Feeble b-Supra Open Soft Sets and the Essential Topological Operators Inspired by Them

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DOI: https://doi.org/10.28924/2291-8639-24-2026-189
Published: Jun 22, 2026
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Tareq M. Al-shami, Husniyah Alzubaidi, Hakeem A. Othman, Seham M. Al-Mekhlafi, Feeble b-Supra Open Soft Sets and the Essential Topological Operators Inspired by Them, Int. J. Anal. Appl., 24 (2026), 189.

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Tareq M. Al-shami, Husniyah Alzubaidi, Hakeem A. Othman, Seham M. Al-Mekhlafi

Abstract

In the article at hand, we expand the classes of feeble α-supra open soft sets, feeble semi-supra open soft sets, and feeble pre-supra open soft sets by introducing the class of feeble b-supra open soft sets. This class is defined by b-supra open subsets of parametric supra topological spaces, so it associates the frameworks of supra topologies and soft supra topologies. We study the basic properties of feeble b-supra open soft sets and point out their behaviours under certain kinds of soft functions and the finite Cartesian product spaces. We also reveal the relationships between this class and certain existing classes, with the aid of illustrative examples. Following this line of research, we make use of the class of feeble b-supra open soft sets and b-closed sets to set up some topological operators in soft settings. We investigate the master features of these operators and derive formulas linking them.

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References

  1. D. Molodtsov, Soft Set Theory–First Results, Comput. Math. Appl. 37 (1999), 19–31. https://doi.org/10.1016/S0898-1221(99)00056-5.
  2. P.K. Maji, A.R. Roy, R. Biswas, An Application of Soft Sets in a Decision Making Problem, Comput. Math. Appl. 44 (2002), 1077–1083. https://doi.org/10.1016/S0898-1221(02)00216-X.
  3. "{O}. Akg"{u}ller, A Soft Set Theoretic Approach to Network Complexity and a Case Study for Turkish Twitter Users, Appl. Soft Comput. 143 (2023), 110344. https://doi.org/10.1016/j.asoc.2023.110344.
  4. N. Malik, M. Shabir, T.M. Al-shami, R. Gul, A. Mhemdi, Medical Decision-Making Techniques Based on Bipolar Soft Information, AIMS Math. 8 (2023), 18185–18205. https://doi.org/10.3934/math.2023924.
  5. O. Dalki li c{c}, Enhancing Relationship Analysis Through Topological Structures Based on Virtual Fuzzy Parameterized Soft Sets, J. Appl. Math. Comput. 72 (2025), 7. https://doi.org/10.1007/s12190-025-02681-z.
  6. O. Dalki li c{c}, Relational Assessment in Hypersoft Sets: a Decision-Maker Driven Approach, Comput. Appl. Math. 45 (2026), 288. https://doi.org/10.1007/s40314-026-03674-9.
  7. P.K. Maji, R. Biswas, A.R. Roy, Soft Set Theory, Comput. Math. Appl. 45 (2003), 555–562. https://doi.org/10.1016/S0898-1221(03)00016-6.
  8. M.I. Ali, Feng Feng, Xiaoyan Liu, W.K. Min, M. Shabir, On Some New Operations in Soft Set Theory, Comput. Math. Appl. 57 (2009), 1547–1553. https://doi.org/10.1016/j.camwa.2008.11.009.
  9. A. .{I}lgin, A. Sezgin, T. Gaketem, Soft Union Tri-bi-ideals of Semigroups, Int. J. Anal. Appl. 23 (2025), 329. https://doi.org/10.28924/2291-8639-23-2025-329.
  10. K. Qin, Z. Hong, On Soft Equality, J. Comput. Appl. Math. 234 (2010), 1347–1355. https://doi.org/10.1016/j.cam.2010.02.028.
  11. M. Shabir, M. Naz, On Soft Topological Spaces, Comput. Math. Appl. 61 (2011), 1786–1799. https://doi.org/10.1016/j.camwa.2011.02.006.
