Coherent weights for pairwise comparison matrices and a mixed-integer linear programming problem

Pairwise comparison matrices (PCMs) have been a long standing technique for comparing alternatives/criteria and their role has been pivotal in the development of modern decision making methods. In order to obtain general results, suitable for several kinds of PCMs proposed in the literature, we focu...

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Bibliographic Details
Published in:Journal of global optimization Vol. 75; no. 1; pp. 143 - 161
Main Author: Cavallo, Bice
Format: Journal Article
Language:English
Published: New York Springer US 01.09.2019
Springer
Springer Nature B.V
Subjects:
Coherence
Comparative analysis
Computer Science
Decision analysis
Decision making
Integer programming
Isomorphism
Linear programming
Mathematical analysis
Mathematical programming
Mathematics
Mathematics and Statistics
Matrix methods
Multiple criterion
Operations Research/Decision Theory
Optimization
Real Functions
Mixed-integer linear programming problem
Isomorphism
Coherent weights
Pairwise comparison matrix
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary:Pairwise comparison matrices (PCMs) have been a long standing technique for comparing alternatives/criteria and their role has been pivotal in the development of modern decision making methods. In order to obtain general results, suitable for several kinds of PCMs proposed in the literature, we focus on PCMs defined over a general unifying framework, that is an Abelian linearly ordered group. The paper deals with a crucial step in multi-criteria decision analysis, that is to obtain coherent weights for alternatives/criteria that are compared by means of a PCM. Firstly, we provide a condition ensuring coherent weights. Then, we provide and solve a mixed-integer linear programming problem in order to obtain the closest PCM, to a given PCM, having coherent weights. Isomorphisms and the mixed-integer linear programming problem allow us to solve an infinity of optimization problems, among them optimization problems concerning additive, multiplicative and fuzzy PCMs.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-019-00797-8