An Algorithm of Judgment Matriz Consistency
The consistency of judgment matrix in Analytic Hierarchy Process is analyzed. By using the concepts of partial relation and chain, this paper proves that a judgment matrix is an ordinal consistent matrix if and only if its elements can be sorted as a chain under a partial order. An “Ordering algorithm has been presented to sort all elements in the order of importance to form a chain. A simple method has been proposed to examine ordinal consistency of a judgment matrix, which is based on a new operation called “Simplification on matrices. It has been shown that a judgment matrix is ordinal consistent if and only if it can be simplified into a matrix of order two. The operations of “Elementary Transformation is used to show that a judgment matrix is ordinal consistent if and only if its elements can be arranged to form a matrix B=(bij)n×n ,bij>1,j=i,r+1,...n and bij<1 for i<j , that is, all of the upper triangle elements of matrix B are bigger than one by a series of elementary transformations. Then, an efficient algorithm has been proposed to examine the ordinal consistency of a judgment matrix, which has an O(n3)time complexity. Finally, an algorithm has been designed to examine and modify the ordinal consistency of a judgment matrix.
Hongmei Liu
College of Science, Three Gorges University,Yichang, China 443002
国际会议
2009 IEEE International Conference on Grey System and Intelligent Services(2009 IEEE灰色系统与服务科学国际会议)
南京
英文
1586-1590
2009-10-20（万方平台首次上网日期，不代表论文的发表时间）