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Generalized consistency and intensity vectors for comparison matrices

✍ Scribed by L. D'Apuzzo; G. Marcarelli; M. Squillante

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
147 KB
Volume
22
Category
Article
ISSN
0884-8173

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✦ Synopsis

A crucial problem in a decision-making process is the determination of a scale of relative importance for a set X Ο­ $x 1 , x 2 , . . . , x n % 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 A Ο­ ~aij !, where a ij is a positive number expressing how much the alternative x i is preferred to the alternative x j . Under a suitable hypothesis of no indifference and transitivity over the matrix A Ο­ ~aij !, the actual qualitative ranking on the set X is achievable. Then a vector tw may represent the actual ranking at two different levels: as an ordinal evaluation vector, or as an intensity vector encoding information about the intensities of the preferences. In this article we focus on the properties of a pairwise comparison matrix A Ο­ ~aij ! linked to the existence of intensity vectors.

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