A gradient method for inconsistency reduction of pairwise comparisons matrices
Abstract
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.
Domains
Differential Geometry [math.DG] General Mathematics [math.GM] Metric Geometry [math.MG] Exactly Solvable and Integrable Systems [nlin.SI] Chaotic Dynamics [nlin.CD] Pattern Formation and Solitons [nlin.PS] Mathematical Physics [math-ph] Quantum Physics [quant-ph] Library and information sciences Business administration Mathematical Physics [math-ph] Operator Algebras [math.OA] Spectral Theory [math.SP] Analysis of PDEs [math.AP]
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