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Year 2022, Volume: 5 Issue: 2, 67 - 80, 01.06.2022

Nihal Taş

https://doi.org/10.33401/fujma.1021120

Abstract

References

  • [1] D. Molodtsov, Soft set theory - first results, Comput. Math. Appl., 37 (1999), 19-31.
  • [2] 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.
  • [3] I˙. Demir, O. B. Özbakır, İ. Yıldız, A contribution to the study of soft proximity spaces, Filomat, 31 (2017), 2023-2034.
  • [4] A. Ç . Güler, G. Kale, Regularity and normality on soft ideal topological spaces, Ann. Fuzzy Math. Inform., 9 (2015), 373-383.
  • [5] Ç. Gündüz, T. Y. Öztürk, S. Bayramov, Separation axioms on neutrosophic soft topological spaces, Turk. J. Math., 43 (2019), 498-510.
  • [6] A. Kandil, O. A. E. Tantawy, S. A. El-Sheikh, A. M. ABD El-Latif, g - operation and decompositions of some forms of soft continuity in soft topological spaces, Ann. Fuzzy Math. Inform., 7 (2014), 181-196.
  • [7] P. K. Maji, R. Biswas, A. R. Roy, Soft set theory, Comput. Math. Appl., 45 (2003), 555-562.
  • [8] S. K. Nazmul, S. K. Samanta, Neighbourhood properties of soft topological spaces, Ann. Fuzzy Math. Inform., 6 (2013), 1-15.
  • [9] A. Özkan, On near soft sets, Turk. J. Math., 43 (2019), 1005-1017.
  • [10] M. Shabir, M. Naz, On soft topological spaces, Comput. Math. Appl., 61 (2011), 1786-1799.
  • [11] J. Thomas, S. J. John, On soft generalized topological spaces, J. New Results Sci., 4 (2014), 1-15.
  • [12] E. D. Yıldırım, A. Ç. Güler, O. B. Özbakir, On soft Ie-Baire spaces. Ann. Fuzzy Math. Inform., 10 (2015), 109-121.
  • [13] E. D. Yıldırım, O. B. Özbakir, On soft Ie-scattered spaces, An. Univ. Oradea, Fasc. Mat., 23 (2016), 137-146.
  • [14] İ. Zorlutuna, M. Akdağ, W. K. Min, S. Atmaca, Remarks on soft topological spaces, Ann. Fuzzy Math. Inform., 3 (2012), 171-185.
  • [15] İ Zorlutuna, H. Ç akır, On continuity of soft mappings, Appl. Math. Inf. Sci., 9 (2015), 403-409.
  • [16] J. C. R. Alcantud, S. C. Rambaud, M. J. M. Torrecillas, Valuation fuzzy soft sets: a flexible fuzzy soft set based decision making procedure for the valuation of assets, Symmetry, 9 (2017), 253.
  • [17] ˙I. Demir, N-soft mappings with application in medical diagnosis, Math. Methods Appl. Sci., 44(8) (2021), 7343-7358.
  • [18] R. I˙rkin, N. Y. Özgür, N. Taş, Optimization of lactic acid bacteria viability using fuzzy soft set modelling, Int. J. Optim. Control, Theor. Appl. (IJOCTA), 8 (2018), 266-275.
  • [19] Dr. A. Kalaichelvi, P. H. Malini, Application of fuzzy soft sets to investment decision making problem, Int. J. Math. Sci. Appl., 1 (2011), 1583-1586.
  • [20] F. Karaca, N. Taş, Decision making problem for life and non-life insurances, J. BAUN Inst. Sci. Technol., 20 (2018), 572-588.
  • [21] N. Y. Özgür, N. Taş, A note on “application of fuzzy soft sets to investment decision making problem”, J. New Theory, 7 (2015), 1-10.
  • [22] N. Taş, N. Y. Özgür, P. Demir, An application of soft set and fuzzy soft set theories to stock management, Süleyman Demirel University J. Nat. Appl. Sci., 21 (2017), 791-196.
