| The Analytic Hierarchy Process (AHP) has been proposed by T. L. Saaty during 1970s. Because valid in dealing with decision-making problems complexity qualitative and quantitative analysis, it has found its application in variety of fields. Such as sociology, economics, management, distribution of resource, transportation, urban rearrangement, behavioral science, military, agriculture, education, medical treatment, environment etc.The crucial step of multi-objective decision-making problem is to determine the judgment matrix and calculate ranking vector in the AHP. However, it's of great importance whether the given judgment matrix is consistency or not, which has direct influence on if or not the ranking vector yielded can reflect the realistic orders of the programs. Therefore, the test and modification approach on the consistency of judgment matrix is a very important aspect in the Analytic Hierarchy Process. Although some methods of test and modification on the consistency of judgment matrix have been put forward and have achieved some success. But some ways more intricate, others lack of certain theoretical basis. Thus looking for a better modification method on the consistency of judgment matrix is still significant.This paper is divided into five parts:In section one, we introduced the Analytic Hierarchy Process.In section two, we give the idea and calculation approach on the principle of AHP.In section three, the terminology consistency of judgment matrix is given. Besides we have established the relationship between ordinal consistency and full consistency.In section four, two modification methods on consistency of judgment matrix are proposed in this paper, these methods is simple but practical.Finally, as an example, we give minute analysis on the material given by China Undergraduate Mathematical Contest in Modeling B title of 1993 - football ranks, to explain the induced matrix method on consistency modification of judgment matrix and the validity and usefulness of it.
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