A NEW TYPE OF HYPER K-SUBALGEBRAS

Title & Authors
A NEW TYPE OF HYPER K-SUBALGEBRAS
Jun, Young Bae; Lee, Kyoung Ja; Kang, Min Su;

Abstract
In this paper, the concept of ($\small{\bar{\in},\bar{\in}{\vee}\var{q}}$)-fuzzy hyper K-subalgebras and fuzzy hyper K-subalgebras with thresholds are introduced, and related properties and characterizations are discussed.
Keywords
hyper K-algebra;($\small{{\in},{\in}{\vee}q}$)-fuzzy hyper K-subalgebra;($\small{\bar{\in},\bar{\in}{\vee}\bar{q}}$)-fuzzy hyper K-subalgebra;fuzzy hyper K-subalgebra with thresholds;
Language
English
Cited by
References
1.
S. K. Bhakat and P. Das, On the definition of a fuzzy subgroup, Fuzzy Sets and Systems 51 (1992), no. 2, 235-241.

2.
S. K. Bhakat and P. Das, (${\in},{\in}Vq$)-fuzzy subgroup, Fuzzy Sets and Systems 80 (1996), no. 3, 359-368.

3.
A. Borumand Saeid, R. A. Borzoei, and M. M. Zahedi, (Weak) implicative hyper K-ideals, Bull. Korean Math. Soc. 40 (1995), no. 1, 123-137.

4.
R. A. Borzooei, Hyper BCK and K-algebras, Ph. D. thesis, Shahid Bahonar University of Kerman, 2000.

5.
R. A. Borzooei, A. Hasankhani, M. M. Zahedi, and Y. B. Jun, On hyper K-algebras, Math. Japon. 52 (2000), no. 1, 113-121.

6.
P. Corsini, A new connection between hypergroups and fuzzy sets, Southeast Asian Bull. Math. 27 (2003), no. 2, 221-229.

7.
P. Corsini and V. Leoreanu, Fuzzy sets and join spaces associated with rough sets, Rend. Circ. Mat. Palermo (2) 51 (2002), no. 3, 527-536.

8.
B. Davvaz, Fuzzy Krasner (m, n)-hyperrings, Comput. Math. Appl. 59 (2010), no. 12, 3879-3891.

9.
B. Davvaz, Fuzzy Hv-groups, Fuzzy Sets and Systems 101 (1999), no. 1, 191-195.

10.
B. Davvaz and P. Corsini, Fuzzy n-ary hypergroups, J. Intell. Fuzzy Systems 18 (2007), no. 4, 377-382.

11.
B. Davvaz, P. Corsini, and V. Leoreanu-Fotea, Fuzzy n-ary subpolygroups, Comput. Math. Appl. 57 (2009), no. 1, 141-152.

12.
B. Davvaz and V. Leoreanu, Applications of interval valued fuzzy n-ary polygroups with respect to t-norms (t-conorms), Comput. Math. Appl. 57 (2009), no. 8, 1413-1424.

13.
Y. B. Jun, Generalizations of (${\in},{\in}\;Vq$)-fuzzy subalgebras in BCK/BCI-algebras, Comput. Math. Appl. 58 (2009), no. 7, 1383-1390.

14.
Y. B. Jun, Note on "(${\alpha},\;{\beta}$)-fuzzy ideals of hemirings", Comput. Math. Appl. 59 (2010), no. 8, 2582-2586.

15.
Y. B. Jun, On (${\alpha},{\beta}$)-fuzzy subalgebras of BCK/BCI-algebras, Bull. Korean Math. Soc. 42 (2005), no. 4, 703-711.

16.
Y. B. Jun, Fuzzy subalgebras of type (${\alpha},\;{\beta}$) in BCK/BCI-algebras, Kyungpook Math. J. 47 (2007), no. 3, 403-410.

17.
Y. B. Jun, On fuzzy hyper K-subalgebras of hyper K-algebras, Sci. Math. 3 (2000), no. 1, 67-75.

18.
Y. B. Jun, K, J, Lee, and C. H. Park, New types of fuzzy ideals in BCK/BCI-algebras, Comput. Math. Appl. 60 (2010), no. 3, 771-785.

19.
Y. B. Jun and W. H. Shim, Fuzzy positive implicative hyper K-ideals of hyper K-algebras, Honam Math. J. 25 (2003), no. 1, 43-52.

20.
Y. B. Jun and W. H. Shim, Fuzzy hyper K-ideals of hyper K-algebras, J. Fuzzy Math. 12 (2004), no. 4, 861-871.

21.
Y. B. Jun and S. Z. Song, Generalized fuzzy interior ideals in semigroups, Inform. Sci. 176 (2006), no. 20, 3079-3093.

22.
Y. B. Jun, M. M. Zahedi, X. L. Xin, and R. A. Borzoei, On hyper BCK-algebras, Ital. J. Pure Appl. Math. 8 (2000), 127-136.

23.
M. S. Kang, Hyper K-subalgebras based on fuzzy points, Commun. Korean Math. Soc. (in print).

24.
O. Kazanci, B. Davvaz, and S. Yamak, Fuzzy n-ary polygroups related to fuzzy points, Comput. Math. Appl. 58 (2009), no. 7, 1466-1474.

25.
V. Leoreanu, Direct limit and inverse limit of join spaces associated with fuzzy sets, Pure Math. Appl. 11 (2000), no. 3, 509-512.

26.
F. Marty, Sur une generalization de la notion de groupe, 8th Congress Math. Scandinaves, Stockholm (1934), 45-49.

27.
V. Murali, Fuzzy points of equivalent fuzzy subsets, Inform. Sci. 158 (2004), 277-288.

28.
P. M. Pu and Y. M. Liu, Fuzzy topology I, Neighborhood structure of a fuzzy point and Moore-Smith convergence, J. Math. Anal. Appl. 76 (1980), no. 2, 571-599.

29.
M. Shabir, Y. B. Jun, and Y. Nawaz, Semigroups characterized by (${\in},\;{\in}\;Vq_k$)-fuzzy ideals, Comput. Math. Appl. 60 (2010), 1473-1493.

30.
M. Shabir, Y. B. Jun, and Y. Nawaz, Characterizations of regular semigroups by (${\alpha},\;{\beta}$)-fuzzy ideals, Comput. Math. Appl. 59 (2010), no. 5, 161-175.

31.
J. Zhan, B. Davvaz, and K. P. Shum, Generalized fuzzy hyperideals of hyperrings, Comput. Math. Appl. 56 (2008), no. 7, 1732-1740.