Weak and strong consistency of an interval comparison matrix

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10419298" target="_blank" >RIV/00216208:11320/20:10419298 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/978-3-030-62509-2_2" target="_blank" >https://doi.org/10.1007/978-3-030-62509-2_2</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-030-62509-2_2" target="_blank" >10.1007/978-3-030-62509-2_2</a>

Result language
angličtina
Original language name
Weak and strong consistency of an interval comparison matrix
Original language description
We consider interval-valued pairwise comparison matrices and two types of consistency - weak (consistency for at least one realization) and strong (acceptable consistency for all realizations). Regarding weak consistency, we comment on the paper [Y. Dong and E. Herrera-Viedma, Consistency-Driven Automatic Methodology to Set Interval Numerical Scales of 2-Tuple Linguistic Term Sets and Its Use in the Linguistic GDM With Preference Relation, IEEE Trans. Cybern., 45(4):780-792, 2015], where, among other results, a characterization of weak consistency was proposed. We show by a counterexample that in general the presented condition is not sufficient for weak consistency. It provides a full characterization only for matrices up to size of three. We also show that the problem of having a closed form expression for weak consistency is closely related with P-completeness theory and that an optimization version of the problem is indeed P-complete. Regarding strong consistency, we present a sufficient condition and a necessary condition, supplemented by a small numerical study on their efficiency. We leave a complete characterization as an open problem.
Czech name
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Czech description
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Project
<a href="/en/project/GA18-04735S" target="_blank" >GA18-04735S: Novel approaches for relaxation and approximation techniques in deterministic global optimization</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
Integrated Uncertainty in Knowledge Modelling and Decision Making
ISBN
978-3-030-62509-2
ISSN
0302-9743
e-ISSN
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Number of pages
11
Pages from-to
15-25
Publisher name
Springer
Place of publication
Cham
Event location
Phuket, Thailand
Event date
Nov 11, 2020
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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