One Improved Method for Analytic Hierarchy Process Based on Least Deviation Method and Particle Swarm Optimization

Much research of theory and application has been done on analytic hierarchy process after it was proposed. But the pair-wise comparison matrix with interval numbers has not been studied very well. In this paper, the indefinite circumstances that exist in the process of decision-making are considered. Therefore, interval numbers are adopted to replace the precise numbers of the judgment matrix when analytic hierarchy process is used. The least deviation method is adopted to calculate the weights of elements according to the interval matrix, which is solved by the particle swarm optimization in order to find the optimal solution. At the same time, the consistency of the matrix is considered. If the consistency of a precise matrix is not acceptable, then the interval matrix based on the precise matrix can solve this problem. The examples are well illustrated this case and the optimal solution is found Anally. As a result, this paper provides one kind of new thought to deal with the interval matrices.