The Research On Ranking Method And Rank Preservation In The Analytic Hierarchy Process

The analytic hierarchy process (AHP) is a scientific decision making, which is hierarchical, structured, qualitative and quantitative. Now, AHP is applied in management decisions, system analysis and many other aspects widely. With the application field expanding, its theory has gradually improved also, but there are still some issues that need to be resolved. Therefore, this thesis discusses and researches the ranking method and rank preservation in AHP.1. Ranking method research. In the study of ranking method of AHP, this thesis considering the judgments have different credibility degrees when the expert doing the pairwise comparison judgment. First of all, two kinds of situations from the subjective and objective are considered so that they can analyze the credibility degrees' weight. Then, the ranking method based on judgment credibility degree is proposed. In the enrichment of FAHP ranking theory, this thesis introducing the relative entropy theory to construct some optimization models, and then complementary judgment matrix ranking method based on relative entropy is proposed. At the same time, the rationality of proposed method is analyzed and its properties are discussed.2. Rank preservation research. This part discusses the strong rank preserva- tion conditions of multiplicative relative entropy ranking method when the elements are increased at first. Then, according to the problem of different ranking methods could derive different sorts, this thesis using the language comparison matrix constructs the media conversion of reciprocal judgment matrix, additive complementary judgment matrix and multiplicative complementary judgment matrix, so that it can research the rank preservation of different ranking method, and the general structure of different ranking formulas for rank preservation are obtained.The first feature of ranking method research in this thesis is the different judgment credibility degree to be considered in alternatives sort, the second is the relative entropy will be introduced into the ranking of complementary judgment matrix. And on the rank preservation research, the thesis is mainly to discuss rank preservation of different ranking methods.