Two important methods are used to transfer algebraic substructures to soft set theory. In the first method, the soft substructure of an algebraic structure is obtained, while in the second method a soft substructure of a soft algebraic structure is obtained. In this paper, we transfer the radical structure of an ideal to a soft set theory in a commutative ring and a semigroup by considering both methods.
AcarU., KoyuncuF. and TanayB., Soft sets and soft rings, Computers and Mathematics with Applications59 (2010), 3458–3463.
2.
AktasH. and CagmanN., Soft sets and soft groups, Information Sciences177 (2007), 2726–2735.
3.
AliM.I., FengF., LiuX., MinW.K. and ShabirM., On some new operations soft set theory, Computers and Mathematics with Applications57(9) (2009), 1547–1553.
4.
AliM.I., ShabirM. and ShumK.P., On soft ideals over semigroups, Southeast Asian Bulletin of Mathematics34 (2010), 595–610.
5.
AtagunA.O. and SezginA., Soft substructures of rings, fields and modules, Computers and Mathematics with Applications61(3) (2011), 592–601.
6.
AtagunA.O and AygunE., Groups of soft sets, Journal of Intelligent Systems30 (2016), 729–733.
7.
AtiyahM. and MacdonaldI.G., Introduction to Commutative Algebra, Addison Wesley, 1994.
8.
ChinnaduraiaV. and KadalarasiaS., Fuzzy soft ideals of near-subraction semigroups, Journal of Linear and Topological Algebra5(3) (2016), 175–186.
9.
FengF., JunY.B. and ZhaoX.Z., Soft semirings, Computers and Mathematics with Applications56 (2008), 2621–2628.
10.
HowieJ.M., An Introduction to Semigroup Theory, Academic Press, 1976.
11.
MajiP.K., BiswasR. and RoyR., Soft set theory, Computers and Mathematics with Applications45 (2003), 555–562.
12.
MajiP.K., BiswasR. and RoyR., An application of soft sets in a decision-making problem, Computers and Mathematics with Applications44 (2003), 1077–1083.
13.
MolodtsovD., Soft set theory first results, Computers and Mathematics with Applications37 (1999), 19–31.
14.
SezginA., AtagunA.O. and AygunE., A note on soft near-rings and idealistic soft near-rings, Filomat25(1) (2011), 53–68.
15.
SezginA. and AtagunA.O., Soft groups and normalistic soft groups, Computers and Mathematics with Applications62(2) (2011), 1457–1467.
16.
ShahT. and MedhitS., Primary decomposition in a soft ring and a soft module, Iranian Journal of Science and Technology38A3 (2014), 311–320.
17.
ZadehL.A., Fuzzy sets, Information and Control8(3) (1965), 338–353.
18.
ZouY. and XiaoZ., Data analysis approaches of soft sets under incomplete informations, Knowledge- Based Systems21 (2008), 941–945.