Advances in Fuzzy Sets and Systems

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FORMULAE FOR THE NUMBER OF DISTINCT FUZZY SUBGROUPS OF SOME RANK-3 GROUPS

Authors

  • I. K. Appiah
  • B. B. Makamba

Keywords:

rank, maximal subgroup, maximal chain, equivalence, fuzzy subgroup, distinguishing factor.

DOI:

https://doi.org/10.17654/0973421X22010

Abstract

In this paper, we classify fuzzy subgroups of some rank-2 and rank-3 finite abelian groups and then present explicit formulae for the number of distinct fuzzy subgroups in each of the cases. We provide illustrative examples as well.

Received: December 2, 2021
Accepted: February 15, 2022

References

I. K. Appiah and B. B. Makamba, Counting distinct fuzzy subgroups of some rank-3 abelian groups, Iran. J. Fuzzy Syst. 14(1) (2017), 163-181.

I. K. Appiah and B. B. Makamba, User-friendly formulae for the numbers of maximal chains for some finite rank abelian groups, Far East J. Math. Sci. (FJMS) 132(1) (2021), 31-62.

S. Branimir and A. Tepavcevic, A note on a natural equivalence relation on fuzzy power set, Fuzzy Sets and Systems 148 (2004), 201-210.

C. Degang, J. Jiashang and W. Congxin and E. C. C. Tsang, Some notes on equivalent fuzzy sets and fuzzy subgroups, Fuzzy Sets and Systems 152 (2005), 403-409.

A. Iranmanesh and H. Naraghi, The connection between some equivalence relations on fuzzy groups, Iran. J. Fuzzy Syst. 8(5) (2011), 69-80.

A. Jain, Fuzzy subgroups and certain equivalence relations, Iran. J. Fuzzy Syst. 3(2) (2006), 75-91.

V. Murali and B. B. Makamba, On an equivalence of fuzzy subgroups I, Fuzzy Sets and Systems 123 (2001), 259-264.

V. Murali and B. B. Makamba, Counting the number of subgroups of an abelian group of finite order, Fuzzy Sets and Systems 144 (2004), 459-470.

S. Ngcibi, V. Murali and B. B. Makamba, Fuzzy subgroups of rank two abelian p-groups, Iran. J. Fuzzy Syst. 7(2) (2010), 149-153.

J. M. Oh, An explicit formula for the number of fuzzy subgroups of a finite abelian p-group of rank two, Iran. J. Fuzzy Syst. 10(6) (2013), 125-133.

A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl. 35 (1971), 512-517.

V. N. Shokeuv, An expression for the number of subgroups of a given order of a finite p-group, Mathematical Notes of the Academy of Sciences of the USSR 12(5) (1972), 774-778.

M. Tarnauceanu and L. Bentea, On the number of subgroups of finite abelian groups, Fuzzy Sets and Systems 159 (2008), 1084-1096.

A. C. Volf, Counting fuzzy subgroups and chains of subgroups, Fuzzy Systems and Artificial Intelligence 10 (2004), 191-200.

Y. Zhang and K. Zou, A note on an equivalence relation on fuzzy subgroups, Fuzzy Sets and Systems 95 (1998), 243-247.

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Published

2022-09-10

Issue

Vol. 27 No. 2 (2022)

Section

Articles

License

Copyright (c) 2022 Pushpa Publishing House, Prayagraj, India

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How to Cite

FORMULAE FOR THE NUMBER OF DISTINCT FUZZY SUBGROUPS OF SOME RANK-3 GROUPS. (2022). Advances in Fuzzy Sets and Systems, 27(2), 189-241. https://doi.org/10.17654/0973421X22010

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