Connectedness in Single-Valued Neutrosophic Soft Grill Topological Spaces

Main Article Content

Yaser Saber

Abstract

The incentive of this article is to continue discovering more interesting results and concepts related to the single-valued neutrosophic soft topological spaces. The concept of the single-valued neutrosophic soft operator φ created from a single-valued neutrosophic soft grill (Kσ, Kτ, Kδ) and a single-valued neutrosophic soft topological space (B, ~T~σ, ~T~ς, ~T~δ) is presented. Connectedness of single-valued neutrosophic soft topological spaces with single-valued neutrosophic soft grills is given. Moreover, the concept of γ-connectedness associated with a single-valued neutrosophic soft operator γ is extended on the set B.

Article Details

References

  1. S.E. Abbas, E. El-sanowsy, A. Atef, On Fuzzy Soft Irresolute Functions, J. Fuzzy. Math. 24 (2016), 465–482.
  2. S.E. Abbas, E. El-sanowsy, A. Atef, Stratified Modeling in Soft Fuzzy Topological Structures, Soft. Comput. 22 (2018), 1603–1613. https://doi.org/10.1007/s00500-018-3004-5.
  3. S.A. Abd El-Baki, Y.M. Saber, Fuzzy Extremally Disconnected Ideal Topological Spaces, Int. J. Fuzzy Log. Intell. Syst. 10 (2010), 1–6.
  4. S. Acharjee, B.C. Tripathy, Some Results on Soft Bitopology, Bol. Soc. Paran. Mat. 35 (2017), 269–279. https://doi.org/10.5269/bspm.v35i1.29145.
  5. B. Ahmad, A. Kharal, On Fuzzy Soft Sets, Adv. Fuzzy Syst. 2009 (2009), 586507. https://doi.org/10.1155/2009/586507.
  6. F. Alsharari, Y.M. Saber, GΘ ?τj τi -Fuzzy Closure Operator, New Math. Nat. Comput. 16 (2020), 123–141. https://doi.org/10.1142/s1793005720500088.
  7. F. Alsharari, Y.M. Saber, F. Smarandache, Compactness on Single-Valued Neutrosophic Ideal Topological Spaces, Neutrosophic Sets Syst. 41 (2021), 127–145.
  8. A. Aygünoglu, V. Çetkin, H. Aygün, An Introduction to Fuzzy Soft Topological Spaces, Hacettepe J. Math. Stat. 43 (2014), 193—204. https://doi.org/10.15672/HJMS.2015449418.
  9. V. Çetkin, A.P. Šostak, H. Aygün, An Approach to the Concept of Soft Fuzzy Proximity, Abstr. Appl. Anal. 2014 (2014), 782583. https://doi.org/10.1155/2014/782583.
  10. C. Gunduz (Aras), S. Bayramov, Some Results on Fuzzy Soft Topological Spaces, Math. Probl. Eng. 2013 (2013), 835308. https://doi.org/10.1155/2013/835308.
  11. A. Kharal, B. Ahmad, Mappings on Fuzzy Soft Classes, Adv. Fuzzy Syst. 2009 (2009), 407890. https://doi.org/10.1155/2009/407890.
  12. B.K. Maji, R. Biswas, A.R. Roy, Fuzzy soft sets, J. Fuzzy Math. 9 (2001), 589–602.
  13. P.K. Maji, A.R. Roy, R. Biswas, An Application of Soft Sets in a Decision Making Problem, Computers Math. Appl. 44 (2002), 1077–1083. https://doi.org/10.1016/s0898-1221(02)00216-x.
  14. D. Molodtsov, Soft Set Theory–First Results, Comput. Math. Appl. 37 (1999), 19–31. https://doi.org/10.1016/s0898-1221(99)00056-5.
  15. D.A. Molodtsov, Describing Dependences Using Soft Sets, J. Comput. Syst. Sci. Int. 40 (2001), 975–982.
  16. Y.M. Saber, M.A. Abdel-Sattar, Ideals on Fuzzy Topological Spaces, Appl. Math. Sci. 8 (2014), 1667–1691. https://doi.org/10.12988/ams.2014.33194.
  17. Y.M. Saber, F. Alsharari, F. Smarandache, An Introduction to Single-Valued Neutrosophic Soft Topological Structure, Soft Comput. 26 (2022), 7107–7122. https://doi.org/10.1007/s00500-022-07150-4.
  18. Y.M. Saber, F. Alsharari, Generalized Fuzzy Ideal Closed Sets on Fuzzy Topological Spaces in Sostak Sense, Int. J. Fuzzy Logic Intell. Syst. 18 (2018), 161–166. https://doi.org/10.5391/ijfis.2018.18.3.161.
  19. Y.M. Saber, F. Alsharari, F. Smarandache, On Single-Valued Neutrosophic Ideals in Sostak Sense, Symmetry. 12 (2020), 193. https://doi.org/10.3390/sym12020193.
  20. Y.M. 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.
  21. Y.M. Saber, F. Alsharari, F. Smarandache, M. Abdel-Sattar, On Single Valued Neutrosophic Regularity Spaces, Comput. Model. Eng. Sci. 130 (2022), 1625–1648. https://doi.org/10.32604/cmes.2022.017782.
  22. A.A. Salama, S.A. Alblowi, Neutrosophic Set and Neutrosophic Topological Spaces, IOSR J. Math. 3 (2012), 31–35. https://doi.org/10.9790/5728-0343135.
  23. A.A. Salama, F. Smarandache, Neutrosophic Crisp Set Theory, Educational Publisher, Columbus, 2015.
  24. F. Smarandache, A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability and Statistics, 6th ed., InfoLearnQuest: Ann Arbor, MI, USA, (2007).
  25. A.P. Šostak, On a Fuzzy Topological Structure, Rend. Circ. Mat. Palermo. Ser. II, Suppl. 11 (1985), 89–103. http://dml.cz/dmlcz/701883.
  26. B. Tanay, M.B. Kandemir, Topological Structure of Fuzzy Soft Sets, Comput. Math. Appl. 61 (2011), 2952–2957. https://doi.org/10.1016/j.camwa.2011.03.056.
  27. H. Wang, F. Smarandache, Y.Q. Zhang, R. Sunderraman, Single Valued Neutrosophic Sets, Multispace Multistruct. 4 (2010), 410–413.
  28. 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.
  29. 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.
  30. L.A. Zadeh, Fuzzy Sets, Inform. Control. 8 (1965), 338–353. https://doi.org/10.1016/s0019-9958(65)90241-x.
  31. A.M. Zahran, S.A.A. El-Baki, Y.M. Saber, Decomposition of Fuzzy Ideal Continuity via Fuzzy Idealization, Int. J. Fuzzy Logic Intell. Syst. 9 (2009), 83–93. https://doi.org/10.5391/ijfis.2009.9.2.083.
  32. A.M. Zahran, S.E. Abbas, S.A. Abd El-baki, Y.M. Saber, Decomposition of Fuzzy Continuity and Fuzzy Ideal Continuity via Fuzzy Idealization, Chaos Solitons Fractals. 42 (2009), 3064–3077. https://doi.org/10.1016/j.chaos.2009.04.010.