  • [23] M. Ali, H. Khan, L. H. Son, F. Smarandache, W. B. Vasantha Kandasamy, New soft set based class of linear algebraic codes, Symmetry, 10 (2018), 510.
  • [24] P. Mani, K. Muthusamy, S. Jafari, F. Smarandache, U. Ramalingam, Decision-making via neutrosophic support soft topological spaces, Symmetry, 10 (2018), 217.
  • [25] G. Ali, M. Akram, A. N. A. Koam, J. C. R. Alcantud, Parameter reductions of bipolar fuzzy soft sets with their decision-making algorithms, Symmetry, 11 (2019), 949.
  • [26] T. H. Şimşekler, Fuzzy soft topological spaces and the related category FST, Turk. J. Math., 43 (2019), 871-878.
  • [27] M. Riaz, K. Naeem, M. Aslam, D. Afzal, F. A. Ahmed Almahdi, S. Shaukat Jamal, Multi-criteria group decision making with Pythagorean fuzzy soft topology, J. Intell. Fuzzy Syst. (Preprint), (2020), 1-18.
  • [28] M. Riaz, S. T. Tehrim, On bipolar fuzzy soft topology with decision-making, Soft Comput., 24(24) (2020), 18259-18272.
  • [29] M. Riaz, K. Naeem, Measurable soft mappings, J. Math., Punjab Univ., 48(2) (2020).
  • [30] M. Riaz, N. Ç ağman, I. Zareef, M. Aslam, N-soft topology and its applications to multi-criteria group decision making, J. Intell. Fuzzy Syst., 36(6) (2019), 6521-6536.
  • [31] A. Açıkgöz, N. Taş, Some new mixed soft sets, MSAEN, 2 (2014), 105-118.
  • [32] A. Açıkgöz, N. A. Taş, T. Noiri, A decomposition of some types of mixed soft continuity in soft topological spaces, Filomat, 30 2016, 379-385.
  • [33] A. Csaszar, Mixed constructions for generalized topologies, Acta Math. Hung., 122 (2009), 153-159.
  • [34] W. K. Min, Mixed q-continuity on generalized topological spaces, Math. Comput. Modelling, 54 (2011), 2597-2601.
  • [35] W. K. Min, Mixed weak continuity on generalized topological spaces, Acta Math. Hung., 132 (2011), 339-347.
  • [36] N. A. Taş, A. Açıkgöz, Some mixed soft operations and extremally soft disconnectedness via two soft topologies, Appl. Math. 5 (2014), 490-500.
  • [37] N. A. Taş, O. B. Özbakır, On some mixed types of continuity on generalized neighborhood systems, J. Adv. Stud. Topol., 5 (2014), 32-43.
  • [38] M. Anitha, R. Selvi, P. Thangavelu, Pasting lemmas for g-continuous functions, Missouri J. Math. Sci., 21 (2009), 28-33.
  • [39] K. Balachandran, P. Sundaram, H. Maki, On generalized continuous maps in topological spaces, Mem. Fac. Sci., Kochi Univ., Ser. A 12 (1991), 5-13.
  • [40] Y. Gnanambal, K. Balachandran, On gpr-continuous functions in topological spaces, Indian J. Pure Appl. Math., 30 (1999), 581-593.
  • [41] K. Kannan, K. C. Rao, Pasting lemmas for some continuous functions, Thai J. Math., 12 (2014), 245-249.
  • [42] D. Vidhya, R. Parimelazhagan, g b-continuous maps and pasting lemma in topological spaces, Int. J. Math. Anal., 6 (2012), 2307-2315.
  • [43] S. Hussain, B. Ahmad, Some properties of soft topological space, Comput. Math. Appl., 62 (2011), 4058-4067.
  • [44] A. Kharal, B. Ahmad, Mappings on soft classes, New Math. Nat. Comput., 7(03) (2011), 471-481.