  12. N. c{C}au{g}man, S. Karatac{s}, S. Enginoglu, Soft Topology, Comput. Math. Appl. 62 (2011), 351–358. https://doi.org/10.1016/j.camwa.2011.05.016.
  13. W.K. Min, A Note on Soft Topological Spaces, Comput. Math. Appl. 62 (2011), 3524–3528. https://doi.org/10.1016/j.camwa.2011.08.068.
  14. M. El-Shafei, M. Abo-Elhamayel, T. Al-Shami, Partial Soft Separation Axioms and Soft Compact Spaces, Filomat 32 (2018), 4755–4771. https://doi.org/10.2298/FIL1813755E.
  15. T.M. Al-shami, Z.A. Ameen, A.A. Azzam, M.E. El-Shafei, Soft Separation Axioms via Soft Topological Operators, AIMS Math. 7 (2022), 15107–15119. https://doi.org/10.3934/math.2022828.
  16. M. Arar, T.M. Al-shami, A Holistic Perspective on Soft Separation Axioms: Addressing Open Problems, Rectifications, and Introducing Novel Classifications, Filomat 39 (2025), 3623–3638. https://doi.org/10.2298/FIL2511623A.
  17. W. Alqurashi, Some Separation Axioms via Soft Somewhat Open Sets, Int. J. Anal. Appl. 22 (2024), 205. https://doi.org/10.28924/2291-8639-22-2024-205.
  18. S. Al-Ghour, H. Al-Saadi, Soft Weakly Connected Sets and Soft Weakly Connected Components, AIMS Math. 9 (2023), 1562–1575. https://doi.org/10.3934/math.2024077.
  19. A. Singh, N.S. Noorie, Remarks on Soft Axioms, Ann. Fuzzy Math. Inform. 14 (2017), 503–513. https://doi.org/10.30948/AFMI.2017.14.5.503.
  20. A. Ayg"unou{g}lu, H. Ayg"un, Some Notes on Soft Topological Spaces, Neural Comput. Appl. 21 (2011), 113–119. https://doi.org/10.1007/s00521-011-0722-3.
  21. T. Hida, A Comparison of Two Formulations of Soft Compactness, Ann. Fuzzy Math. Inform. 8 (2014), 511–525.
  22. T.M. Al-shami, A. Mhemdi, R. Abu-Gdairi, M.E. El-Shafei, Compactness and Connectedness via the Class of Soft Somewhat Open Sets, AIMS Math. 8 (2023), 815–840. https://doi.org/10.3934/math.2023040.
  23. A. Kharal, B. Ahmad, Mappings on Soft Classes, New Math. Nat. Comput. 07 (2011), 471–481. https://doi.org/10.1142/S1793005711002025.
  24. I. Zorlutuna, H. c{C}akir, On Continuity of Soft Mappings, Appl. Math. Inf. Sci. 9 (2015), 403–409. https://doi.org/10.12785/amis/090147.
  25. T.M. Al-shami, L.D.R. Kov cinac, Almost Soft Menger and Weakly Soft Menger Spaces, Appl. Comput. Math. 21 (2022), 35–51. https://doi.org/10.30546/1683-6154.21.1.2022.35.
  26. S. Al Ghour, Z.A. Ameen, Maximal Soft Compact and Maximal Soft Connected Topologies, Appl. Comput. Intell. Soft Comput. 2022 (2022), 9860015. https://doi.org/10.1155/2022/9860015.
  27. I. Demir, An Approach to the Concept of Soft Vietoris Topology, Int. J. Anal. Appl. 12 (2016), 198–206.
  28. I. Demir, R. Bozyigit, Some Fixed Soft Point Theorems on a New Soft Topology Related to a Self Soft Mapping, Ital. J. Pure Appl. Math. 42 (2019), 36–50.
  29. A. Rawshdeh, H. Al-Jarrah, T. Al-Shami, Soft Expandable Spaces, Filomat 37 (2023), 2845–2858. https://doi.org/10.2298/FIL2309845R.
