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Characterizations of consistent pairwise comparison matrices over abelian linearly ordered groups
Author(s) -
Cavallo Bice,
D'Apuzzo Livia
Publication year - 2010
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.20438
Subject(s) - pairwise comparison , abelian group , consistency (knowledge bases) , consistency index , mathematics , matrix (chemical analysis) , discrete mathematics , combinatorics , statistics , physics , materials science , rheology , composite material , thermodynamics
We consider the framework of pairwise comparison matrices over abelian linearly ordered groups. We introduce the notion of ⊙‐proportionality that allows us to provide new characterizations of the consistency, efficient algorithms for checking the consistency and for building a consistent matrix. Moreover, we provide a new consistency index. © 2010 Wiley Periodicals, Inc.