Supra finite soft-open sets and applications to operators and continuity

Volume 35, Issue 2, pp 120--135 https://dx.doi.org/10.22436/jmcs.035.02.01

Publication Date: April 18, 2024 Submission Date: February 18, 2024 Revision Date: February 29, 2024 Accteptance Date: March 19, 2024

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 140 Downloads
• 489 Views

Authors

F. A. Abu Shaheen - Department of Scientific Basic Sciences, Faculty of Arts and Educational Sciences, Middle East University, Amman, Jordan. T. M. Al-Shami - Department of Mathematics, Sana'a University, P.O. Box 1247, Sana'a, Yemen. - Department of Engineering Mathematics \(\&\) Physics, Faculty of Engineering \(\&\) Technology, Future University, New Cairo, Egypt. M. Arar - Department of Mathematics, College of Sciences and Humanities in Aflaj, Prince Sattam bin Abdulaziz University, Riyadh, Saudi Arabia. O. G. El-Barbary - Information System Department, Faculty of Computer and Informatics, Tanta University, Egypt.

Abstract

In this article, we study the concept of finite open sets in the spaces of supra soft-topologies. We aim by defining this concept to furnish the researchers with a tool they generate new forms of topological concepts via supra soft-topologies such as continuity, compactness, separation axioms, etc. We discuss the main properties of this concept and prove that this class of soft sets is neither infra soft-topology nor supra soft-topology. Also, we reveal its connections with other celebrated generalizations of supra soft-open sets and conclude the conditions they guarantee the equivalence between them. After that, we display some soft operators, like interior and closure, inspired by the classes of supra finite soft-open and supra finite soft-closed sets. Finally, we set forth some types of continuity defined by these classes and describe their main characterizations and behaviors in different cases such as decomposition theorems and transition between the realms of of supra soft-topologies and their parametric supra topologies. The obtained results and implementations are articulated with the aid of some counterexamples.

Share and Cite

Keywords

• Supra finite soft-open set
• supra soft-topology
• soft operators
• soft continuity

MSC

•  54A40
•  03E72
•  54C99

References

• [1] A. M. Abd El-latif, Soft supra strongly generalized closed sets, J. Intell. Fuzzy Syst., 31 (2016), 1311–1317
  • View Article
  • Google Scholar
  • MATH


• [2] A. M. Abd El-latif, Novel types of supra soft operators via supra soft sd-sets and applications, AIMS Math., 9 (2024), 6586–6602
  • View Article
  • MathSciNet
  • Google Scholar


• [3] D. Abuzaid, S. Al Ghour, Three new soft separation axioms in soft topological spaces, AIMS Math., 9 (2024), 4632–4648
  • View Article
  • MathSciNet
  • Google Scholar


• [4] M. Akdag, A. Ozkan, Soft -open sets and soft -continuous functions, Abstr. Appl. Anal., 2014 (2014), 7 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [5] J. C. R. Alcantud, Soft open bases and a novel construction of soft topologies from bases for topologies, Mathematics, 8 (2020), 1–12
  • View Article
  • Google Scholar


• [6] J. C. R. Alcantud, T. M. Al-shami, A. A. Azzam, Caliber and chain conditions in soft topologies, Mathematics, 9 (2021), 1–15
  • View Article
  • Google Scholar


• [7] S. Al-Ghour, Boolean algebra of soft Q-sets in soft topological spaces, Appl. Comput. Intell. Soft Comput., 2022 (2022), 1–9
  • View Article
  • Google Scholar


• [8] M. I. Ali, F. Feng, X. Liu, W. K. Min, M. Shabir, On some new operations in soft set theory, Comput. Math. Appl., 57 (2009), 1547–1553
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [9] H. H. Al-jarrah, A. Rawshdeh, T. M. Al-shami, On soft compact and soft Lindel¨of spaces via soft regular closed sets, Afr. Mat., 33 (2022), 16 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [10] T. M. Al-shami, Utilizing supra -open sets to generate new types of supra compact and supra lindel¨of spaces, Facta Univ. Ser. Math. Inform., 32 (2017), 151–162
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [11] T. M. Al-shami, Soft somewhere dense sets on soft topological spaces, Commun. Korean Math. Soc., 33 (2018), 1341– 1356
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [12] T. M. Al-shami, Comments on some results related to soft separation axioms, Afr. Mat., 31 (2020), 1105–1119
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [13] T. M. Al-shami, Paracompactness on supra topological spaces, J. Linear Topol. Algeb., 9 (2020), 121–127
  • View Article
  • Google Scholar
  • MATH


