Union and Intersection Fuzzy Subhypergroups
- Department of Mathematics, Faculty of Sciences, Gorgan Branch,Islamic Azad University,Gorgan, Iran.
- Department of Mathematics, GolestanUniversity, Gorgan, Iran.
In this paper, some properties of union and intersection fuzzy subhypergroups are discussed.
Generally, intersection family of fuzzy subhypergroups of a hypergroup is fuzzy subhypergroup,
but, union family of fuzzy subhypergroups of a hypergroup is not fuzzy subhypergroup. We give
some conditions such that this family is fuzzy subhypergroup.
- Fuzzy sets
- Fuzzy subhypergroup.
M. Asghari-Larimi, B. Davvaz, Hyperstructures associated to arithmetic functions, ArsCombitoria, 97 (2010), 51-63.
M. Asghari-Larimi, V. Leoreanu-Fotea, A connection between hypergroupoids and L-Fuzzy Sets of Type 2, Italian J. of Pure and Appl. Math., 26 (2009), 207-216.
P. Corsini, A new connection between hypergroups and fuzzy sets, Southeast, Asian Bull.Math. , 27 (2003), 221-229.
P. Corsini, Prolegomena of hypergroup theory, Second edition, Aviani editor (1993)
P. Corsini , Join spaces, power sets, fuzzy sets, Algebraic hyperstructures and applications (Iasi, 1993), 45-52, Hadronic Press, Palm Harbor, FL (1994)
P. Corsini, V. Leoreanu-Fotea, Applications of hyperstructure theory, Advances in Mathematics, Kluwer Academic Publishers, Dordrecht (2003)
B. Davvaz, V. Leoreanu-Fotea, Hyperring theory and Applications, Hadronic Press, Inc,115, Palm Harber, USA (2009)
N. Kuroki, On fuzzy ideals and fuzzy bi-ideals in semigroups, Fuzzy Sets and Systems, 5 (1981), 203-215.
W.-J. Liu, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets and Systems , 8 (1982), 133- 139.
F. Marty, Sur une generalization de la notion de groupe, 8th Congress Math. Scandenaves,Stockholm, (1934), 45-49.
J. N. Mordeson, K. R. Bhutani, A. Rosenfeld, Fuzzy Group Theory, World Scientific, Singapore (2005)
T. K. Mukherjee, M. K. Sen, On fuzzy ideals of a ring (1), Fuzzy Sets and Systems, 21 (1987), 99-104.
A. Rosenfield, Fuzzy groups, J. Math. Appl. , 35 (1971), 512-517.
T. Vougiouklis, Hyperstructures and their representations, Hadronic Press, Inc, 115, PalmHarber, USA (1994)
L. A. Zadeh, Fuzzy Sets, Inform and Control , 8 (1965), 338-353.