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AIMS Mathematics

2024, Volume 9, Issue 3: 6379-6410. doi: 10.3934/math.2024311
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Research article

Soft closure spaces via soft ideals

  • 1.
    Department of Mathematics, College of Science, Jazan University, P.O. Box. 114, Jazan 45142, Saudi Arabia
  • 2.
    Mathematics Department, Faculty of Science, Sohag University, Sohag 82524, Egypt
  • 3.
    Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt
  • Received: 13 December 2023 Revised: 25 January 2024 Accepted: 29 January 2024 Published: 05 February 2024

  • MSC : 54A05, 54D10, 54D05, 54A10, 54C40

  • This paper was devoted to defining new soft closure operators via soft relations and soft ideals, and consequently new soft topologies. The resulting space is a soft ideal approximation. Many of the well known topological concepts were given in the soft set-topology. Particularly, it introduced the notations of soft accumulation points, soft continuous functions, soft separation axioms, and soft connectedness. Counterexamples were introduced to interpret the right implications. Also, a practical application of the new soft approximations was explained by an example of a real-life problem.

    Citation: Rehab Alharbi, S. E. Abbas, E. El-Sanowsy, H. M. Khiamy, Ismail Ibedou. Soft closure spaces via soft ideals[J]. AIMS Mathematics, 2024, 9(3): 6379-6410. doi: 10.3934/math.2024311

    Related Papers:

  • This paper was devoted to defining new soft closure operators via soft relations and soft ideals, and consequently new soft topologies. The resulting space is a soft ideal approximation. Many of the well known topological concepts were given in the soft set-topology. Particularly, it introduced the notations of soft accumulation points, soft continuous functions, soft separation axioms, and soft connectedness. Counterexamples were introduced to interpret the right implications. Also, a practical application of the new soft approximations was explained by an example of a real-life problem.


