Management of uncertain pairwise comparisons in AHP through probabilistic concepts

Fast and judicious decision-making is paramount for the success of many activities and processes. However, various degrees of difficulty may affect the achievement of effective and optimal solutions. Decisions should ideally meet the best trade-off among as many of the involved factors as possible, especially in the case of complex problems. Substantial cognitive and technical skills are indispensable, while not always sufficient, to carry out optimal evaluations. One of the most common causes of wrong decisions derives from uncertainty and vagueness in making forecasts or attributing judgments. The literature shows numerous efforts towards the optimization and modeling of uncertain contexts by means of probabilistic approaches. This paper proposes the use of probability theory to estimate uncertain expert judgments within the framework of the analytic hierarchy process and, more specifically, within a linearization scheme developed by the authors. After describing the necessary probabilistic concepts of interest, the main results are developed. These results can be summarized as using various kinds of random variables with uncertainty embodied in undecided pairwise comparisons. A case study focused on the maintenance management of an industrial water distribution system exemplifies the approach