Pairwise Comparison Matrices in Decision-Making

Pairwise comparison is any process of comparing entities in pairs to judge which of each entity is preferred, or has a greater amount of some quantitative property, or whether or not the two entities are identical. The method of pairwise comparisons is used in the scientific study of preferences, attitudes, voting systems, social choice, public choice, requirements engineering, and multi-agent artificial information (AI) systems. In psychology literature, it is often referred to as “paired comparison”. In the multi-criteria decision-making context, a pairwise comparison method is a helpful tool to determine the weighted ranking of alternatives or criteria. The entry of the preference matrix can assume different meanings: it can be a preference ratio (multiplicative case) or a preference difference (additive case), or, it belongs to the unit interval [0; 1] and measures the distance from the indifference that is expressed by 0.5 (fuzzy case). When comparing two elements, the decision-maker assigns the value from a scale to any pair of alternatives representing the element of the pairwise preference matrix. Here, we investigate particularly the relations between the transitivity and consistency of preference matrices that are understood differently with respect to the type of preference matrix. By various methods for deriving priorities from various types of preference matrices, we obtain the corresponding priority vectors for the final ranking of alternatives. Illustrative numerical examples are provided.