A New Algorithm on Sequencing the Importance of Alln Alternatives to an Upper-Level Attribute in AHP

The problem of sequencing the importance degree of all n alternatives to an upper-levelattribute in terms of a given criterion scales is very important and basic in the analytic hierarchy process(AHP). It needs a given criterion scales to get a paired comparison matrix which must be consistency,then obtain the importance weight of each alternative based on the matrix. In practical applicationhowever, the paired comparison matrix is usually inconsistency. In this paper, a completely new methodis presented on sequencing the alternatives in AHP, It does not need a given criterion scales and thepaired comparison matrix and can directly obtain the importance weight of each alternative. It notonly keeps the real transitivity among the alternatives, but also keeps the relative importance betweenarbitrary near two alternatives in the ranked sequence. Finally, two illustrating examples are given.