• [14] T. M. Al-shami, Compactness on soft topological ordered spaces and its application on the information system, J. Math., 2021 (2021), 12 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [15] T. M. Al-shami, On soft separation axioms and their applications on decision-making problem, Math. Probl. Eng., 2021 (2021), 12 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [16] T. M. Al-shami, Homeomorphism and quotient mappings in infra soft topological spaces, J. Math., 2021 (2021), 10 pages
  • View Article
  • Google Scholar


• [17] T. M. Al-shami, Complete Hausdorffness and complete regularity on supra topological spaces, J. Appl. Math., 2021 (2021), 7 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [18] T. M. Al-shami, Soft somewhat open sets: Soft separation axioms and medical application to nutrition, Comput. Appl. Math., 41 (2022), 22 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [19] 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), 1–18
  • View Article
  • Google Scholar


• [20] T. M. Al-shami, I. Alshammari, Rough sets models inspired by supra-topology structures, Artif. Intell. Rev., 56 (2023), 6855–6883
  • View Article
  • Google Scholar


• [21] T. M. Al-shami, M. Arar, R. Abu-Gadiri, Z. A. Ameen, On weakly soft -open sets and weakly soft -continuity, J. Intell. Fuzzy Syst., 45 (2023), 6351–6363
  • View Article
  • Google Scholar


• [22] T. M. Al-shami, R. A. Hosny, R. Abu-Gadiri, M. Arar, A novel approach to study soft preopen sets inspired by classical topologies, J. Intell. Fuzzy Syst., 45 (2023), 6339–6350
  • View Article
  • Google Scholar


• [23] T. M. Al-shami, R. A. Hosny, A. Mhemdi, R. Abu-Gadiri, S. Saleh, Weakly soft b-open sets and their usages via soft topologies: A novel approach, J. Intell. Fuzzy Syst., 45 (2023), 7727–7738
  • View Article
  • Google Scholar


• [24] T. M. Al-shami, L. D. R. Koˇcinac, The equivalence between the enriched and extended soft topologies, Appl. Comput. Math., 18 (2019), 149–162
  • View Article
  • Google Scholar
  • MATH


• [25] T. M. Al-shami, L. D. R. Koˇcinac, Almost soft Menger and weakly soft Menger spaces, Appl. Comput. Math., 21 (2022), 35–51
  • View Article
  • Google Scholar
  • MATH


• [26] T. M. Al-shami, A. Mhemdi, On soft parametric somewhat-open sets and applications via soft topologies, Heliyon, 9 (2023), 1–15
  • View Article
  • Google Scholar


• [27] T. M. Al-shami, A. Mhemdi, A weak form of soft -open sets and its applications via soft topologies, AIMS Math., 8 (2023), 11373–11396
  • View Article
  • Google Scholar


• [28] T. M. Al-shami, A. Mhemdi, Approximation operators and accuracy measures of rough sets from an infra-topology view, Soft Comput., 27 (2023), 1317–1330
  • View Article
  • Google Scholar


• [29] T. M. Al-shami, A. Mhemdi, A. M. A. El-latif, F. A. A. Shaheen, Finite soft-open sets: characterizations, operators and continuity, AIMS Math., 9 (2024), 10363–10385
  • View Article
  • MathSciNet
  • Google Scholar


• [30] 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), 1–16
  • View Article
  • Google Scholar


• [31] 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
  • View Article
  • MathSciNet
  • Google Scholar


• [32] T. M. Al-shami, A. Mhemdi, A. Rawshdeh, H. Al-jarrah, Soft version of compact and Lindel¨of spaces using soft somewhere dense set, AIMS Math., 6 (2021), 8064–8077
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [33] T. M. Al-shami, A. Mhemdi, A. Rawshdeh, H. H. Al-jarrah, ON WEAKLY SOFT SOMEWHAT OPEN SETS, Rocky Mountain J. Math., 54 (2024), 13–30
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [34] B. A. Asaad, Results on soft extremally disconnectedness of soft topological spaces, J. Math. Comput. Sci., 17 (2017), 448–464
  • View Article
  • Google Scholar
  • MATH


• [35] A. Ayg¨unoˇ glu, H. Ayg¨ un, Some notes on soft topological spaces, Neural Comput. Appl., 21 (2021), 113–119
  • View Article
  • Google Scholar


• [36] N. C¸ a˘gman, S. Karatas¸, S. Enginoglu, Soft topology, Comput. Math. Appl., 62 (2011), 351–358
  • View Article
  • MathSciNet
  • Google Scholar


• [37] B. Chen, Soft semi-open sets and related properties in soft topological spaces, Appl. Math. Inf. Sci., 7 (2013), 287–294
  • View Article
  • MathSciNet
  • Google Scholar


• [38] O. Dalkılıc¸, N. Demirtas, Algorithms for Covid-19 outbreak using soft set theory: estimation and application, Soft Comput., 27 (2023), 3203–3211
  • View Article
  • Google Scholar


