Radicals of soft intersectıonal ideals in semigroups
Abstract
In this paper, we introduce IS-radical, IS-quasi radical, IS-interior radical and IS-nil radical in semigroups. We obtain radical structures that will contribute to the theoretical studies of soft sets. We consider the ideal structures of intersectional soft sets in semigroups and we define IS-radical, IS-quasi radical, IS-interior radical and IS-nil radical. We use two different methods to define the soft radicals and give the results. In our study, we also give several examples and propositions to see differences among these structures.
Keywords
Soft radical, IS-radical, IS-quasi radical, IS-interior radical, IS-nil radical
References
- [1] Molodtsov D., Soft Set Theory First Results, Comput. Math. Appl., 37 (1999) 19–31.
- [2] Maji P.K., Biswas R., Roy, R., An Application of Soft Sets in A Decision-Making Problem, Comput. Math. Appl., 44 (2002) 1077–1083.
- [3] Maji P.K., Biswas R., Roy R., Soft Set Theory, Comput. Math. Appl., 45 (2003) 555–562.
- [4] Feng F., Li Y., Fotea V.L., Application of Level Soft Sets in Decision Making Based on İnterval-Valued Fuzzy Soft Sets, Comput. Math. Appl., 60 (2010) 1756-1767.
- [5] Feng F., Li Y., Cagman N. Generalized Uni–İnt Decision Making Schemes Based on Choice Value Soft Sets, Eur. J. Oper. Res., 220 (2012) 162–170.
- [6] Cagman N., Enginoglu S., Soft Set Theory and Uni–İnt Decision Making, Eur. J. Oper. Res., 207 (2010) 848–855.
- [7] Aygun E., Soft Matrix Product and Soft Cryptosystem, Filomat, 32:19 (2018) 6519–6530.
- [8] Aygun E., Kamacı H., Some Generalized Operations in Soft Set Theory and Their Role in Similarity and Decision Making, J. Intell. Fuzzy Syst., 36 (2019) 6537–6547.
- [9] Aktas H., Cagman N., Soft Sets and Soft Groups, Inform. Sci., 177 (2007) 2726-2735.
- [10] Feng F., Jun Y.B., Zhao X.Z. Soft Semirings, Comput. Math. Appl., 56 (2008) 2621–2628.