Reconstruction methods for AHP pairwise matrices: How reliable are they?

Habitually, decision-makers are exposed to situations that require a lot of knowledge and expertise. Therefore, they need tools to help them choose the best possible alternatives. Analytic hierarchical process (AHP) is one of those tools and it is widely used in many fields. While the use of AHP is very simple, there is a situation that becomes complex: the consistency of the pairwise matrices. In order to obtain the consistent pairwise matrix from the inconsistent one, reconstruction methods can be used, but they cannot guarantee getting the right matrix according to the judgments of the decision maker. This situation does not allow proper evaluation of methods reliability, i.e. it is not possible to obtain a reliable ranking of alternatives based on an inconsistent matrix. In this work, a new way to evaluate the reliability of matrix reconstruction methods is proposed. This technique uses a novel measure for alternatives ranking comparison (based on element positions and distances), which is introduced in order to compare several matrix reconstruction methods. Finally, in order to demonstrate the extensibility of this new reliability measure, two reconstruction methods based on bio-inspired models (a Genetic Algorithm and the Firefly Algorithm) are presented and evaluated by using the aforementioned reliability measure.