On Kemeny Optimization Scheme for Fuzzy Set of Relations

Serhii O. Mashchenko; Olena A. Kapustian; Bruno Rubino

doi:10.3390/axioms12121067

Axioms (Nov 2023)

On Kemeny Optimization Scheme for Fuzzy Set of Relations

Serhii O. Mashchenko,
Olena A. Kapustian,
Bruno Rubino

Affiliations

Serhii O. Mashchenko: Faculty of Computer Science and Cybernetics, Taras Shevchenko National University of Kyiv, 64/13, Volodymyrska Street, 01601 Kyiv, Ukraine
Olena A. Kapustian: Faculty of Computer Science and Cybernetics, Taras Shevchenko National University of Kyiv, 64/13, Volodymyrska Street, 01601 Kyiv, Ukraine
Bruno Rubino: Department of Engineering and Information Sciences and Mathematics, University of L’Aquila, 67100 L’Aquila, Italy

DOI: https://doi.org/10.3390/axioms12121067
Journal volume & issue: Vol. 12, no. 12
p. 1067

Abstract

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The present paper investigated the aggregation of individual preferences into a group fuzzy preference relation for a fuzzy set of decision-makers (DMs). This aggregation is based on the Kemeny optimization scheme. It was proven that this group relation is a Type-2 fuzzy relation (T2FR). The decomposition approach was used to analyze the group T2FR. It is shown that the group T2FR can be decomposed according to secondary membership grades into a finite collection of Type-1 fuzzy relations. Each of them is a group fuzzy relation for a crisp set of DMs, which is the corresponding α-cut of the original fuzzy set of DMs. Illustrative examples are given.

Published in Axioms

ISSN: 2075-1680 (Online)
Publisher: MDPI AG
Country of publisher: Switzerland
LCC subjects: Science: Mathematics
Website: http://www.mdpi.com/journal/axioms

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