New look at the inconsistency analysis in the pairwise-comparisons-based prioritization problems

Abstract

The main goal of the multiple-criteria decision analysis is to create a ranking of available decision-alternatives, which is conventionally achieved by estimation of their priority weights. Among the most widely used prioritization methodologies is the Analytic Hierarchy Process (AHP). The prioritization methods that are used under the AHP scheme are based upon pairwise comparison matrix (PCM) that contains the decision-makers' evaluations of the priority-weights-ratios. In praxis, these evaluations are usually erroneous and as a result, the PCM is inconsistent. Because serious inconsistency makes the data contained in the PCM useless it is important to distinguish between useful and useless PCMs. In this paper, a novel principle for the assessment of the inconsistency-indices-usefulness is introduced. It is proposed to take into account their relationship with the correctness of the final ranking of the alternatives – a crucial and natural criterion for the performance of the indices. To find the best one in this regard, various inconsistency indices (both well-known and new) are compared via simulation experiments. Next, a new PCM-acceptance method is proposed. In this method, regression models that relate the probability of incorrect-ranking occurrence to the indices values, are used to assist the decision-making process. Those models enable decision-makers to accept or reject the PCMs, based on the assessment of incorrect-ranking risk. Thus, in contrast to the procedure still supported by the classical AHP, that new approach is based on sound statistical concepts and complies with the modern risk-analysis-based uncertain-decision-making.