区间判断矩阵权重求解的可疑点定理及应用

针对区间判断的权重求解问题,将区间判断矩阵的样本空间映射于n(n-1)/2维向量空间,通过数学推导证明排序权重与向量的各分量之间满足一定条件下的严格单调关系,找出极值存在的可疑点,并证明了权重求解的可疑点定理。给出该定理的简单应用———可疑点组合方法求解的步骤,最后通过算例说明可疑点组合方法的可行性及优越性。

Possible point theory of interval judgment matrix and its application

In order to solve the problem of calculating the weight vector from interval judgment matrix,the sample spaces of interval judgment matrix is mapped to n(n1)/2-dimensions space.It is proved that The strict monotony relation exists between weights and the elements in the vector under some conditions.Then the possible point theory is deducted which means when the weight order gets its extremum the element of the vector equal the possible point.The theory provides a new thought to calculating the weight vector from interval judgment matrix.Also a simple application is given by calculating all combinations of the possible points is given.An example is given to show the process of the method.