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A gradient method for inconsistency reduction of pairwise comparisons matrices
Jean-Pierre Magnot, Jiří Mazurek, Viera Čerňanová · 2021-08-05 · via math.ST updates on arXiv.org

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.

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