A new algorithm to compute fuzzy subgroups of a finite group

Adeel Farooq; Musawwar Hussain; Muhammad Yousaf; Ahmad N. Al-Kenani; Adeel Farooq; Musawwar Hussain; Muhammad Yousaf; Ahmad N. Al-Kenani

doi:10.3934/math.20231060

AIMS Mathematics

2023, Volume 8, Issue 9: 20802-20814. doi: 10.3934/math.20231060

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A new algorithm to compute fuzzy subgroups of a finite group

1.
Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan
2.
Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

Received: 22 February 2023 Revised: 13 June 2023 Accepted: 19 June 2023 Published: 29 June 2023
MSC : Primary 20N25, 03E72; Secondary 05E15, 20D30, 20D60

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 $.
- fuzzy subgroups,
- quaternion group,
- dihedral group,
- maximal chains
Citation: Adeel Farooq, Musawwar Hussain, Muhammad Yousaf, Ahmad N. Al-Kenani. A new algorithm to compute fuzzy subgroups of a finite group[J]. AIMS Mathematics, 2023, 8(9): 20802-20814. doi: 10.3934/math.20231060

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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 $.

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