  30. M. Akdag, A. Ozkan, Soft $alpha$-Open Sets and Soft $alpha$-Continuous Functions, Abstr. Appl. Anal. 2014 (2014), 891341. https://doi.org/10.1155/2014/891341.
  31. S. Al Ghour, Boolean Algebra of Soft $Q$-Sets in Soft Topological Spaces, Appl. Comput. Intell. Soft Comput. 2022 (2022), 5200590. https://doi.org/10.1155/2022/5200590.
  32. H.H. Al-Jarrah, A. Rawshdeh, T.M. Al-shami, On Soft Compact and Soft Lindel"of Spaces via Soft Regular Closed Sets, Afrika Mat. 33 (2022), 23. https://doi.org/10.1007/s13370-021-00952-z.
  33. B. Chen, Soft Semi-Open Sets and Related Properties in Soft Topological Spaces, Appl. Math. Inf. Sci. 7 (2013), 287–294. https://doi.org/10.12785/amis/070136.
  34. T.M. Al-Shami, L.D.R. Kocinac, The Equivalence between the Enriched and Extended Soft Topologies, Appl. Comput. Math. 18 (2019), 149–162.
  35. A.S. Mashhour, A.A. Allam, F.S. Mahmoud, F.H. Kheder, On Supra Topological Spaces, Indian J. Pure Appl. Math. 14 (1983), 502–510.
  36. T.M. Al-Shami, Complete Hausdorffness and Complete Regularity on Supra Topological Spaces, J. Appl. Math. 2021 (2021), 5517702. https://doi.org/10.1155/2021/5517702.
  37. M.E. El-Shafei, A.H. Zakari, T.M. Al-Shami, Some Applications of Supra Preopen Sets, J. Math. 2020 (2020), 9634206. https://doi.org/10.1155/2020/9634206.
  38. M.E. El-Shafei, M. Abo-elhamayel, T. Al-shami, On Supra $R$-Open Sets and Some Applications on Topological Spaces, J. Prog. Res. Math. 8 (2016), 1237–1248.
  39. A.M. Kozae, M. Shokry, M. Zidan, Supra Topologies for Digital Plane, AASCIT Commun. 3 (2016), 1–10.
  40. T.M. Al-Shami, I. Alshammari, Rough Sets Models Inspired by Supra-Topology Structures, Artif. Intell. Rev. 56 (2022), 6855–6883. https://doi.org/10.1007/s10462-022-10346-7.
  41. S.A. El-Sheikh, A.M. Abd El-latif, Decompositions of Some Types of Supra Soft Sets and Soft Continuity, Int. J. Math. Trends Technol. 9 (2014), 37–56. https://doi.org/10.14445/22315373/IJMTT-V9P504.
  42. T.M. Al-shami, J.C.R. Alcantud, A.A. Azzam, Two New Families of Supra-Soft Topological Spaces Defined by Separation Axioms, Mathematics 10 (2022), 4488. https://doi.org/10.3390/math10234488.
  43. A.M. Abd El-latif, Decomposition of Supra Soft Locally Closed Sets and Supra SLC-Continuity, Int. J. Nonlinear Anal. Appl. 9 (2018), 13–25. https://doi.org/10.22075/ijnaa.2018.12727.1651.
  44. A.M. Abd El-latif, A.A. Azzam, R. Abu-Gdairi, M. Aldawood, M.H. Alqahtani, New Versions of Maps and Connected Spaces via Supra Soft SD-Operators, PLoS One 19 (2024), e0304042. https://doi.org/10.1371/journal.pone.0304042.
  45. A.M. Abd El-latif, M.H. Alqahtani, F.A. Gharib, Strictly Wider Class of Soft Sets via Supra Soft $delta$-Closure Operator, Int. J. Anal. Appl. 22 (2024), 47. https://doi.org/10.28924/2291-8639-22-2024-47.
  46. F.A. Abu Shaheen, T.M. Al-Shami, M. Arar, O.G. El-Barbary, Supra Finite Soft-Open Sets and Applications to Operators and Continuity, J. Math. Comput. Sci. 35 (2024), 120–135. https://doi.org/10.22436/jmcs.035.02.01.
