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A numerical tool for multiattribute ranking problems
Author(s) -
Cardoso Domingos Moreira,
de Sousa Jorge Freire
Publication year - 2003
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.10074
Subject(s) - pairwise comparison , ranking (information retrieval) , binary relation , extension (predicate logic) , mathematics , preference , set (abstract data type) , relation (database) , preference relation , mathematical optimization , variety (cybernetics) , order (exchange) , computer science , artificial intelligence , data mining , discrete mathematics , statistics , economics , programming language , finance
A large variety of techniques have been developed to solve or approximate the solution of multiattribute ranking problems. From such techniques, several implicit or explicit partial orders, defined on the same set of alternatives, are obtained (in many cases, by pairwise comparisons) with the goal of determining a linear order. Often, this goal is attained by assigning positive weights to each partial order relation. However, the imprecise judgments of the pairwise comparisons as well as other factors lead to inconsistencies which have been analyzed in an extensive literature devoted to this type of problem. In this paper, numerical results about linear extensions of weighted sum relations are applied to the recognition of pairwise imprecise judgments between alternatives as well as to the confirmation of a ranking solution as a linear extension of a quasi‐order defined by a weighted sum of binary preference relations. © 2003 Wiley Periodicals, Inc.