Characterization of ternary semigroups in terms of (∈, ∈ ∨qk) ideals

[1] J. Ahsan, Kui Yuan Li, M. Shabir, Semigroups characterized by their fuzzy
bi-ideals, The J. Fuzzy Math. 10 (2) (2002) 441-449.
[2] S.K. Bhakat, (∈ ∨q)-level subset, Fuzzy Sets and Systems, 103 (1999)
529-533.
[3] S.K. Bhakat, P. Das, On the definition of a fuzzy subgroup, Fuzzy Sets
and Systems, 51 (1992) 235-241.
[4] S.K. Bhakat, P. Das, (∈, ∈ ∨q)-fuzzy subgroups, Fuzzy Sets and Systems
80 (1996) 359-368.[5] S.K. Bhakat, P. Das, Fuzzy subrings and ideals redefined, Fuzzy Sets and
Systems, 81 (1996) 383 − 393.
[6] P.S. Das, Fuzzy groups and level subgroups, J. Math. Anal. Appl. 84 (1981)
264-269.
[7] B. Davvaz, (∈, ∈ ∨q)-fuzzy subnearrings and ideals, Soft Comput, 10
(2006) 206 − 211.
[8] V.N. Dixit, S. Dewan, A note on quasi and bi-ideals in Ternary Semi-
groups, Internat. J. Math and Math. Sci. 18 (3) (1995) 501-508.
[9] T.K. Dutta, S. Kar, On ternary semifields, Math. Gen. Algebra Appl,
Vol. 24(2004) pp. 445-454.
[10] T.K. Dutta S. Kar, On Prime ideals and Prime Radical of Ternary Semir-
ings, Bull. Cal. Math. Soc., 97(5) (2005) 185-198.
[11] T. K. Dutta S. Kar, A note on regular ternary semirings,” KYUNGPOOK
Math. J., 46 (2006) 357-365.
[12] A. Iampan, Lateral ideals of ternary semigroups. Ukrainian Math. Bull.,
4 (2007) 517-526.
[13] A. Iampan, The Minimality and Maximality of Left (Right) Ideals in
Ternary Semigroups, Int. J. Contemp. Math. Sci., 5 (49) (2010) 2409 -
2417.
[14] Y.B. Jun, S.Z. Song, Generalized fuzzy interior ideals in semigroups, In-
formation Sci., 176 (2006) 3079-3093.
[15] Y. B. Jun, Generalization of (∈, ∈ ∨q)-fuzzy sub algebras in BCK/BCI-
algebras, Comput. Math. Appl., 58 (2009) 1383-1390.
[16] Y.B. Jun, Y. Xu, J. Ma, Redefined fuzzy implicative filters, Inform. Sci.
177 (2007) 1422-1429..
[17] O. Kazanci S. Yamak, Generalized fuzzy bi-ideals of semigroup, Soft Com-
put, DOI 10.1007/s00500-008-0280-5.
[18] S. Kar, On Ideals in ternary semirings, Int. J. Math. Gen. Sci., 18 (2005)
3015-3023.
[19] S. Kar, B.K. Maity, Congruences on ternary semigroups. J. Chugcheong
Math. Soc., 20 (2007) 191-200.
246 Anwar Zeb, Gul Zaman, Inayat Ali Shah, Asghar Khan
[20] A. Khan, Y. B. Jun , M. Z. Abbas, Characterizations of ordered semi-
groups in terms of (∈, ∈ ∨q)-fuzzy interior ideals, Neural Computing and
Applications, DOI 10.1007/s00521-010-0463-8.
[21] N. Kuroki, Fuzzy bi-ideals in semigroups, Comment. Math. Univ. St. Pauli
XXVIII-1 (1979) 17-21.
[22] D.H. Lehmer, A ternary analogue of abelian groups, Amer. J. Math.,
(1932) 329-338.
[23] V. Murali, Fuzzy points of equivalent fuzzy subsets, Inform. Sci. 158 (2004)
277-288.
[24] P.M. Pu, Y.M. Liu, Fuzzy topology I, Neighbourhood sructure if a fuzzy
point and Moore-Smith convergence, J. Math. Anal. Appl. 76 (1980) 571-
599.
[25] M.A. Rezvi, J. Mahmood, On prime fuzzy bi-ideals in ternary semigroups,
submitted.
[26] M.A. Rezvi, J. Mahmood, Prime fuzzy ideals in ternary semigroups, sub-
mitted.
[27] M.L. Santiago, Regular ternary semigroups. Bull. Calcutta Math. Soc., 82
(1990) 67-71.
[28] M. Shabir, Y.B. Jun, Y. Nawaz, Semigroups characterized by (∈, ∈ ∨q)-
fuzzy ideals, Comput. Math. Appl., 60 (2010) 1473-1493.
[29] M. Shabir, Y.B. Jun, Y. Nawaz, Characterizations of regular semi-
groups by ( , )-fuzzy ideals, Comput. Math. with Appli., (2009),
doi:10.1016/j.camwa.2009.07.062.
[30] F.M. Sioson, Ideal theory in ternary semigroups, Math. Japon., 10 (1965)
63-84.
[31] L.A. Zadeh, Fuzzy Sets, Inform. & Control 8 (1965) 338 -353.