灰色多属性决策的模糊互补判断矩阵排序方法

以灰色系统理论的思想和方法为基础,探讨了决策方案的属性值为区间灰数的灰色多属性决策问题,提出了解决这种灰色决策问题的决策方法.根据区间灰数的本质特征,首先定义了两区间灰数的新的相离度和构建了基于相离度的灰色区间关联系数公式与灰色区间相时关联系数公式;其次通过引入方案间优势度和优势度比较矩阵概念及其计算公式,证明了方案间优势度比较矩阵为模糊互补判断矩阵,从而给出了方案的排序.实例分析说明了所提出的灰色决策方法的合理性及其算法的有效性.

Priority method of fuzzy complementary judgment matrix for grey multiple attribute decision-making

Based on grey system theory,the grey multiple attribute decision-making problem is discussed,in which the attribute values are interval grey numbers and the decision-making method for this grey decision-making is presented.Firstly,according to essentials of interval grey number,a new definition of deviation degree between two interval grey numbers is given,and the incidence degree coefficient formula and the relative incidence degree coefficient formula based on deviation degree for interval grey numbers are constructed by using analytical technique.Secondly,the concepts and formulas for predominance strength and predominance comparative matrix between alternatives are introduced,the predominance comparative matrix is proven to be a fuzzy complementary judgment matrix,and the alternative is ranked according to the priority method of fuzzy complementary judgment matrix.An example shows the rationality of grey decision-making approach and the validity of the algorithms mentioned above.