Dealing with Non-Reciprocal Matrices in the Additive and Fuzzy Preference Relations Theoretical Frameworks

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19520%2F25%3AA0000570" target="_blank" >RIV/47813059:19520/25:A0000570 - isvavai.cz</a>

Result on the web

<a href="https://www.sciencedirect.com/science/article/pii/S0888613X25001811" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0888613X25001811</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.ijar.2025.109540" target="_blank" >10.1016/j.ijar.2025.109540</a>

Result language

angličtina

Original language name

Dealing with Non-Reciprocal Matrices in the Additive and Fuzzy Preference Relations Theoretical Frameworks

Original language description

Many multiple-criteria decision aiding methods apply the so-called multiplicative pairwise comparisons, where the comparisons have the form of a ratio expressing how many times one entity is more important (or preferred) than another. Besides the multiplicative system, additive and fuzzy preference relations systems have been proposed for pairwise comparisons in recent decades. These systems are appealing for their intuitive use and natural properties, but they are not as intensively studied as their multiplicative counterpart. Namely, studies on inconsistency and non-reciprocity in particular, in both theoretical frameworks, are rather scarce and fragmented. Therefore, our study focuses on the problem of non-reciprocity in both frameworks and fills the current gaps in its understanding and evaluation. We introduce measures of non-reciprocity in the additive and fuzzy preference relations frameworks compatible with a previously published measure of non-reciprocity in the multiplicative framework, and we show that all measures are specific representations of a general measure of non-reciprocity based on an Alo-group approach. Further on, we show that new measures are endowed with a set of desirable properties. Furthermore, we perform Monte Carlo simulations on randomly generated non-reciprocal matrices both in additive and fuzzy systems and provide percentile tables allowing decision makers to decide whether a level of non-reciprocity of a given PC matrix is acceptable or not.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2025

Confidentiality

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

Name of the periodical

International Journal of Approximate Reasoning

ISSN

0888-613X

e-ISSN

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Volume of the periodical

187

Issue of the periodical within the volume

prosinec

Country of publishing house

US - UNITED STATES

Number of pages

12

Pages from-to

1-12

UT code for WoS article

001559962500004

EID of the result in the Scopus database

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