Why We Need Desirable Properties in Pairwise Comparison Methods?

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19520%2F24%3AA0000446" target="_blank" >RIV/47813059:19520/24:A0000446 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1002/mcda.70002" target="_blank" >http://dx.doi.org/10.1002/mcda.70002</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1002/mcda.70002" target="_blank" >10.1002/mcda.70002</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Why We Need Desirable Properties in Pairwise Comparison Methods?

Popis výsledku v původním jazyce

Pairwise comparison matrices (PCMs) are inevitable tools in some important multiple-criteria decision-making methods, for example AHP/ANP, TOPSIS, PROMETHEE and others. In this paper, we investigate some important properties of PCMs which influence the generated priority vectors for the final ranking of the given alternatives. The main subproblem of the Analytic Hierarchy Process (AHP) is to calculate the priority vectors, that is, the weights assigned to the elements of the hierarchy (criteria, sub-criteria, and/or alternatives or variants), by using the information provided in the form of a pairwise comparison matrix. Given a set of elements, and a corresponding pairwise comparison matrix, whose entries evaluate the relative importance of the elements with respect to a given criterion, the final ranking of the given alternatives is evaluated. We investigate some important and natural properties of PCMs called the desirable properties, particularly, the non-dominance, consistency, intensity and coherence, which influence the generated priority vectors. Usually, the priority vector is calculated based on some well-known method, for example, the Eigenvector Method, the Arithmetic Mean Method, the Geometric Mean Method, the Least Square Method, and so forth. The novelty of our approach is that the priority vector is calculated as the solution of an optimization problem where an error objective function is minimised with respect to constraints given by the desirable properties. The properties of the optimal solution are discussed and some illustrating examples are presented. The corresponding software tool has been developed and demonstrated in some examples.

Název v anglickém jazyce

Why We Need Desirable Properties in Pairwise Comparison Methods?

Popis výsledku anglicky

Pairwise comparison matrices (PCMs) are inevitable tools in some important multiple-criteria decision-making methods, for example AHP/ANP, TOPSIS, PROMETHEE and others. In this paper, we investigate some important properties of PCMs which influence the generated priority vectors for the final ranking of the given alternatives. The main subproblem of the Analytic Hierarchy Process (AHP) is to calculate the priority vectors, that is, the weights assigned to the elements of the hierarchy (criteria, sub-criteria, and/or alternatives or variants), by using the information provided in the form of a pairwise comparison matrix. Given a set of elements, and a corresponding pairwise comparison matrix, whose entries evaluate the relative importance of the elements with respect to a given criterion, the final ranking of the given alternatives is evaluated. We investigate some important and natural properties of PCMs called the desirable properties, particularly, the non-dominance, consistency, intensity and coherence, which influence the generated priority vectors. Usually, the priority vector is calculated based on some well-known method, for example, the Eigenvector Method, the Arithmetic Mean Method, the Geometric Mean Method, the Least Square Method, and so forth. The novelty of our approach is that the priority vector is calculated as the solution of an optimization problem where an error objective function is minimised with respect to constraints given by the desirable properties. The properties of the optimal solution are discussed and some illustrating examples are presented. The corresponding software tool has been developed and demonstrated in some examples.

Druh

J_SC - Článek v periodiku v databázi SCOPUS

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA21-03085S" target="_blank" >GA21-03085S: Párové porovnání a data mining při podpoře rozhodovacích procesů</a><br>

Návaznosti

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

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

JOURNAL OF MULTI-CRITERIA DECISION ANALYSIS

ISSN

1057-9214

e-ISSN

1099-1360

Svazek periodika

31

Číslo periodika v rámci svazku

5-6

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

10

Strana od-do

1-10

Kód UT WoS článku

—

EID výsledku v databázi Scopus

2-s2.0-85211237442