Study On The Consistency Between Judgment Matrices And Their Priority Vectors In AHP

The analytic hierarchy process (AHP) proposed by Saaty, received people's prevalent attentions and a great deal researches of it. 1～9 scale and consistency check are the classical contents, and priority algorithms are the soul of the analytic hierarchy process.After reviewing lots of literatures at home and abroad on AHP, this paper beginning with the basic theory and steps of AHP, then specified the study process of priority algorithms and consistency check. With the research deeply, the paper points out not only the judgment error existing in judgment matrices, but also the conflict error between the judgment matrices and priority vector, then the definition and algorithms of conflict error are proposed. Using different algorithms, we get different priority vectors, and then the conflict errors are vary. This paper applies the method of simulation statistics to the five representative priority algorithms, and then cumulates the threshold values of conflict errors via 1000 3 to 9 judgment matrices generated on random, which are the checking standard of conflict errors. Then these threshold values are compared, and the rank preservations of five priority algorithms are proved. Finally, from two demonstrations, it is proved that the consistency check of conflict error is reasonable, and the research of five priority algorithms'rank preservations is credible. The study production is further perfect the theory of the consistency check in AHP.