AN EXPLICIT FORMULA FOR FUZZY SUBGROUPS OF THE ABELIAN GROUP Z2pn × Z2, n ≥ 1, p ≥ 3
Keywords:
Recurrence relation, Isomorphism classes, Enumerative techniques, Fuzzy equivalence relation, Fuzzy subgroups
Abstract
In this paper, we characterise distinct fuzzy subgroups of the abelian group Z2pn ×Z2, using an enumerative technique derived from the set of representatives of isomorphism classes of subgroups and their sizes. We formulate a linear non-homogeneous recurrence relation of degree one with constant coefficients and apply both the associated linear homogeneous and particular solutions to derive an explicit formula for the number of fuzzy subgroups.
References
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[2] P. S. Das. Fuzzy groups and level subgroups. Journal of Mathematical Analysis and Applications, 84(1):264–269, 1981.
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[5] K. H. Rosen. Discrete Mathematics and Its Applications. McGraw-Hill Companies, New York, 1998.
[6] A. Rosenfeld. Fuzzy subgroups. Journal of Mathematical Analysis and Applications, 35(3):512–517, 1971.
[7] M. T˘arn˘auceanu, L. Bentea. On the number of fuzzy subgroups of finite abelian groups. Fuzzy Sets and Systems, 159(9):1084–1096, 2008.
[8] A. C. Volf. Counting fuzzy subgroups and chains of subgroups. Fuzzy Systems & Artificial Intelligence, 10(4):191–200, 2004.
[9] L. A. Zadeh. Fuzzy sets. Information and Control, 8(3):338–353, 1965.
[2] P. S. Das. Fuzzy groups and level subgroups. Journal of Mathematical Analysis and Applications, 84(1):264–269, 1981.
[3] B. B. Makamba, V. Murali. Counting the number of fuzzy subgroups of an abelian group of order pnqm. Fuzzy Sets and Systems, 144(3):459–470, 2004.
[4] M. E. Ogiugo, A. Seghal. The number of chains of subgroups for certain finite alternating groups. Annals of Pure and Applied Mathematics, 22(1):65–70, 2020.
[5] K. H. Rosen. Discrete Mathematics and Its Applications. McGraw-Hill Companies, New York, 1998.
[6] A. Rosenfeld. Fuzzy subgroups. Journal of Mathematical Analysis and Applications, 35(3):512–517, 1971.
[7] M. T˘arn˘auceanu, L. Bentea. On the number of fuzzy subgroups of finite abelian groups. Fuzzy Sets and Systems, 159(9):1084–1096, 2008.
[8] A. C. Volf. Counting fuzzy subgroups and chains of subgroups. Fuzzy Systems & Artificial Intelligence, 10(4):191–200, 2004.
[9] L. A. Zadeh. Fuzzy sets. Information and Control, 8(3):338–353, 1965.
Published
2025-12-29
How to Cite
OGIUGO, M. E., ADEBISI, S. A., OGUNFOLU, O. B., & ENIOLUWAFE, M. (2025). AN EXPLICIT FORMULA FOR FUZZY SUBGROUPS OF THE ABELIAN GROUP Z2pn × Z2, n ≥ 1, p ≥ 3. Unilag Journal of Mathematics and Applications, 5(2), 14 - 21. Retrieved from https://lagjma.unilag.edu.ng/article/view/2827
Section
Articles
Copyright (c) 2025 MIKE EKPEN OGIUGO, SUNDAY ADESINA ADEBISI, OLUSOLA BAMIDELE OGUNFOLU, MICHAEL ENIOLUWAFE
This work is licensed under a Creative Commons Attribution 4.0 International License.
