Generalized Consistency and Representation of Preferences by Pairwise Comparisons

A crucial problem in a decision making process is the determination of a scale of relative importance for a set X of alternatives either with respect to a criterion C or an expert E. A widely used tool in Multicriteria Decision Making is the pairwise comparison matrix constituted by positive numbers expressing how much each alternative is preferred to each other. Under suitable hypothesis of no indifference and transitivity over the matrix the actual qualitative ranking on the set X is achievable. We focus on the properties weaker than the consistency and linked to theexistence of cardinal evaluation vectors.