正互反矩阵一致性的一个充要条件

A Necessary and Sufficient Condition on the Consistency of Positive Reciprocal Matrices

层次分析法是一种实用的多维决策方法。在这种分析法中将一个复杂的无结构问题按照属性的不同把它的元素分成若干组,形成互不相交的层次。

The analytical hierarchy process is a practical multidimensional decision method.Based on this method, the elements of a complex and unstructured problem are,according to their different properties,divided into a few groups which form non—intersecting hierarchy.The elements of the above hierarchy govern all or some of the elements of the next.The hierarchy which has these properties is called ascending hierarchy.The inner relationship of the ascending hierarchy is quite comlex.The hierarchy structures of the decision factors are often expressed in terms of matrices,and one of these matrices is just positive reciprocal matrix.In this pa- per,a necessary and sufficient condition on the consistency of positive reciprocal matrices is given.