New generalizations of soft sets in soft topological spaces and their applications

Al-Jumaili, Alaa M. F.

doi:10.47974/JIM-1755

Open Access Research Article

New generalizations of soft sets in soft topological spaces and their applications

^*Alaa M. F. Al-JumailiCorresponding authoreps.alaamahmood.farhan@uoanbar.edu.iqDepartment of Mathematics College of Education for Pure Sciences University of AnbarAnbar, IraqView full profile →

* Corresponding author · click or hover a name for details

pp. 705–713Vol. 27Issue 4June 2024DOI: 10.47974/JIM-1755XML

Received:: 17 Oct 2023
Published Online:: 31 May 2024
Article type:: Research Article
Language:: EN
Article no.:: JIM-1755
Pages:: 705–713

Abstract

The fundamental objective of the present this article is to display a complete description of novel ideas of generalized soft open and closed sets in soft topological spaces, which are defined as δ-ß-open and δ-ß-closed sets. Various essential properties and characterizations related to these ideas of generalized soft sets have been studied. In addition, the relationship between several well-known ideas of generalized soft open sets such as soft δ-pre-open, soft δ-semi-open, soft pre-open, soft E-open, soft ß-open sets, and soft δ-ß-open sets over the soft topological spaces have been investigated. Furthermore, several appropriate examples to support our main outcomes have been provided.

Keywords

Softδ-ß-open sets Soft δ-ß-closed sets Soft δ-ß-interior Soft δ-ß-closure

Subject Classifications

Primary (54C08)Secondary (54C10)

References

[1] D. Molodtsov. Soft set theory-first results, Comput. Math. Appl. 37(4-5), 19–31 (1999).
[2] D. Molodtsov, V. Y. Leonov, and D. V. Kovkov, Soft sets technique and its application, Nechetkie Sistemyi Myagkie Vychisleniya, 1(1), 8–39 (2006).
[3] P. K. Maji, R. Biswas, and A. R. Roy, Fuzzy soft sets, Journal of Fuzzy Mathematics, 9 (3), 589–602 (2001).
[4] I. Zorlutuna, M. Akdag, W. K. Min, and S. Atmaca, Remarks on soft topological spaces, Ann. Fuzzy Math. Inf, 3 (2), 171–185 (2012).
[5] P. K. Maji, R. Biswas, R. Roy. An application of soft sets in a decision making problem, Computers and Mathematics with Applications, 44, 1077-1083 (2002).
[6] P. K. Maji R. Biswas, R. Roy. Soft set theory, Computers and Mathematics with Applications, 45, 555-562 (2003).
[7] A. Kharral, B. Ahmad. Mappings on soft classes, New Mathematics and Natural Computations, 7 (3), 471–481 (2011).
[8] M.Shabir, M.Naz, on soft topological spaces, comput. math. appl. 61(7), 1786-99 (2011).
[9] S. Hussain, B. Ahmad. Some Properties of Soft Topological Spaces, Computers and Mathematics with Applications 62, 4058-4067 (2011).
[10] M. Akdag, A. Ozkan. Soft b-open sets and soft b-continuous functions. Math. Sci. 8 (124), (2014), DOI 10.1007/s40096-014-0124-71-7.
[11] M. Akdag, A. Ozkan. Soft α-open sets and soft α-continuous functions. Abstr. Appl. Anal. Art ID 891341, 1-7 (2014).
[12] M. Anjan and B. Debnath. On soft e-Open sets and soft e-Continuity in soft Topological space, Journal of New Theory, (15), 1-18 (2017).
[13] A. M. F. AL. Jumaili and A. Ahmed. Farhan, Another Certain form of Soft Compact and Soft Closed Spaces, 2021 International Conference on Advanced Computer Applications, (ACA2021 Iraq, 978-1-6654-3503-1/21/$31.00 ©2021 IEEE.
[14] Shubham Sharma & Ahmed J. Obaid. Mathematical modelling, analysis and design of fuzzy logic controller for the control of ventilation systems using MATLAB fuzzy logic toolbox, Journal of Interdisciplinary Mathematics, 23:4, 843-849 (2020), DOI: 10.1080/09720502.2020.1727611.
[15] Shelash, Hader Baqer , Ahmad, Hasanain Hamid & Obaid, Ahmed J. On characterizations some of subgroups of the dihedral group D2n, Journal of Discrete Mathematical Sciences and Cryptography, 1-6, DOI: 10.47974/JDMSC-1553.

Views: 229Downloads: 6Citations: 2