Research on Consistency of the Complex Interval Judgement Matrix in AHP

The weighted geometric mean method(WGMM) has been the most commonly used method in the analytic hierarchy process(AHP) for combining individual opinions to form a group opinion. In this paper, we study the consistency of the WGMM in group decision and prove that the weighted geometric mean complex interval judgement matrix (WGMIM) is of acceptable consistency under the condition that all interval matrices for the same decision|making problem are of acceptable consistency. Thus, research on consistency of group decision in AHP is further developed and a theory basis for the application of the WGMM is also made.