A gradient method for inconsistency reduction of pairwise comparisons matrices

@article{64367,
   author = {Magnot, JeanandPierre and Mazurek, Jiří and Čerňanová, Viera},
   article_location = {USA},
   article_number = {152},
   keywords = {Gradient method; Inconsistency indicator; Pairwise comparisons; Priority vector},
   language = {eng},
   issn = {0888-613X},
   journal = {International Journal of Approximate Reasoning},
   title = {A gradient method for inconsistency reduction of pairwise comparisons matrices},
   url = {https://www.sciencedirect.com/science/article/pii/S0888613X22001645?dgcid=rss_sd_all},
   volume = {Neuveden},
   year = {2022}
}

TY  - JOUR
ID  - 64367
AU  - Magnot, Jean-Pierre - Mazurek, Jiří - Čerňanová, Viera
PY  - 2022
TI  - A gradient method for inconsistency reduction of pairwise comparisons matrices
JF  - International Journal of Approximate Reasoning
VL  - Neuveden
IS  - 152
SP  - 46-58
EP  - 46-58
SN  - 0888613X
KW  - Gradient method
KW  - Inconsistency indicator
KW  - Pairwise comparisons
KW  - Priority vector
UR  - https://www.sciencedirect.com/science/article/pii/S0888613X22001645?dgcid=rss_sd_all
N2  - We investigate an application of a mathematically robust minimization method - the gradient method - to the consistencization problem of 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 leads to non-equivalent consistencization procedures.
ER  - 

MAGNOT, Jean-Pierre, Jiří MAZUREK a Viera ČERŇANOVÁ. A gradient method for inconsistency reduction of pairwise comparisons matrices. \textit{International Journal of Approximate Reasoning}. USA, 2022, Neuveden, č.~152, s.~46-58. ISSN~0888-613X.