一致性区间数判断矩阵的性质及排序

讨论了具有序传递性的区间数判断矩阵的性质,给出了一致性区间数判断矩阵具有序传递性的一个充要条件.在此基础上,证明了一致性区间效判断矩阵的权值可行域中所有向量的分量在不劣于的次序关系下具有完全相同的排列次序.因此,用权值可行域的顶点的算术平均或几何平均作为一致性区间数判断矩阵的排序向量是合理的.

On the Properties and Priority Method of a Consistent Interval Comparison Matrix

We discuss the properties of an interval judgment matrix with transitivity and propose a sufficient and necessary condition that a consistent interval judgment matrix is of transitivity.On the base of these theory,we prove that any vector in the feasible region of the priority weights on the consistent interval judgment matrix,exhibit the same rank order in the sense of the ith alternative not being inferior to the jth alternative.Thus, it is a simple and reasonable priority method using the arithmetic mean or geometric mean of all the vertices of the feasible region to generate the priority weights of a consistent interval judgment matrix.