On Study of the Fractal Dimension of the Vector

The paper obtains approximation error limit in no cross-hierarchy through connection on the analytic hierarchy process, multivariate linear regression model and PROGRAMMING nonlinear programming. In addition, weight calculation is unified by algorithm of vector decomposition dimension and quasi orthogonal weight, calculated through corresponding to the objective value. That overcomes subjective and difficult degeneration in constructing pairwise comparison matrix in analytic hierarchy process. By computer simulation, the result obtained, using algorithm of vector decomposition dimension and quasi orthogonal weigh are better than that from the analytic hierarchy process, by 2% in terms of accuracy. Therefore, the algorithm has application and replicability.