The Research Of Decision-making Method Based On Reciprocal Judgment Matrix

The analytic hierarchy process (AHP) is widely used in many fields. However, many theories problem haven's solved .and some approaches have many shortcomings. Therefore, new approaches should be put forward .The mainly research results are these:Firstly, we proposed a nonlinear programming model for improving the consistency of comparison matrix, by which the consistency ratio value of the modified matrix is less than that of the original one. Then a genetic simulated annealing algorithm was designed to solve the nonlinear programming model. At last we gave an algorithm to derive a positive reciprocal matrix with acceptable consistency, and then the convergence theorem for the given algorithm is established.Secondly, a method is proposed to find out the most paradoxical judgment in the pairwise comparison Matrix. By using it, the number of three-way intransitivities (the cycles of length three) will decrease to the greatest degree in every iterative. On the other hand, based on minimizing the number of adjusted judgments, we also discuss how to transform a pairwise comparison matrix to one without contradictory judgments.Thirdly, we reveal the relation between scales and the consistency of judgment matrices. Then we construct 75000 judgment matrices that are neither random nor illogical and prove that these judgment matrices can be classified into equivalents. By computing the consistency index of these judgment matrices, we give a simulation-based evaluation of several scales.Finally, it was proved that both the weighted geometric mean complex judgment and the weighted arithmetical mean complex judgment will converge in probability at impersonal priority vector if the perturbation factors in judgments that experts given is stochastic. This result is of importance to group decision.