New soft operators related to supra soft $ \delta_i $-open sets and applications

Alaa M. Abd El-latif; Mesfer H. Alqahtani; Alaa M. Abd El-latif; Mesfer H. Alqahtani

doi:10.3934/math.2024150

AIMS Mathematics

2024, Volume 9, Issue 2: 3076-3096. doi: 10.3934/math.2024150

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New soft operators related to supra soft $ \delta_i $-open sets and applications

Alaa M. Abd El-latif ^{1,2
,
,},
Mesfer H. Alqahtani ³

1.
Mathematics Department, College of Sciences and Arts, Northern Border University, Rafha 91911, Saudi Arabia
2.
Mathematics Department, Faculty of Education, Ain Shams University, Roxy, 11341, Cairo, Egypt
3.
Department of Mathematics, University College of Umluj, University of Tabuk, Tabuk 48322, Saudi Arabia

Received: 27 November 2023 Revised: 20 December 2023 Accepted: 22 December 2023 Published: 02 January 2024
MSC : 54A05, 54B05, 54C08, 54C10

This project aimed to introduce the notion of supra soft $ \delta_i $-open sets in supra soft topological spaces. Also, we declared the differences between the new concept and other old generalizations. We presented new operators such as supra soft $ \delta_i $-interior, supra soft $ \delta_i $-closure, supra soft $ \delta_i $-boundary and supra soft $ \delta_i $-cluster. We found out many deviations to our new operators; to name a few: If $ int^s_{\delta_i}(F, E) = (F, E) $, then it doesn't imply that $ (F, E) \in SOS_{\delta_i}(X) $. Furthermore, we applied this notion to define new kinds of mappings, like supra soft $ \delta_i $-continuous mappings, supra soft $ \delta_i $-irresolute mappings, supra soft $ \delta_i $-open mappings and supra soft $ \delta_i $-closed mappings. We studied their main properties in special to distinguish between our new notions and the previous generalizations. It has been pointed out in this work that many famous previous studies have been investigated here; in fact, I believe that this is an extra justification for the work included in this manuscript.
Citation: Alaa M. Abd El-latif, Mesfer H. Alqahtani. New soft operators related to supra soft $ \delta_i $-open sets and applications[J]. AIMS Mathematics, 2024, 9(2): 3076-3096. doi: 10.3934/math.2024150

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Abstract

This project aimed to introduce the notion of supra soft $ \delta_i $-open sets in supra soft topological spaces. Also, we declared the differences between the new concept and other old generalizations. We presented new operators such as supra soft $ \delta_i $-interior, supra soft $ \delta_i $-closure, supra soft $ \delta_i $-boundary and supra soft $ \delta_i $-cluster. We found out many deviations to our new operators; to name a few: If $ int^s_{\delta_i}(F, E) = (F, E) $, then it doesn't imply that $ (F, E) \in SOS_{\delta_i}(X) $. Furthermore, we applied this notion to define new kinds of mappings, like supra soft $ \delta_i $-continuous mappings, supra soft $ \delta_i $-irresolute mappings, supra soft $ \delta_i $-open mappings and supra soft $ \delta_i $-closed mappings. We studied their main properties in special to distinguish between our new notions and the previous generalizations. It has been pointed out in this work that many famous previous studies have been investigated here; in fact, I believe that this is an extra justification for the work included in this manuscript.

