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Shabir, Muhammad; Ali, Muhammad Irfan

Soft ideals and generalized fuzzy ideals in semigroups. (English) Zbl 1178.20061

New Math. Nat. Comput. 5, No. 3, 599-615 (2009).
Summary: A soft semigroup over a semigroup is a collection of subsemigroups. Similarly, a soft ideal over a semigroup is a collection of ideals of the semigroup. As a natural consequence, the idea of soft ideals of a soft semigroup originates. Soft ideals over a semigroup with a fixed set of parameters form a distributive lattice. Soft sets are a very handy tool. Soft ideals over a semigroup characterize generalized fuzzy ideals and fuzzy ideals with thresholds of \(S\).

Cited in 13 Documents

MSC:

20N25 Fuzzy groups
20M12 Ideal theory for semigroups

Keywords:

soft sets; soft semigroups; soft ideals; fuzzy ideals; generalized fuzzy ideals; fuzzy ideals with thresholds
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\textit{M. Shabir} and \textit{M. I. Ali}, New Math. Nat. Comput. 5, No. 3, 599--615 (2009; Zbl 1178.20061)
Full Text: DOI

References:

[1] Ahsan J., The Journal of Fuzzy Mathematics 6
[2] DOI: 10.1016/0165-0114(93)90145-8 · Zbl 0793.20067
[3] DOI: 10.1016/0165-0114(93)90441-J · Zbl 0796.16038
[4] DOI: 10.1016/j.ins.2006.12.008 · Zbl 1119.03050
[5] DOI: 10.1016/S0165-0114(98)00029-3 · Zbl 0948.20049
[6] DOI: 10.1016/S0165-0114(97)00158-9 · Zbl 0931.20057
[7] DOI: 10.1016/0165-0114(95)00157-3 · Zbl 0870.20055
[8] DOI: 10.1016/0165-0114(95)00202-2 · Zbl 0878.16025
[9] Biswas R., Bull. Polish Acad. of Sciences 42
[10] DOI: 10.1016/j.camwa.2004.10.036 · Zbl 1074.03510
[11] DOI: 10.1007/s00500-005-0472-1 · Zbl 1084.16040
[12] DOI: 10.1016/j.ins.2003.10.001 · Zbl 1072.16042
[13] Howie J. M., An Introduction to Semigroup Theory (1976) · Zbl 0355.20056
[14] DOI: 10.1016/j.ins.2005.09.002 · Zbl 1102.20058
[15] DOI: 10.1155/S0161171201006299 · Zbl 1004.20061
[16] Kim Y. H., The J. of Fuzzy Mathematics 12 pp 561–
[17] DOI: 10.1016/S0020-0255(96)00274-5 · Zbl 0916.20046
[18] DOI: 10.1016/0020-0255(91)90037-U · Zbl 0714.20052
[19] DOI: 10.1016/S0898-1221(02)00216-X · Zbl 1044.90042
[20] DOI: 10.1016/S0898-1221(03)00016-6 · Zbl 1032.03525
[21] Maji P. K., J. of Compt. and Appl. Math. 203 pp 412–
[22] DOI: 10.1016/0022-247X(80)90048-7 · Zbl 0447.54006
[23] DOI: 10.1016/S0898-1221(99)00056-5 · Zbl 0936.03049
[24] DOI: 10.1016/0165-0114(89)90266-2 · Zbl 0677.16021
[25] DOI: 10.1007/BF02936584 · Zbl 1076.16516
[26] DOI: 10.1007/BF01001956 · Zbl 0501.68053
[27] DOI: 10.1016/0022-247X(71)90199-5 · Zbl 0194.05501
[28] DOI: 10.1155/IJMMS.2005.163 · Zbl 1076.20048
[29] DOI: 10.1016/j.ins.2004.12.010 · Zbl 1088.20041
[30] DOI: 10.1016/S0020-0255(98)00012-7 · Zbl 0934.03071
[31] DOI: 10.1016/S0165-0114(02)00443-8 · Zbl 1024.20048
[32] Zadeh L. A., Inform. and Control 8 pp 267–
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.