On Orthogonal Projections on the Space of Consistent Pairwise Comparisons Matrices

• Autorzy: Koczkodaj Waldemar W. , Smarzewski Ryszard , Szybowski Jacek

Identyfikatory

DOI

10.3233/FI-2020-1910

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

approximation; inconsistency; inner product; orthogonal basis; pairwise comparisons

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2020
• Tom: Vol. 172, nr 4
• Strony: 379--397
• Opis fizyczny: Bibliogr. 23 poz.

Twórcy

autor

Koczkodaj Waldemar W.

• Computer Science, Laurentian University, Sudbury, Ontario P3E 2C6, Canada

autor

Smarzewski Ryszard

• Institute of Mathematics and Cryptology, Faculty of Cybernetics, Military University of Technology, ul. Kaliskiego 2, 00-908 Warsaw, Poland

autor

Szybowski Jacek

• AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Krakow, Poland

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).