Affiliations: [a] Computer Science, Laurentian University, Sudbury, Ontario P3E 2C6, Canada. wkoczkodaj@cs.laurentian.ca | [b] Institute of Mathematics and Cryptology, Faculty of Cybernetics, Military University of Technology, ul. Kaliskiego 2, 00-908 Warsaw, Poland. ryszard.smarzewski@gmail.com | [c] AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Krakow, Poland. szybowsk@agh.edu.pl
Correspondence:
[†]
Address for correspondence: AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Krakow, Poland.
Note: [*] Supported by the National Science Centre, Poland as a part of the project no. 2017/25/B/HS4/01617, and by the Faculty of Applied Mathematics of AGH UST within the tasks subsidized by the Polish Ministry of Science and Higher Education, grant no. 16.16.420.054.
Abstract: In this study, the orthogonalization process for different inner products is applied to pairwise comparisons. Properties of consistent approximations of a given inconsistent pairwise comparisons matrix are examined. A method of a derivation of a priority vector induced by a pairwise comparison matrix for a given inner product has been introduced. The mathematical elegance of orthogonalization and its universal use in most applied sciences has been the motivating factor for this study. However, the finding of this study that approximations depend on the inner product assumed, is of considerable importance.
