A new algorithm for computing priority vector of pairwise comparisons matrix with fuzzy elements

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19520%2F22%3AA0000285" target="_blank" >RIV/47813059:19520/22:A0000285 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/abs/pii/S0020025522011501" target="_blank" >https://www.sciencedirect.com/science/article/abs/pii/S0020025522011501</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.ins.2022.10.030" target="_blank" >10.1016/j.ins.2022.10.030</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A new algorithm for computing priority vector of pairwise comparisons matrix with fuzzy elements

Popis výsledku v původním jazyce

Applying the Analytic Hierarchy Process (AHP) in a decision making (DM) problem, fuzzy elements are appropriate whenever the decision maker is uncertain about the value of his/her evaluation of the relative importance of the elements in question, i.e., criteria and/or alternatives. The method, often called the fuzzy AHP, is also used when aggregating crisp pairwise comparisons of a group of decision makers in the group DM problem. In this paper, the DM problem is formulated in a general setting using pairwise comparisons matrices with elements from an Abelian linearly ordered group (alo-group). Such an approach enables extensions of traditional multiplicative, additive, or fuzzy approaches. Here, we propose some desirable properties (consistency, coherency, and intensity) of priority vectors, and derive sufficient conditions for the existence of priority vectors with those properties. In general, the most popular methods for deriving the priority vector – the Eigenvector Method and the Geometric Mean Method – do not always provide priority vectors having these desirable properties. Here, we formulate a new solution algorithm for deriving the priority vector based on a specific optimization problem satisfying the desirable properties under appropriate assumptions. Two illustrating examples of the algorithm are presented and discussed.

Název v anglickém jazyce

A new algorithm for computing priority vector of pairwise comparisons matrix with fuzzy elements

Popis výsledku anglicky

Applying the Analytic Hierarchy Process (AHP) in a decision making (DM) problem, fuzzy elements are appropriate whenever the decision maker is uncertain about the value of his/her evaluation of the relative importance of the elements in question, i.e., criteria and/or alternatives. The method, often called the fuzzy AHP, is also used when aggregating crisp pairwise comparisons of a group of decision makers in the group DM problem. In this paper, the DM problem is formulated in a general setting using pairwise comparisons matrices with elements from an Abelian linearly ordered group (alo-group). Such an approach enables extensions of traditional multiplicative, additive, or fuzzy approaches. Here, we propose some desirable properties (consistency, coherency, and intensity) of priority vectors, and derive sufficient conditions for the existence of priority vectors with those properties. In general, the most popular methods for deriving the priority vector – the Eigenvector Method and the Geometric Mean Method – do not always provide priority vectors having these desirable properties. Here, we formulate a new solution algorithm for deriving the priority vector based on a specific optimization problem satisfying the desirable properties under appropriate assumptions. Two illustrating examples of the algorithm are presented and discussed.

Druh

J_imp - Článek v periodiku v databázi Web of Science

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

2022

Kód důvěrnosti údajů

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

Název periodika

Information Sciences

ISSN

0020-0255

e-ISSN

—

Svazek periodika

615

Číslo periodika v rámci svazku

November 2022

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

15

Strana od-do

103-117

Kód UT WoS článku

000890939400006

EID výsledku v databázi Scopus

2-s2.0-85139857378