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Fuzzy Subgroups of Rank Two Abelian p-Group | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 12، دوره 7، شماره 2، شهریور 2010، صفحه 149-153 اصل مقاله (173.47 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2010.183 | ||
| نویسندگان | ||
| S Ngcibi1؛ V Murali* 2؛ B. B Makamba3 | ||
| 1Department of Mathematics (P\&A), University of Fort Hare, Alice, 5700, South Africa | ||
| 2Department of Mathematics (P\&A), Rhodes University, Grahamstown, 6140, South Africa | ||
| 3B. B. Makamba, Department of Mathematics (P\&A), University of Fort Hare, Alice, 5700, South Africa | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Equivalence؛ Fuzzy subgroup؛ p-groups؛ Keychain | ||
| مراجع | ||
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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. | ||
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