2021/08/04 by Magnot, Jean-Pierre, Mazurek, Jiří, Čerňanová, Viera · 1 citation
#49M15 #90B50 #91B06 #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Rings and Algebras (math.RA) #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.2108.04034
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.