Fuzzy Subgroups of Rank Two Abelian p-Group

Document Type : Research Paper

Authors

1 Department of Mathematics (P\&A), University of Fort Hare, Alice, 5700, South Africa

2 Department of Mathematics (P\&A), Rhodes University, Grahamstown, 6140, South Africa

3 B. B. Makamba, Department of Mathematics (P\&A), University of Fort Hare, Alice, 5700, South Africa

Abstract

In this paper we enumerate fuzzy subgroups, up to a natural equivalence, of some finite abelian p-groups of rank two where p is any prime number. After obtaining the number of maximal chains of subgroups, we count fuzzy subgroups using inductive arguments. The number of such fuzzy subgroups forms a polynomial in p with pleasing combinatorial coefficients. By exploiting the order, we label the subgroups of maximal chains in a special way which enables us to count the number of fuzzy subgroups.

Keywords

References

bibitem{mur:01} V.Murali, and B.B.Makamba, On an Equivalence of Fuzzy Subgroups I , Fuzzy Sets and Systems, 123 (2001) 163-168.
bibitem{mur:03} V.Murali and B.B. Makamba, On an Equivalence of Fuzzy Subgroups II, Fuzzy sets and Systems, 136 (2003), 93-104.
bibitem{mur:04} V.Murali and B.B. Makamba, Counting the number of fuzzy subgroups of an abelian group of order $p^n q^m$, Fuzzy sets and Systems, 144 (2004), 459-470.
bibitem{ros:71} A.Rosenfeld, Fuzzy Groups, J. Math. Anal. Appl., 35 (1971) 512-517.
bibitem{zad:65} L.A.Zadeh, Fuzzy sets, Inform. and control, 8 (1965) 338-353.
Iranian Journal of Fuzzy Systems
Volume 7, Issue 2 - Serial Number 2
May and June 2010
Pages 149-153

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