  47. A.M. Abd El-latif, Novel Types of Supra Soft Operators via Supra Soft sd-Sets and Applications, AIMS Math. 9 (2024), 6586–6602. https://doi.org/10.3934/math.2024321.
  48. D. Abuzaid, S. Al-Ghour, Supra Soft Omega-Open Sets and Supra Soft Omega-Regularity, AIMS Math. 10 (2025), 6636–6651. https://doi.org/10.3934/math.2025303.
  49. A.M. Abd El-latif, R. Abu-Gdairi, A. Azzam, F. Gharib, K. Aldwoah, Supra Soft Somewhat Open Sets: Characterizations and Continuity, Eur. J. Pure Appl. Math. 18 (2025), 5863. https://doi.org/10.29020/nybg.ejpam.v18i2.5863.
  50. A.M. Abd El-latif, Specific Types of Lindel"{o}fness and Compactness Based on Novel Supra Soft Operator, AIMS Math. 10 (2025), 8144–8164. https://doi.org/10.3934/math.2025374.
  51. T.M. Al-shami, S. Saleh, M. Jameel, Defining a New Type of $alpha$-Supra Open Soft Sets Using Parametric Supra Topologies, Sana'a Univ. J. Appl. Sci. Technol. 4 (2026), 1950–1958. https://doi.org/10.59628/jast.v4i4.2704.
  52. T.M. Al-shami, F.A. Abu Shaheen, A.A. Azzam, M. Omran, Feeble Semi-Supra Open Soft Sets and Their Applications on Supra Soft Topologies, Int. J. Anal. Appl. 24 (2026), 70. https://doi.org/10.28924/2291-8639-24-2026-70.
  53. T.M. Al-shami, A.A. Azzam, Expanding Soft Supra-Topology by Using Pre Supra-Open Subsets Inspired by Its Parametric Supra-Topologies, Submitted.
  54. T.M. Al-shami, A. Mhemdi, R. Abu-Gdairi, A Novel Framework for Generalizations of Soft Open Sets and Its Applications via Soft Topologies, Mathematics 11 (2023), 840. https://doi.org/10.3390/math11040840.
  55. T.M. Al-shami, M. Arar, R. Abu-Gdairi, Z.A. Ameen, On Weakly Soft $beta$-Open Sets and Weakly Soft $beta$-Continuity, J. Intell. Fuzzy Syst. 45 (2023), 6351–6363. https://doi.org/10.3233/JIFS-230858.
  56. T.M. Al-shami, R.A. Hosny, R. Abu-Gdairi, M. Arar, A Novel Approach to Study Soft Preopen Sets Inspired by Classical Topologies, J. Intell. Fuzzy Syst. 45 (2023), 6339–6350. https://doi.org/10.3233/JIFS-230191.
  57. T.M. Al-shami, A. Mhemdi, A Weak Form of Soft $alpha$-Open Sets and Its Applications via Soft Topologies, AIMS Math. 8 (2023), 11373–11396. https://doi.org/10.3934/math.2023576.
  58. T.M. Al-shami, A. Mhemdi, On Soft Parametric Somewhat-Open Sets and Applications via Soft Topologies, Heliyon 9 (2023), e21472. https://doi.org/10.1016/j.heliyon.2023.e21472.
  59. S. Nazmul, S.K. Samanta, Neighbourhood Properties of Soft Topological Spaces, Ann. Fuzzy Math. Inform. 6 (2013), 1–15.
  60. F. Feng, C. Li, B. Davvaz, M.I. Ali, Soft Sets Combined with Fuzzy Sets and Rough Sets: A Tentative Approach, Soft Comput. 14 (2009), 899–911. https://doi.org/10.1007/s00500-009-0465-6.
  61. T.M. Al-shami, Homeomorphism and Quotient Mappings in Infrasoft Topological Spaces, J. Math. 2021 (2021), 3388288. https://doi.org/10.1155/2021/3388288.