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    [1] Z. Pawlak, Rough sets, Int. J. Comput. Inform. Sci., 11 (1982), 341–356.
    [2] T. M. Al-shami, An improvement of rough sets' accuracy measure using containment neighborhoods with a medical application, Inform. Sciences, 569 (2021), 110–124. https://doi.org/10.1016/j.ins.2021.04.016 doi: 10.1016/j.ins.2021.04.016
    [3] T. M. Al-shami, Topological approach to generate new rough set models, Complex Intell. Syst., 8 (2022), 4101–4113. https://doi.org/10.1007/s40747-022-00704-x doi: 10.1007/s40747-022-00704-x
    [4] M. Hosny, T. M. Al-shami, A. Mhemdi, Novel approaches of generalized rough approximation spaces inspired by maximal neighbourhoods and ideals, Alex. Eng. J., 69 (2023), 497–520. https://doi.org/10.1016/j.aej.2023.02.008 doi: 10.1016/j.aej.2023.02.008
    [5] H. Mustafa, T. M. Al-shami, R. Wassef, Rough set paradigms via containment neighborhoods and ideals, Filomat, 37 (2023), 4683–4702. https://doi.org/10.2298/FIL2314683M doi: 10.2298/FIL2314683M
    [6] A. A. Allam, M. Y. Bakeir, E. A. Abo-Tabl, New approach for basic rough set concepts, Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing, RSFDGrC 2005, Lecture Notes in Computer Science, Springer, Berlin, Heidelberg, 3641 (2005), 64–73. https://doi.org/10.1007/11548669_7
    [7] A. A. Allam, M. Y. Bakeir, E. A. Abo-Tabl, New approach for closure spaces by relations, Acta Math. Acad. Paedag. Nyregyhziensis, 22 (2006), 285–304. https://doi.org/10.1016/j.midw.2006.03.006 doi: 10.1016/j.midw.2006.03.006
    [8] A. Kandil, S. A. El-Sheikh, M. Hosny, M. Raafat, Bi-ideal approximation spaces and their applications, Soft Comput., 24 (2020), 12989–13001. https://doi.org/10.1007/s00500-020-04720-2 doi: 10.1007/s00500-020-04720-2
    [9] E. A. Abo-Tabl, A comparison of two kinds of definitions of rough approximations based on a similarity relation, Inform. Sciences, 181 (2011), 2587–2596. https://doi.org/10.1016/j.ins.2011.01.007 doi: 10.1016/j.ins.2011.01.007
    [10] J. H. Dai, S. C. Gao, G. J. Zheng, Generalized rough set models determined by multiple neighborhoods generated from a similarity relation, Soft Comput., 22 (2018), 2081–2094. https://doi.org/10.1007/s00500-017-2672-x doi: 10.1007/s00500-017-2672-x
    [11] T. M. Al-Shami, Maximal rough neighborhoods with a medical application, J. Amb. Intel. Hum. Comput., 2022, 1–12. https://doi.org/10.1007/s12652-022-03858-1
    [12] D. Molodtsov, Soft set theory-first results, Comput. Math. Appl., 37 (1999), 19–31. https://doi.org/10.1016/S0898-1221(99)00056-5 doi: 10.1016/S0898-1221(99)00056-5
    [13] 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
    [14] M. I. Ali, F. Feng, X. Y. 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 doi: 10.1016/j.camwa.2008.11.009
    [15] 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
    [16] M. I. Ali, M. Shabir, Logic connectives for so13 set431d f442 soft sets, IEEE T. Fuzzy Syst., 22 (2013), 1431–1442. https://doi.org/10.1007/s40278-013-1808-8 doi: 10.1007/s40278-013-1808-8
    [17] M. Shabir, R. S. Kanwal, M. I. Ali, Reduction of nformation system, Soft Comput., 24 (2020), 10801–10813. https://doi.org/10.1007/s00500-019-04582-3 doi: 10.1007/s00500-019-04582-3
    [18] N. Rehman, A. Ali, M. I. Ali, C. Park, SDMGRS: Soft dominance based multi granulation rough sets and their applications in conflict analysis problems, IEEE Access, 6 (2018), 31399–31416. https://doi.org/10.1109/ACCESS.2018.2841876 doi: 10.1109/ACCESS.2018.2841876
    [19] 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 doi: 10.3934/math.2023924
    [20] Z. A. Ameen, T. M. Al-shami, R. Abu-Gdairi, A. Mhemdi, The relationship between ordinary and soft algebras with an application, MDPI Math., 11 (2023), 2035. https://doi.org/10.3390/math11092035 doi: 10.3390/math11092035
    [21] A. Kandil, O. A. E. Tantawy, S. A. El-Sheikh, A. M. A. El-latif, Soft ideal theory soft local function and generated soft topological spaces, Appl. Math. Inform. Sci., 8 (2014), 1595–1603. https://doi.org/10.12785/amis/080413 doi: 10.12785/amis/080413
    [22] A. C. Guler, E. D. Yildirim, O. Ozbakir, Rough approximations based on different topologies via ideals, Turk. J. Math., 46 (2022), 1177–1192. https://doi.org/10.55730/1300-0098.3150 doi: 10.55730/1300-0098.3150
    [23] M. Hosny, Topological approach for rough sets by using J-nearly concepts via ideals, Filomat, 34 (2020), 273–286. https://doi.org/10.2298/FIL2002273H doi: 10.2298/FIL2002273H
    [24] M. Hosny, Idealization of j-approximation spaces, Filomat, 34 (2020), 287–301. https://doi.org/10.2298/FIL2002287H doi: 10.2298/FIL2002287H
    [25] M. Hosny, T. M. Al-shami, Rough set models in a more general manner with applications, AIMS Math., 7 (2022), 18971–19017. https://doi.org/10.3934/math.20221044 doi: 10.3934/math.20221044
    [26] T. M. Al-shami, D. Ciucci, Subset neighborhood rough sets, Knowl.-Based Syst., 137 (2022), 07868. https://doi.org/10.1016/j.knosys.2021.107868 doi: 10.1016/j.knosys.2021.107868
    [27] T. M. Al-Shami, M. Hosny, Improvement of approximation spaces using maximal left neighborhoods and ideals, IEEE Access, 10 (2022), 79379–79393. https://doi.org/10.1109/ACCESS.2022.3194562 doi: 10.1109/ACCESS.2022.3194562
    [28] A. A. Azzam, Z. A. Ameen, T. M. Al-shami, M. E. El-Shafei, Generating soft topologies via soft set operators, MDPI Symmetry, 14 (2022), 914. https://doi.org/10.3390/sym14050914 doi: 10.3390/sym14050914
    [29] I. Ibedou, S. E. Abbas, Generalization of rough fuzzy sets based on a fuzzy ideal, Iran. J. Fuzzy Syst., 20 (2023), 27–38. https://doi.org/10.22111/ijfs.2023.7344 doi: 10.22111/ijfs.2023.7344
    [30] S. E. Abbas, S. El-Sanowsy, H. M. Khiamy, Certain approximation spaces using local functions via idealization, Sohag J. Sci., 8 (2023), 311–321. https://doi.org/10.21608/sjsci.2023.201184.1072 doi: 10.21608/sjsci.2023.201184.1072
    [31] S. E. Abbas, E. El-Sanowsy, H. M. Khiamy, New approach for closure spaces by relations via ideals, Ann. Fuzzy Math. Inform., 26 (2023), 59–81.
    [32] F. Feng, M. I. Ali, M. Shabir, Soft relations applied to semigroups, Filomat, 27 (2013), 1183–1196. https://doi.org/10.2298/FIL1307183F doi: 10.2298/FIL1307183F
    [33] S. Al Ghour, On soft generalized $\omega$-closed sets and soft T 1/2 spaces in soft topological spaces, MDPI Axioms, 11 (2022), 194. https://doi.org/10.3390/axioms11050194 doi: 10.3390/axioms11050194
    [34] S. Al Ghour, Soft complete continuity and soft strong continuity in soft topological spaces, MDPI Axioms, 12 (2023), 78. https://doi.org/10.3390/axioms12010078 doi: 10.3390/axioms12010078
    [35] 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 doi: 10.3934/math.2022828
    [36] J. B. Liu, Y. Bao, W. T. Zheng, Analyses of some structural properties on a class of hierarchical scale-free networks, Fractals, 30 (2022), 2250136. https://doi.org/10.1142/S0218348X22501365 doi: 10.1142/S0218348X22501365
    [37] J. B. Liu, N. Salamat, M. Kamran, S. Ashraf, R. H. Khan, Single-valued neutrosophic set with quaternion information: A promising approach to assess image quality, Fractals, 31 (2023), 1–10. https://doi.org/10.1142/S0218348X23400741 doi: 10.1142/S0218348X23400741
    [38] G. Nordo, A soft embedding theorem for soft topological spaces, In: Developments and Novel Approaches in Nonlinear Solid Body Mechanics, Springer, Cham, 2020, 37–57. https://doi.org/10.1007/978-3-030-50460-1_5
    [39] A. Allam, T. H. Ismail, R. Muhammed, A new approach to soft belonging, J. Ann. Fuzzy Math. Inform., 13 (2017), 145–152. https://doi.org/10.30948/afmi.2017.13.1.145 doi: 10.30948/afmi.2017.13.1.145
    [40] I. Zorlutuna, M. Akdag, W. K. Min, S. Atmaca, Remarks on soft topological spaces, Ann. Fuzzy Math. Inform., 3 (2012), 171–185. https://doi.org/10.1136/vr.e5655 doi: 10.1136/vr.e5655
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