THE CONNECTION BETWEEN SOME EQUIVALENCE RELATIONS ON FUZZY SUBGROUPS

Document Type : Research Paper

Authors

1 Department of Mathematics, Tarbiat Modares University, P.O. Box: 14115-137, Tehran, Iran

2 Tarbiat Modares University, P.O. Box: 14115-137, Tehran, Iran

Abstract

This paper, deals with some equivalence relations in fuzzy subgroups.
Further the probability of commuting two fuzzy subgroups of some
finite abelian groups is defined.

Keywords


\bibitem{BhJaNa:BAA}
P. B. Bhattacharya, S. K. Jain and S. R. Nagpaul, {\it Basic
abstarct algebra}, Cambridge University, 1986.
\bibitem{DeJi:SNEFSFS}
C. Degang and J. Jiashang, {\it Some notes on equivalence fuzzy
sets and fuzzy subgroups}, Fuzzy Sets and Systems, {\bf 152} (2005), 403-409.
\bibitem{DiKuAj:LSUFS}
V. N. Dixit, R. Kumar and N. Ajmal, {\it Level subgroups and union of fuzzy subgroups},
Fuzzy Sets and Systems, {\bf 37} (1990), 359-371.
\bibitem{Gust:WPTTGEC}
W. H. Gustafson, {\it What is the probability that two group
elements commute}?, Amer. Math. Monthly, {\bf 80} (1973), 1031-1034.
\bibitem{Hung:Alg}
T. W. Hungerford, {\it Algebra}, Springer, New york, 1974.
\bibitem{Jain:FSCER}
A. Jain, {\it Fuzzy subgroup and certain equivalence relations},
Iranian Journal of Fuzzy Systems, {\bf 3}\textbf{(2)} (2006),
75-91.
\bibitem{MaMu:ACFS}
 M. Mashinchi and M. Mukaidonon, {\it A classification of fuzzy subgroups},
 Ninth Fuzzy System Symposium, Sapporo, ~Japan, (1992), 649-652.
\bibitem{MaMu:OFSC}
M. Mashinchi and M. Mukaidonon, {\it On fuzzy subgroups
classification}, Reserch Report of Meiji University Japan, {\bf 9}\textbf{(65)} (1993), 31-36.
\bibitem{MoBhRo:FGT}
J. N. Mordeson, K. R. Bhutani and A. Rosenfeld, {\it Fuzzy group
theory}, Springer-verlag, 2005.
\bibitem{MurMak:OEFS}
V. Murali and B. B. Makamba, {\it On an equivalence of fuzzy
subgroups $I$}, Fuzzy Sets and Systems, {\bf 123} (2001), 259-264.
\bibitem{MurMak:CNFSAGO}
V. Murali and B. B. Makamba, {\it Counting the number of fuzzy
subgroups of an abelian group of order $p^{n}q^{m}$}, Fuzzy Sets
and Systems, {\bf 144} (2004), 459-470.
\bibitem{Ray:IFG}
S. Ray, {\it Isomorphism fuzzy groups}, Fuzzy Sets and Systems, {\bf 50} (1992), 201-207.
\bibitem{She:WPAFGE}
G. J. Sherman, {\it What is the probability, an automorphism
fixes a group element}, American Mathematics Montly, {\bf 82} (1975), 261-264.
\bibitem{TaBe:NFSFAG}
M. T\u{a}rn\u{a}uceanu and L. Bentea, {\it On the number of fuzzy
subgroups of finite abelian groups}, Fuzzy Sets and Systems, {\bf 159} (2008), 1084-1096.
\bibitem{ZhKa:ANERFS}
Y. Zhang and  K. Zou, {\it A note on an equivalence relation
on fuzzy subgroups}, Fuzzy Sets and Systems, {\bf 95} (1998), 243-247.