Judgement Matrix And Its Application,

Analytic Hierarchy Process (AHP) is a hierarchical and structural decision-making method that combines qualitative analysis with quantitative analysis. Its key step is to establish judgments matrices and get priority vectors for objects to be compairde from them. As to the methods of getting priority, it has been developed from single eigenvector method to forty priority methods by now. And many new methods are still brought forward continually. But so far there hasn't been any research conducted on the comparison of these priority methods. Therefore, the thesis chooses comparison of priority methods as research object.The thesis sums up the existing priority methods and classifies them simply into two categories: approximate algorithm and optimization algorithm. Simple methods, eigenvector method, gradient eigenvector method are regarded as approximate algorithm. Optimization algorithms are divided into deviation methods, square methods, operational research methods and especial methods. Then the thesis summarizes four approaches to establish priority methods.The main part of this thesis is the synthetical comparison and analysis of numerous priority methods. The thesis compares these priority methods from five aspects: basicl properties of priority methods, such as compatibility, permutation invariability, symmetry and harmony; the adjacencies of priority vector to reality vector; the fitness of priority vector to judgement matrix; rank preservation under the strong condition; rank preservation. Then it draws the following conclusions: CSM is the best method and EM, DLAM, DREM, GDSM, ADSM are inferior to CSM.The thesis also redefines enterprise competitiveness based on the viewpoints of many experts and scholars, and establishes the evaluation index system, and then uses AHP to compare the competitiveness of four enterprises. CSM is adopted in computation of the priority of judgments matrices.