Soft k-Uni Ideals of Semirings and its Algebraic Applications

Year 2018, , 281 - 294, 30.12.2018

Filiz Çıtak

https://doi.org/10.21597/jist.410038

Cited By: 3

Abstract

In this paper, firstly, information about soft set introduced by Molodtsov is given. Then, the operations

on the soft set are introduced. After then a definition of soft uni-k-ideal of a semiring by using the union operation

of sets is given. Finally, some algebraic applications by using soft uni-k-ideal are investigated.

Keywords

Soft sets, k-ideals, soft uni-ideals, soft k-uni ideals

Yarıhalkaların Esnek k-Birleşimsel İdealleri ve Cebirsel Uygulamaları

Abstract

Bu çalışmada, ilk olarak Molodtsov tarafından ortaya atılan esnek küme teorisi hakkında bilgi verildi. Sonra

esnek küme üzerindeki işlemler tanıtıldı. Daha sonra kümelerin birleşim işlemi kullanılarak bir yarıhalkanın esnek

birleşimsel k-ideal tanımı verildi. Son olarak, esnek birleşimsel k-ideali kullanılarak bazı cebirsel uygulamalar

araştırıldı.

Keywords

Esnek kümeler, k-idealler, esnek birleşimsel idealler, esnek k-birleşimsel idealler

References

• Acar U., Koyuncu F. and Tanay B., Soft Sets and Soft Rings, Computers and Mathematics with Applications., 59 (2010) 3458-3463.
• Aktaş H. and Çağman N., Soft Sets and Soft Groups, Information Sciences, 177 (2007) 2726-2735.
• Ali M.I., Feng F., Liu X., Min W.K. and Shabir M., On Some New Operations in Soft Set Theory, Computers and Mathematics with Application, 57 (2009) 1547-1553.
• Ali M.I., Shabir M. and Naz M., Algebraic Structures of Soft Sets Associated with New Operations, Computers and Mathematics with Application, 61 (2011) 2647-2654.
• Atagün A.O. and Sezgin A., Int-Soft Substructures of Groups and Semirings with Applications, Applied Mathematics & Information Sciences 11-1 (2017) 105-113.
• Çağman N. and Enginoğlu S., Soft Set Theory and uni-int Decision Making, European Journal of Operational Research 207 (2010) 848-855.
• Çağman N., Çıtak F. and Aktaş H., Soft int-group and its Applications to Group Theory, Neural Computing and Applications 21 (2012) 151-158.
• Çıtak F. and Çağman N., Soft int-rings and its Algebraic Applications, Journal of Intelligent and Fuzzy Systems 28 (2015) 1225-1233.
• Feng F., Jun Y.B. and Zhao X., Soft Semirings, Computers and Mathematics with Applications 56 (2008) 2621-2628.
• Golan J.S., The Theory of Semirings with Applications in Mathematics and Theoritical Computer Science, Longman Scientific and Technical, U.K., 1992.
• Jana C. and Pal M., Applications of New Soft Intersection Set on Groups, Annals of Fuzzy Mathematics and Informatics 11-6 (2016) 923-944.
• Jun Y.B. and Park C.H., Applications of Soft Sets in Ideal Theory of BCK/BCI-Algebras, Information Sciences 178 (2008) 2466-2475.
• Jun Y.B., Lee K.J. and Zhan J., Soft p-Ideals of Soft BCI-Algebras, Computers and Mathematics with Applications 58 (2009) 2060-2068.
• La Torre D.R., On h-Ideals and k-Ideals in Hemirings, Publicationes Mathematicae Debrecen 12 (1965) 219-226.
• Lee J.H., Kong I.S., Kim H.S. and Jung J.U., Generalized int-Soft Subsemigroups, Annals of Fuzzy Mathematics and Informatics 8-6 (2014) 869-887.
• Ma X., Zhan J. and Ali M.I., Applications of a Kind of Novel Z-Soft Fuzzy Rough Ideals to Hemirings, Journal of Intelligent and Fuzzy Systems 32-3 (2017) 1-12.
• Maji P.K., Biswas R. and Roy A.R., Soft Set Theory, Computers and Mathematics with Applications 45 (2003) 555-562.
• Molodtsov D.A., Soft Set Theory-First Results, Computers and Mathematics with Applications 37 (1999) 19-31.
• Sezgin A., Çağman N. and Atagün A.O., Uni-Soft Substructures of Groups, Annals of Fuzzy Mathematics and Informatics 9-2 (2015) 235-246.
• Sezgin A., Characterizations of Certain Classes of Semigroups via Soft Intersection Ideals, Italian Journal of Pure and Applied Mathematics 38-1 (2017).
• Sun Q.M., Zhang Z.L. and Liu J., Soft Sets and Soft Modules, Lecture Notes in Computer Science 5009 (2008) 403-409.
• Zhan J. and Jun Y.B., Soft BL-Algebras Based on Fuzzy Sets, Computers and Mathematics with Applications 59-6 (2010) 2037-2046.
• Zhan J. and Xu Y., Soft Lattice Implication Algebras Based on Fuzzy Sets, Hacettepe Journal of Mathematics and Statistics 40-4 (2011) 483-492.