Estimating priorities from relative deviations in pairwise comparison matrices

Abstract

The problem of deriving the priority vector from a pairwise comparison matrix is at the heart of multiple-criteria decision-making problems. Existing prioritization methods mostly model the inconsistency in relative preference–the ratio of two preference weights–by allowing for a small deviation, either additively or multiplicatively. In this study, we alternatively allow for a deviation in each of the two preference weights, which we refer to as the relative deviation interconnection. Under this framework, we consider both relative additive and multiplicative deviation cases and define two types of norms capturing the magnitudes of the deviations, which gives rise to four conic programming models for minimizing the norms of the deviations. Through the model structures, we analyze the signs of the deviations. This further allows us to establish the expressiveness of our framework, which covers the logarithmic least-squares method and the goal-programming method. Using numerical examples, we show that our models perform comparably against existing prioritization methods, efficiently identify unusual and false observations, and provide further suggestions for reducing inconsistency.