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Issue:Counting the number of intuitionistic fuzzy subgroups of finite Abelian groups of different order: Difference between revisions

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# Atanassov, K. [[Issue:Intuitionistic fuzzy sets|Intuitionistic fuzzy sets]], Fuzzy Sets and Systems, Vol. 20, 1986, No. 1,
# Atanassov, K. [[Issue:Intuitionistic fuzzy sets|Intuitionistic fuzzy sets]], Fuzzy Sets and Systems, Vol. 20, 1986, No. 1, 87–96.
87–96.
# Neeraj, D., P. K. Sharma. Different possibilities of fuzzy subgroups of a cyclic group I, Advances in Fuzzy Sets and Systems, Vol. 12, 2012, No. 2, 101–109.
# Neeraj, D., P. K. Sharma. Different possibilities of fuzzy subgroups of a cyclic group I, Advances in Fuzzy Sets and Systems, Vol. 12, 2012, No. 2, 101–109.
# Hur, K., H. W. Kang, H. K. Song. Intuitionistic fuzzy subgroups and subrings, Honam Math. J., Vol. 25, 2003, No. 1, 19–40.
# Hur, K., H. W. Kang, H. K. Song. Intuitionistic fuzzy subgroups and subrings, Honam Math. J., Vol. 25, 2003, No. 1, 19–40.
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# Chen, Y., Y. Jiang, S. Jia. On the number of fuzzy subgroups of finite Abelian ''p''-groups, International Journal of Algebra, Vol. 6, 2011, No. 5, 233–238.
# Chen, Y., Y. Jiang, S. Jia. On the number of fuzzy subgroups of finite Abelian ''p''-groups, International Journal of Algebra, Vol. 6, 2011, No. 5, 233–238.
# Zadeh, L. A. Fuzzy sets, Information and Control, Vol. 8, 1965, 338–353.
# Zadeh, L. A. Fuzzy sets, Information and Control, Vol. 8, 1965, 338–353.


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Revision as of 20:41, 5 February 2014

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http://ifigenia.org/wiki/issue:nifs/19/4/42-47
Title of paper: Counting the number of intuitionistic fuzzy subgroups of finite Abelian groups of different order
Author(s):
Neeraj Doda
Hindu College, Amritsar, India
neerajdoda11@yahoo.com
P. K. Sharma
Hindu College, Amritsar, India
pk_Sharma7@rediffmail.com
Published in: "Notes on IFS", Volume 19, 2013, Number 4, pages 42—47
Download:  PDF (108  Kb, File info)
Abstract: In this paper, we have defined double keychain, double pinned flag and equivalence classes of intuitionistic fuzzy subgroups of a group by using an equivalence relation. We have also determined the formulae to count the number of distinct intuitionistic fuzzy subgroups of finite Abelian groups; in particular the intuitionistic fuzzy subgroups of p-groups and that of [math]\displaystyle{ Z_{p^2} \times Z_q }[/math], where p and q are distinct primes.
Keywords: Double pins, Double keychain, Double pinned flag, Equivalence, Intuitionistic fuzzy subgroup.
AMS Classification: 08A72, 20N25, 03F55.
References:
  1. Atanassov, K. Intuitionistic fuzzy sets, Fuzzy Sets and Systems, Vol. 20, 1986, No. 1, 87–96.
  2. Neeraj, D., P. K. Sharma. Different possibilities of fuzzy subgroups of a cyclic group I, Advances in Fuzzy Sets and Systems, Vol. 12, 2012, No. 2, 101–109.
  3. Hur, K., H. W. Kang, H. K. Song. Intuitionistic fuzzy subgroups and subrings, Honam Math. J., Vol. 25, 2003, No. 1, 19–40.
  4. Murali, V., B. B. Makamba. On an equivalence of fuzzy subgroups I, Fuzzy Sets and Systems, Vol. 123, 2001, 259–264.
  5. Murali, V., B. B. Makamba. On an equivalence of fuzzy subgroups II, Fuzzy Sets and Systems, Vol. 136, 2003, 93–104.
  6. Murali, V., B. B. Makamba. Counting the number of fuzzy subgroups of an Abelian group of order pn qm, Fuzzy Sets and Systems, Vol. 144, 2004, 459–470.
  7. Rosenfeld, A. Fuzzy groups, Journal of Mathematical Analysis and Applications, Vol. 35, 1971, 512–517.
  8. Sharma, P. K. (α, β)-Cut of intuitionistic fuzzy groups, International mathematical forum, Vol. 6, 2011, No. 53, 2605–2614.
  9. Raden, S., A. G. Ahmad, The number of fuzzy subgroups of finite cyclic groups, International Mathematical Forum, Vol. 6, 2011, No. 20, 987–994.
  10. Tarnauceanu, M., L. Bentea. On the number of fuzzy subgroups of finite Abelian groups, Fuzzy Sets and Systems, Vol. 159, 2008, 1084–1096.
  11. Chen, Y., Y. Jiang, S. Jia. On the number of fuzzy subgroups of finite Abelian p-groups, International Journal of Algebra, Vol. 6, 2011, No. 5, 233–238.
  12. Zadeh, L. A. Fuzzy sets, Information and Control, Vol. 8, 1965, 338–353.
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