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. Tu{a}rnu{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.