摘要
基于灰色系统理论的思想和方法,探讨了决策方案的属性值为区间灰数、属性权重及各决策人的权威权重完全未知的灰色多属性群决策问题。通过分析,引入了个体理想最优方案向量、理想专家、方案间优势度和方案集中方案间优势比较矩阵等概念。根据区间灰数的本质特征,定义了两区间灰数的新的相离度,构建了基于两区间灰数相离度的灰色区间关联系数公式及灰色关联度。建立了基于投影的特征向量法和模糊互补判断矩阵排序方法的两种决策算法,给出的算法避免了权重的计算。文中实例分析说明了所提出的灰色多属性群决策方法的合理性及其算法的有效性。
Based on grey system theory, the grey attribute group decision--making problem is discussed, in which the attribute values are interval grey numbers and the attribute weights and authoritative weights are unknown. The concepts of individual imagined optimum vector, ideal expert, and predominance strength and predominance comparative matrix in the alternatives are presented by using analytical tech- nique. According to essentials of interval grey number, a new definition of deviation degree between two interval grey numbers is given, and an incidence degree coefficient formula based on deviation degree for interval grey numbers is constructed. Two algorithms that are the eigenvector method based on projection and priority method of fuzzy complementary ~udgment matrix for this grey group decision--making are presented, in which attribute weights and authoritative weights of decision--makers are unknown. These algorithms avoid the calculation of attribute weights and authoritative weights. An example shows the ra- tionality of grey attribute group decision--making method and the validity of the algorithms mentioned above.
出处
《中国管理科学》
CSSCI
2008年第5期146-152,共7页
Chinese Journal of Management Science
基金
国家自然科学基金资助项目(70473037)
关键词
区间灰数
灰色关联度
理想专家
特征向量
模糊互补判断矩阵
群决策
interval grey number
grey incidence degree
ideal expert
eigenvector
fuzzy complementary judgment matrix
eigenvector
group decision-- making
