Weak and strong consistency of an interval comparison matrix

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Weak and strong consistency of an interval comparison matrix

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Weak and strong consistency of an interval comparison matrix

Popis výsledku anglicky

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.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

50201 - Economic Theory

Projekt

<a href="/cs/project/GA18-04735S" target="_blank" >GA18-04735S: Nové přístupy pro relaxační a aproximační techniky v deterministické globální optimalizaci</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Integrated Uncertainty in Knowledge Modelling and Decision Making

ISBN

978-3-030-62509-2

ISSN

0302-9743

e-ISSN

—

Počet stran výsledku

11

Strana od-do

15-25

Název nakladatele

Springer

Místo vydání

Cham

Místo konání akce

Phuket, Thailand

Datum konání akce

11. 11. 2020

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

—