• [39] J. Dontchev, On submaximal spaces, Tamkang J. Math., 26 (1995), 243–250
  • View Article
  • Google Scholar


• [40] S. A. El-Sheikh, A. M. Abd El-latif, Decompositions of some types of supra soft sets and soft continuity, Int. J. Math. Trends Tech., 9 (2014), 37–56
  • View Article
  • Google Scholar


• [41] M. E. El-Shafei, M. Abo-Elhamayel, T. M. Al-shami, Partial soft separation axioms and soft compact spaces, Filomat, 32 (2018), 4755–4771
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [42] M. E. El-Shafei, A. H. Zakari, T. M. Al-shami, Some applications of supra preopen sets, J. Math., 2020 (2020), 11 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [43] F. Feng, C. X. Li, B. Davvaz, M. I. Ali, Soft sets combined with fuzzy sets and rough sets: A tentative approach, Soft Comput., 14 (2010), 899–911
  • View Article
  • Google Scholar
  • MATH


• [44] T. Hida, A comparison of two formulations of soft compactness, Ann. Fuzzy Math. Inform., 8 (2014), 511–525
  • View Article
  • Google Scholar
  • MATH


• [45] A. Kharal, B. Ahmad, Mappings on soft classes, New Math. Nat. Comput., 7 (2011), 471–481
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [46] M. Kiris¸ci, -soft sets and medical decision-making application, Int. J. Comput. Math., 98 (2021), 690–704
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [47] L. D. R. Koˇcinac, T. M. Al-shami, V. C¸ etkin, Selection principles in the context of soft sets: Menger spaces, Soft Comput., 25 (2021), 12693–12702
  • View Article
  • Google Scholar
  • MATH


• [48] A. M. Kozae, M. Shokry, M. Zidan, Supra topologies for digital plane, AASCIT Commun., 3 (2016), 1–10
  • View Article
  • Google Scholar


• [49] P. K. Maji, R. Biswas, A. R. Roy, Soft set theory, Comput. Math. Appl., 45 (2003), 555–562
  • View Article
  • MathSciNet
  • Google Scholar


• [50] 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
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [51] N. Malik, M. Shabir, T. M. Al-shami, R. Gul, M. Arar, A novel decision-making technique based on T-rough bipolar fuzzy sets, J. Math. Comput. Sci., 33 (2024), 275–289
  • View Article
  • Google Scholar


• [52] W. K. Min, A note on soft topological spaces, Comput. Math. Appl., 62 (2011), 3524–3528
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [53] D. Molodtsov, Soft set theory—first results, Comput. Math. Appl., 37 (1999), 19–31
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [54] SK. Nazmul, S. K. Samanta, Neighbourhood properties of soft topological spaces, Ann. Fuzzy Math. Inform., 6 (2013), 1–15
  • View Article
  • Google Scholar
  • MATH


• [55] E. Peyghan, B. Samadi, A. Tayebi, About soft topological spaces, J. New Results Sci., 2 (2013), 60–75
  • View Article
  • Google Scholar


• [56] A. A. Rawshdeh, H. H. Al-jarrah, T. M. Al-shami, Soft expandable spaces, Filomat, 37 (2023), 2845–2858
  • View Article
  • MathSciNet
  • Google Scholar


• [57] A. S. Salama, Topological solution for missing attribute values in incomplete information tables, Inf. Sci., 180 (2010), 631–639
  • View Article
  • Google Scholar


• [58] M. Shabir, M. Naz, On soft topological spaces, Comput. Math. Appl., 61 (2011), 1786–1799
  • View Article
  • MathSciNet
  • Google Scholar


• [59] A. Singh, N. S. Noorie, Remarks on soft axioms, Ann. Fuzzy Math. Inform., 14 (2017), 503–513
  • View Article
  • Google Scholar
  • MATH


• [60] S. Yan, W. Yu, Formal verification of a topological spatial relations model for geographic information systems in Coq, Mathematics, 11 (2023), 1–18
  • View Article
  • Google Scholar


• [61] H.-L. Yang, X. Liao, S.-G. Li, On soft continuous mappings and soft connectedness of soft topological spaces, Hacet. J. Math. Stat., 44 (2015), 385–398
  • View Article
  • Google Scholar
  • MATH


• [62] I. Zorlutuna, M. Akdag, W. K. Min, S. Atmaca, Remarks on soft topological spaces, Ann. Fuzzy Math. Inform., 3 (2012), 171–185
  • View Article
  • Google Scholar
  • MATH


• [63] ˙I. Zorlutuna, H. C¸ akır, On continuity of soft mappings, Appl. Math. Inf. Sci., 9 (2015), 403–409
  • View Article
  • MathSciNet
  • Google Scholar