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Research Article | Open Access

A new algorithm to compute fuzzy subgroups of a finite group

Adeel Farooq1( ), Musawwar Hussain1, Muhammad Yousaf1, Ahmad N. Al-Kenani2
Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan
Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia
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Abstract

The enumeration of fuzzy subgroups is a complex problem. Several authors have computed results for special instances of groups. In this paper, we present a novel algorithm that is designed to enumerate the fuzzy subgroups of a finite group. This is achieved through the computation of maximal chains of subgroups. This approach is also useful for writing a program to compute the number of fuzzy subgroups. We provide further elucidation by computing the number of fuzzy subgroups of the groups Q 8 and D 8 .

Keywords

fuzzy subgroupsquaternion groupdihedral groupmaximal chains
CLC number: Primary 20N25, 03E72; Secondary 05E15, 20D30, 20D60

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AIMS Mathematics
Volume 8 Issue 9,
September 2023
Pages 20802-20814
DOI: 10.3934/math.20231060

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Cite this article:
Farooq A, Hussain M, Yousaf M, et al. A new algorithm to compute fuzzy subgroups of a finite group. AIMS Mathematics, 2023, 8(9): 20802-20814. https://doi.org/10.3934/math.20231060

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Received: 22 February 2023
Revised: 13 June 2023
Accepted: 19 June 2023
Published: 15 September 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)