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Mathematics > Rings and Algebras

arXiv:2108.04034 (math)
[Submitted on 4 Aug 2021 (v1), last revised 16 Jul 2022 (this version, v2)]

Title:A gradient method for inconsistency reduction of pairwise comparisons matrices

Authors:Jean-Pierre Magnot, Jiří Mazurek, Viera Čerňanová
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Abstract:We investigate an application of a mathematically robust minimization method -- the 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.
Comments: 1 figure, several corrections and precisions
Subjects: Rings and Algebras (math.RA); Numerical Analysis (math.NA); Optimization and Control (math.OC); Statistics Theory (math.ST)
MSC classes: 49M15, 90B50, 91B06
Cite as: arXiv:2108.04034 [math.RA]
  (or arXiv:2108.04034v2 [math.RA] for this version)
  https://doi.org/10.48550/arXiv.2108.04034

Submission history

From: Jean-Pierre Magnot [view email]
[v1] Wed, 4 Aug 2021 17:09:33 UTC (45 KB)
[v2] Sat, 16 Jul 2022 07:58:42 UTC (46 KB)
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