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The Analytic Hierarchy Process(AHP), which was introduced by Saaty in 1970s, is a systematized, hierarchical and fairly practical multi-attribute decision making method, it is combined with qualitative analysis and quantitative analysis. As an useful tool of multi-attribute decision making, the AHP has been applied to many areas, such as politics, economy, military, business management and so on. This thesis mainly includes the following several aspects:Firstly, based on the logical relation between the elements and the weights of fuzzy complementary comparison matrix with a parameter, the weights’ relations between two different parameters are obtained. As long as solving the weights whenθ=e, the weights of other parameters can be received by the proposed relations.Secondly, through the mutual transformation between real (interval) reciprocal comparison matrix and supplementary comparison matrix, as well as the research of interval weights’relations between two kinds of comparison matrices. The interval weights of the multiplicative consistent interval supplementary comparison matrix can be obtained by solving the consistent interval comparison matrix use the mathematics ideology of "naturalization", and the steps of generating interval weights from the multiplicative consistent interval complementary comparison matrix are summarized.Finally, an algorithm is proposed based on the definition of additive consistency of interval supplementary comparison matrix. According to the algorithm, the consistent information of the interval supplementary comparison matrix can be collected to a column, and based on the column, the interval weights of the interval supplementary compariosn matrix can be obtained by establishing mathematical models.
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