References

[1]	A. S. Mashhour, A. A. Allam, F. S. Mahmoud, F. H. Khedr, On supra topological spaces, Indian J. Pure Appl. Math., 4 (1983), 502–510.
[2]	A. Alpers, Digital topology: regular sets and root images of the cross-median filter, J. Math. Imaging. Vis., 17 (2002), 7–14. https://doi.org/10.1023/A:1020766406935 doi: 10.1023/A:1020766406935
[3]	A. M. Kozae, M. Shokry, M. Zidan, Supra topologies for digital plane, AASCIT Commun., 3 (2016), 1–10.
[4]	T. M. Al-shami, I. Alshammari, Rough sets models inspired by supra-topology structures, Artif. Intell. Rev., 56 (2023), 6855–6883. https://doi.org/10.1007/s10462-022-10346-7 doi: 10.1007/s10462-022-10346-7
[5]	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.
[6]	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 doi: 10.1016/j.camwa.2011.02.006
[7]	A. M. Abd El-latif, On soft supra compactness in supra soft topological spaces, Tbilisi Math. J., 11 (2018), 169–178. https://doi.org/10.32513/tbilisi/1524276038 doi: 10.32513/tbilisi/1524276038
[8]	A. M. Abd El-latif, Supra soft $b$-connectedness Ⅰ: supra soft $b$-irresoluteness and separateness, Creat. Math. Inform., 25 (2016), 127–134. https://doi.org/10.37193/CMI.2016.02.02 doi: 10.37193/CMI.2016.02.02
[9]	A. M. Abd El-latif, Supra soft $b$-connectedness Ⅱ: some types of supra soft $b$-connectedness, Creat. Math. Inform., 26 (2017), 1–8. https://doi.org/10.37193/CMI.2017.01.01 doi: 10.37193/CMI.2017.01.01
[10]	W. Rong, F. Lin, Soft connected spaces and soft paracompact spaces, Int. J. Appl. Math. Stat., 51 (2013), 667–681.
[11]	A. M. Abd El-latif, Soft supra strongly generalized closed sets, J. Intell. Fuzzy Syst., 31 (2016), 1311-1317. https://doi.org/10.3233/IFS-162197 doi: 10.3233/IFS-162197
[12]	A. Kandil, O. A. E. Tantawy, S. A. El-Sheikh, A. M. Abd El-latif, Supra generalized closed soft sets with respect to an soft ideal in supra soft topological spaces, Appl. Math. Inf. Sci., 8 (2014), 1731–1740.
[13]	L. Lincy, A. Kalaichelvi, Supra soft regular open sets, supra soft regular closed sets and supra soft regular continuity, Int. J. Pure Appl. Math., 119 (2018), 1075–1079.
[14]	Z. G. Ergül, S. Yüksel, Supra regular generalized closed sets in supra soft topological spaces, Ann. Fuzzy Math. Inform., 11 (2016), 349–360.
[15]	A. M. Abd El-latif, R. A. Hosny, Supra semi open soft sets and associated soft separation axioms, Appl. Math. Inf. Sci., 10 (2016), 2207–2215. https://doi.org/10.18576/amis/100623 doi: 10.18576/amis/100623
[16]	A. M. Abd El-latif, R. A. Hosny, Supra soft separation axioms and supra irresoluteness based on supra $b$-open soft sets, Gazi Univ. J. Sci., 29 (2016), 845-854.
[17]	A. M. Abd El-latif, Supra soft separation axioms based on supra $\beta$-open soft sets, Math. Sci. Lett., 5 (2016), 121-129. https://doi.org/10.18576/msl/050202 doi: 10.18576/msl/050202
[18]	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 doi: 10.3390/math10234488
[19]	T. M. Al-shami, M. E. El-Shafei, Two types of separation axioms on supra soft topological spaces, Demonstr. Math., 52 (2019), 147–165. https://doi.org/10.1515/dema-2019-0016 doi: 10.1515/dema-2019-0016
[20]	C. G. Aras, S. Bayramov, Results of some separation axioms in supra soft topological spaces, TWMS J. Appl. Eng. Math., 9 (2019), 58–63.
[21]	C. G. Aras, S. Bayramov, Separation axioms in supra soft bitopological spaces, Filomat, 32 (2018), 3479–3486. https://doi.org/10.2298/FIL1810479G doi: 10.2298/FIL1810479G
[22]	S. Saleh, T. M. Al-shami, L. R. Flaiha, M. Arare, R. Abu-Gdairif, $R_i$-separation axioms via supra soft topological spaces, J. Math. Comput. Sci., 32 (2024), 263–274. https://doi.org/10.22436/jmcs.032.03.07 doi: 10.22436/jmcs.032.03.07
[23]	A. M. Abd El-latif, S. Karataş, Supra $b$-open soft sets and supra $b$-soft continuity on soft topological spaces, J. Math. Comput. Appl. Res., 5 (2015), 1–18.
[24]	A. Kandil, O. A. E. Tantawy, S. A. El-Sheikh, A. M. Abd El-latif, $\gamma$-operation and decompositions of some forms of soft continuity in soft topological spaces, Ann. Fuzzy Math. Inform., 7 (2014), 181–196.
[25]	T. M. Al-shami, M. E. El-Shafei, On supra soft topological ordered spaces, Arab J. Basic Appl. Sci., 26 (2019), 433–445. https://doi.org/10.1080/25765299.2019.1664101 doi: 10.1080/25765299.2019.1664101
[26]	S. W. Askandar, A. A. Mohammed, Soft ii-open sets in soft topological spaces, Open Access Library J., 7 (2020), 1–18. https://doi.org/10.4236/oalib.1106308 doi: 10.4236/oalib.1106308
[27]	B. Chen, Soft semi-open sets and related properties in soft topological spaces, Appl. Math. Inf. Sci., 7 (2013), 287–294.
[28]	G. Ilango, M. Ravindran, On soft preopen sets in soft topological spaces, Int. J. Math. Res., 5 (2013), 399–409.
[29]	A. Kandil, O. A. E. Tantawy, S. A. El-Sheikh, A. M. Abd El-latif, Soft ideal theory, Soft local function and generated soft topological spaces, Appl. Math. Inf. Sci., 8 (2014), 1595–1603. https://doi.org/10.12785/amis/080413 doi: 10.12785/amis/080413
[30]	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 doi: 10.3934/math.2023576
[31]	T. M. Al-shami, A. Murad, R. Abu-Gdairi, A. A. Zanyar, 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 doi: 10.3233/JIFS-230858
[32]	B. Ahmad, A. Kharal, Mappings on soft classes, New Math. Nat. Comput., 7 (2011), 471–481. https://doi.org/10.1142/S1793005711002025 doi: 10.1142/S1793005711002025
[33]	D. A. 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
[34]	I. Zorlutuna, M. Akdag, W. K. Min, S. Atmaca, Remarks on soft topological spaces, Ann. Fuzzy Math. Inform., 3 (2012), 171–185.
[35]	A. Kandil, O. A. E. Tantawy, S. A. El-Sheikh, A. M. Abd El-latif, Soft semi separation axioms and some types of soft functions, Ann. Fuzzy Math. Inform., 8 (2014), 305–318.
[36]	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. https://doi.org/10.1007/s00500-022-07627-2 doi: 10.1007/s00500-022-07627-2

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