Single-Valued Neutrosophic Roughness via Ideals

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-22-2024-38
Published: Feb 27, 2024
Cite as:
Fahad Alsharari, Single-Valued Neutrosophic Roughness via Ideals, Int. J. Anal. Appl., 22 (2024), 38.

Main Article Content

Fahad Alsharari

Abstract

In this paper, we connect the idea of single-valued neutrosophic ideal to the concept of single-valued neutrosophic approximation space to define the concept of single-valued neutrosophic ideal approximation spaces. We present the single-valued neutrosophic ideal approximation interior operator intψΦ and the single-valued neutrosophic ideal approximation closure operator clψΦ, and we present the single-valued neutrosophic ideal approximation preinterior operator pintψΦ and the single-valued neutrosophic ideal approximation pre-closure operator pclψΦ about this concerning single-valued neutrosophic ideal defined on the single-valued neutrosophic approximation space (χ˜,ϕ) related with some single-valued neutrosophic set ψ∈ξχ˜. Also, we present single-valued neutrosophic separation axioms, single-valued neutrosophic connectedness, and single-valued neutrosophic compactness in single-valued neutrosophic approximation spaces and single-valued neutrosophic ideal approximation spaces as well, and prove the associations in between.

Article Details

References

  1. F. Smarandache, A Unifying Field in Logics, Neutrosophy: Neutrosophic Probability, Set and Logic, American Research Press, Rehoboth, (1999).
  2. A.A. Salama, F. Smarandache, Neutrosophic Crisp Set Theory, The Educational Publisher, Columbus, 2015.
  3. A.A. Salama, S.A. Alblowi, Neutrosophic Set and Neutrosophic Topological Spaces, IOSR J. Math. 3 (2012), 31–35.
  4. H. Wang, F.Y. Smarandache, Q. Zhang, Single valued neutrosophic sets, Multispace Multistruct. 4 (2010), 410–413.
  5. Y. Saber, F. Alsharari, F. Smarandache, On Single-Valued Neutrosophic Ideals in Šostak Sense, Symmetry. 12 (2020), 193. https://doi.org/10.3390/sym12020193.
  6. Y. Saber, F. Alsharari, F. Smarandache, M. Abdel-Sattar, Connectedness and Stratification of Single-Valued Neutrosophic Topological Spaces, Symmetry. 12 (2020), 1464. https://doi.org/10.3390/sym12091464.
  7. F. Alsharari, Y.M. Saber, F. Smarandache, Compactness on Single-Valued Neutrosophic Ideal Topological Spaces, Neutrosophic Sets Syst. 41 (2021), 127–145.
  8. Y. Saber, F. Alsharari, F. Smarandache, M. Abdel-Sattar, On Single Valued Neutrosophic Regularity Spaces, Computer Model. Eng. Sci. 130 (2022), 1625–1648. https://doi.org/10.32604/cmes.2022.017782.
  9. F. Alsharari, Y.M. Saber, GΘ*τiτj-Fuzzy Closure Operator, New Math. Nat. Comput. 16 (2020), 123–141. https://doi.org/10.1142/s1793005720500088.
  10. F. Alsharari, Y.M. Saber, Separation axioms on fuzzy ideal topological spaces in Šostak sense, Int. J. Adv. Appl. Sci. 7 (2020), 78–84. https://doi.org/10.21833/ijaas.2020.02.011.
  11. Y.M. Saber, F. Alsharari, Generalized Fuzzy Ideal Closed Sets on Fuzzy Topological Spaces in Šostak Sense, Int. J. Fuzzy Logic Intell. Syst. 18 (2018), 161–166. https://doi.org/10.5391/ijfis.2018.18.3.161.
  12. Z. Pawlak, Rough sets, Int. J. Comput. Inf. Sci. 11 (1982), 341–356. https://doi.org/10.1007/bf01001956.
  13. X. Chen, Q. Li, Construction of Rough Approximations in Fuzzy Setting, Fuzzy Sets Syst. 158 (2007), 2641–2653. https://doi.org/10.1016/j.fss.2007.05.016.
  14. D. Dubois, H. Prade, Rough Fuzzy Sets and Fuzzy Rough Sets, Int. J. Gen. Syst. 17 (1990), 191–209. https://doi.org/10.1080/03081079008935107.
  15. Z. Li, T. Xie, Roughness of Fuzzy Soft Sets and Related Results, Int. J. Comput. Intell. Syst. 8 (2015), 278–296. https://doi.org/10.1080/18756891.2015.1001951.
  16. G. Liu, Generalized Rough Sets Over Fuzzy Lattices, Inf. Sci. 178 (2008), 1651–1662. https://doi.org/10.1016/j.ins.2007.11.010.
  17. W. Wu, Generalized Fuzzy Rough Sets, Inf. Sci. 151 (2003), 263–282. https://doi.org/10.1016/s0020-0255(02)00379-1.
  18. Z. Pei, D. Pei, L. Zheng, Topology vs Generalized Rough Sets, Int. J. Approx. Reason. 52 (2011), 231–239. https://doi.org/10.1016/j.ijar.2010.07.010.
  19. I. Ibedou, S.E. Abbas, Fuzzy Rough Sets With a Fuzzy Ideal, J. Egypt. Math. Soc. 28 (2020), 36. https://doi.org/10.1186/s42787-020-00096-2.
  20. M. Irfan Ali, A Note on Soft Sets, Rough Soft Sets and Fuzzy Soft Sets, Appl. Soft Comput. 11 (2011), 3329–3332. https://doi.org/10.1016/j.asoc.2011.01.003.
  21. D. Boixader, J. Jacas, J. Recasens, Upper and Lower Approximations of Fuzzy Sets, Int. J. Gen. Syst. 29 (2000), 555–568. https://doi.org/10.1080/03081070008960961.
  22. W.Z. Wu, A Study on Relationship Between Fuzzy Rough Approximation Operators and Fuzzy Topological Spaces, in: L. Wang, Y. Jin (Eds.), Fuzzy Systems and Knowledge Discovery, Springer, Berlin, Heidelberg, 2005: pp. 167–174. https://doi.org/10.1007/11539506_21.
  23. A.M. Abd El-Latif, Generalized Soft Rough Sets and Generated Soft Ideal Rough Topological Spaces, J. Intell. Fuzzy Syst. 34 (2018), 517–524. https://doi.org/10.3233/jifs-17610.
  24. J. Mahanta, P.K. Das, Fuzzy Soft Topological Spaces, J. Intell. Fuzzy Syst. 32 (2017), 443–450. https://doi.org/10.3233/jifs-152165.
  25. C.L. Chang, Fuzzy Topological Spaces, J. Math. Anal. Appl. 24 (1968), 182–190. https://doi.org/10.1016/0022-247x(68)90057-7.
  26. J. Ye, A Multicriteria Decision-Making Method Using Aggregation Operators for Simplified Neutrosophic Sets, J. Intell. Fuzzy Syst. 26 (2014), 2459–2466. https://doi.org/10.3233/ifs-130916.
  27. H.L. Yang, Z.L. Guo, Y. She, X. Liao, On Single Valued Neutrosophic Relations, J. Intell. Fuzzy Syst. 30 (2016), 1045–1056. https://doi.org/10.3233/ifs-151827.