Complementary Judgment Matrix Method with Imprecise Information for Multicriteria Decision-Making

The complementary judgment matrix (CJM) method is an MCDA (multicriteria decision aiding) method based on pairwise comparisons. As in AHP, the decision-maker (DM) can specify his/her preferences using pairwise comparisons, both between different criteria and between different alternatives with respect to each criterion. The DM specifies his/her preferences by allocating two nonnegative comparison values so that their sum is 1. We measure and pinpoint possible inconsistency by inconsistency errors . We also compare the consistency of CJM and AHP trough simulation. Because preference judgments are always more or less imprecise or uncertain, we introduce a way to represent the uncertainty through stochastic distributions, and a computational method to treat the uncertainty. As in Stochastic Multicriteria Acceptability Analysis (SMAA), we consider different uncertainty levels: precise comparisons, imprecise comparisons with a stochastic distribution, and missing comparisons between criteria. We compute rank acceptability indices for the alternatives, describing the probability of an alternative to obtain a given rank considering the level of uncertainty and study the influence of the uncertainty on the SMAA-CJM results.