives are ranked by the size of the relative superior membership degree. An example illustrates the validity and efficiency of the grey multi-attribute risk group decision-making.