Pairwise comparisons matrix decomposition into approximation and orthogonal component using Lie theory

Autor:	Yusuf Yayli, Victor W. Marek, Waldemar W. Koczkodaj
Rok vydání:	2021
Předmět:	Pure mathematics Applied Mathematics Lie group Theoretical Computer Science Matrix decomposition Artificial Intelligence Product (mathematics) Lie algebra Decomposition method (queueing theory) Hadamard product Pairwise comparison Lie theory Software Mathematics
Zdroj:	International Journal of Approximate Reasoning. 139:201-210
ISSN:	0888-613X
DOI:	10.1016/j.ijar.2021.09.009
Popis:	This paper examines the use of Lie group and Lie Algebra theory to construct the geometry of pairwise comparisons matrices. The Hadamard product (also known as coordinatewise, coordinate-wise, elementwise, or element-wise product) is analyzed in the context of inconsistency and inaccuracy by the decomposition method. The two designed components are the approximation and orthogonal components. The decomposition constitutes the theoretical foundation for the multiplicative pairwise comparisons.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::ead33a1c94f6f498e78d776a6ec69f3a https://doi.org/10.1016/j.ijar.2021.09.009 Zobrazit plný text záznamu Full Text from ScienceDirect