A gradient method for inconsistency reduction of pairwise comparisons matrices

Jean-Pierre Magnot (1) , Jiří Mazurek , Viera Cernanova (2)

1 LAREMA - Laboratoire Angevin de Recherche en Mathématiques
2 Trnava University

We investigate an application of a mathematically robust minimization methodthe gradient method-to the consistencization problem of a pairwise comparisons (PC) matrix. Our approach sheds new light on the notion of a priority vector and leads naturally to the definition of instant priority vectors. We describe a sample family of inconsistency indicators based on various ways of taking an average value, which extends the inconsistency indicator based on the "sup"-norm. We apply this family of inconsistency indicators both for additive and multiplicative PC matrices to show that the choice of various inconsistency indicators lead to non-equivalent consistencization procedures.

Mots clés: gradient method; inconsistency indicator; pairwise comparisons; priority vector

Domaines: Géométrie différentielle [math.DG]; Mathématiques générales [math.GM]; Géométrie métrique [math.MG]; Systèmes Solubles et Intégrables [nlin.SI]; Dynamique Chaotique [nlin.CD]; Formation de Structures et Solitons [nlin.PS]; Physique mathématique [math-ph]; Physique Quantique [quant-ph]; Sciences de l'information et de la communication; Gestion et management; Physique mathématique [math-ph]; Algèbres d'opérateurs [math.OA]; Théorie spectrale [math.SP]; Equations aux dérivées partielles [math.AP]

Jean-Pierre Magnot, Jiří Mazurek, Viera Cernanova. A gradient method for inconsistency reduction of pairwise comparisons matrices. 2021. ⟨hal-03313878⟩