An Analytic Approach for Synthesizing Comparison Matrices in AHP

摘要

In AHP, judgements of decision makers are represented by positive reciprocal matrices (pairwise comparison matrices) with ratio judgements representing the preference of a decision maker. Each decision maker's opinion is characterized by a pairwise comparison matrix in the AHP. Under group decision environment, a group comparison matrix has to be drawn from the matrices of the members of the group as the consensus of the group. In 2001, Yeh, Kerng and Lin [11] proposed a goal programming method to synthesize the pairwise comparison matrices into a consensus matrix for the group. Yeh et al. proposed a generic algorithm to find a solution approximating the objective function proposed by them. In this paper, we are going to show that their formulation can be solved analytically and the optimal solution can be easily computed.