Computing fuzzy subgroups of some special cyclic groups
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In this paper, we discuss the number of distinct fuzzy subgroups of the group $\mathbb{Z}_{p^n}\times \mathbb{Z}_{q^m}\times \mathbb{Z}_r$, $m=1,2,3$ where $p,q,r$ are distinct primes for any $n\in \mathbb{Z}^+$ using the criss-cut method that was proposed by Murali and Makamba in their study of distinct fuzzy subgroups. The criss-cut method first establishes all the maximal chains of the subgroups of a group $G$ and then counts the distinct fuzzy subgroups contributed by each chain. In this paper, all the formulae for calculating the number of these distinct fuzzy subgroups are given in polynomial form.
Abstract
In this paper, we discuss the number of distinct fuzzy subgroups of the group $\mathbb{Z}_{p^n}\times \mathbb{Z}_{q^m}\times \mathbb{Z}_r$, $m=1,2,3$ where $p,q,r$ are distinct primes for any $n\in \mathbb{Z}^+$ using the criss-cut method that was proposed by Murali and Makamba in their study of distinct fuzzy subgroups. The criss-cut method first establishes all the maximal chains of the subgroups of a group $G$ and then counts the distinct fuzzy subgroups contributed by each chain. In this paper, all the formulae for calculating the number of these distinct fuzzy subgroups are given in polynomial form.
참고문헌 (12)
- B. B. Makamba, "Studies in fuzzy groups", PhD, pp.1992
- Michael M. Munywoki, "Classifying fuzzy subgroups of the abelian group $\mathbb{Z}_{p_1}\times \mathbb{Z}_{p_2}\times\cdots \times \mathbb{Z}_{p_n}$ for distinct primes $p_1, p_2,\cdots, p_n$", ANNALS OF FUZZY MATHEMATICS AND INFORMATICS, 13(2), pp.289~296 (2017), 기초자연과학연구소[DOI]
- V. Murali, "On an equivalence of fuzzy subgroups I", Fuzzy Sets and Systems, 123(2), pp.259~264 (2001), Elsevier BV[DOI]
- V. Murali, "On an equivalence of fuzzy subgroups II", Fuzzy Sets and Systems, 136(1), pp.93~104 (2003), Elsevier BV[DOI]
- V. Murali, "Counting the number of fuzzy subgroups of an abelian group of order pnqm", Fuzzy Sets and Systems, 144(3), pp.459~470 (2004), Elsevier BV[DOI]
- V. Murali, "On methods of counting preferential fuzzy subgroups", Adv. Fuzzy Sets Syst, 3(1), pp.21~42 (2008)
- O. Ndiweni, "The classi cation of some fuzzy subgroups of nite groups under a natural equivalence and its extension, with particular emphasis on the number of equivalence classes", MS, pp.2007
- O. Ndiweni, "Distinct fuzzy subgroups of some dihedral groups", Adv. Fuzzy Sets Syst, 9(1), pp.65~91 (2011)
- Azriel Rosenfeld, "Fuzzy groups", Journal of Mathematical Analysis and Applications, 35(3), pp.512~517 (1971), Elsevier BV[DOI]
- Howard Sherwood, "Products of fuzzy subgroups", Fuzzy Sets and Systems, 11(1-3), pp.79~89 (1983), Elsevier BV[DOI]
- P.Sivaramakrishna Das, "Fuzzy groups and level subgroups", Journal of Mathematical Analysis and Applications, 84(1), pp.264~269 (1981), Elsevier BV[DOI]
- L. A. Zadeh, "Fuzzy sets", Information and Control, 8, pp.338~353 (1965)