Two New Versions of the Pasting Lemma via Soft Mixed Structure

Year 2022, Volume: 5 Issue: 2, 67 - 80, 01.06.2022

Nihal Taş

https://doi.org/10.33401/fujma.1021120

Abstract

In this paper, we present two new generalizations of the pasting lemma using soft mixed structure. To do this, we introduce the notions of a $(\tau _{1},\tau _{2})$-$g$-closed soft set and a $(\tau _{1},\tau _{2})$-$gpr$% -closed soft set. We establish the notions of mixed $g$-soft continuity and mixed $gpr$-soft continuity between two soft topological spaces $(X,\tau _{1},\Delta _{1})$, $(X,\tau _{2},\Delta _{1})$ and a soft topological space $(X,\tau ,\Delta _{2})$. Finally we prove two new versions of the pasting lemma using the mixed $g$-soft continuous mapping and the mixed $gpr$-soft continuous mapping.

Keywords

Pasting lemma $(\tau _{1}\tau _{2})$-$g$-closed soft $ (\tau _{1}\tau _{2})$-$gpr$-closed soft

References

  • [1] D. Molodtsov, Soft set theory - first results, Comput. Math. Appl., 37 (1999), 19-31.
  • [2] 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.
  • [3] I˙. Demir, O. B. Özbakır, İ. Yıldız, A contribution to the study of soft proximity spaces, Filomat, 31 (2017), 2023-2034.
  • [4] A. Ç . Güler, G. Kale, Regularity and normality on soft ideal topological spaces, Ann. Fuzzy Math. Inform., 9 (2015), 373-383.
  • [5] Ç. Gündüz, T. Y. Öztürk, S. Bayramov, Separation axioms on neutrosophic soft topological spaces, Turk. J. Math., 43 (2019), 498-510.
  • [6] A. Kandil, O. A. E. Tantawy, S. A. El-Sheikh, A. M. ABD El-Latif, g - operation and decompositions of some forms of soft continuity in soft topological spaces, Ann. Fuzzy Math. Inform., 7 (2014), 181-196.
  • [7] P. K. Maji, R. Biswas, A. R. Roy, Soft set theory, Comput. Math. Appl., 45 (2003), 555-562.
  • [8] S. K. Nazmul, S. K. Samanta, Neighbourhood properties of soft topological spaces, Ann. Fuzzy Math. Inform., 6 (2013), 1-15.
  • [9] A. Özkan, On near soft sets, Turk. J. Math., 43 (2019), 1005-1017.
  • [10] M. Shabir, M. Naz, On soft topological spaces, Comput. Math. Appl., 61 (2011), 1786-1799.
  • [11] J. Thomas, S. J. John, On soft generalized topological spaces, J. New Results Sci., 4 (2014), 1-15.
  • [12] E. D. Yıldırım, A. Ç. Güler, O. B. Özbakir, On soft Ie-Baire spaces. Ann. Fuzzy Math. Inform., 10 (2015), 109-121.
  • [13] E. D. Yıldırım, O. B. Özbakir, On soft Ie-scattered spaces, An. Univ. Oradea, Fasc. Mat., 23 (2016), 137-146.
  • [14] İ. Zorlutuna, M. Akdağ, W. K. Min, S. Atmaca, Remarks on soft topological spaces, Ann. Fuzzy Math. Inform., 3 (2012), 171-185.
  • [15] İ Zorlutuna, H. Ç akır, On continuity of soft mappings, Appl. Math. Inf. Sci., 9 (2015), 403-409.
  • [16] J. C. R. Alcantud, S. C. Rambaud, M. J. M. Torrecillas, Valuation fuzzy soft sets: a flexible fuzzy soft set based decision making procedure for the valuation of assets, Symmetry, 9 (2017), 253.
  • [17] ˙I. Demir, N-soft mappings with application in medical diagnosis, Math. Methods Appl. Sci., 44(8) (2021), 7343-7358.
  • [18] R. I˙rkin, N. Y. Özgür, N. Taş, Optimization of lactic acid bacteria viability using fuzzy soft set modelling, Int. J. Optim. Control, Theor. Appl. (IJOCTA), 8 (2018), 266-275.
  • [19] Dr. A. Kalaichelvi, P. H. Malini, Application of fuzzy soft sets to investment decision making problem, Int. J. Math. Sci. Appl., 1 (2011), 1583-1586.
  • [20] F. Karaca, N. Taş, Decision making problem for life and non-life insurances, J. BAUN Inst. Sci. Technol., 20 (2018), 572-588.
  • [21] N. Y. Özgür, N. Taş, A note on “application of fuzzy soft sets to investment decision making problem”, J. New Theory, 7 (2015), 1-10.
  • [22] N. Taş, N. Y. Özgür, P. Demir, An application of soft set and fuzzy soft set theories to stock management, Süleyman Demirel University J. Nat. Appl. Sci., 21 (2017), 791-196.
  • [23] M. Ali, H. Khan, L. H. Son, F. Smarandache, W. B. Vasantha Kandasamy, New soft set based class of linear algebraic codes, Symmetry, 10 (2018), 510.
  • [24] P. Mani, K. Muthusamy, S. Jafari, F. Smarandache, U. Ramalingam, Decision-making via neutrosophic support soft topological spaces, Symmetry, 10 (2018), 217.
  • [25] G. Ali, M. Akram, A. N. A. Koam, J. C. R. Alcantud, Parameter reductions of bipolar fuzzy soft sets with their decision-making algorithms, Symmetry, 11 (2019), 949.
  • [26] T. H. Şimşekler, Fuzzy soft topological spaces and the related category FST, Turk. J. Math., 43 (2019), 871-878.
  • [27] M. Riaz, K. Naeem, M. Aslam, D. Afzal, F. A. Ahmed Almahdi, S. Shaukat Jamal, Multi-criteria group decision making with Pythagorean fuzzy soft topology, J. Intell. Fuzzy Syst. (Preprint), (2020), 1-18.
  • [28] M. Riaz, S. T. Tehrim, On bipolar fuzzy soft topology with decision-making, Soft Comput., 24(24) (2020), 18259-18272.
  • [29] M. Riaz, K. Naeem, Measurable soft mappings, J. Math., Punjab Univ., 48(2) (2020).
  • [30] M. Riaz, N. Ç ağman, I. Zareef, M. Aslam, N-soft topology and its applications to multi-criteria group decision making, J. Intell. Fuzzy Syst., 36(6) (2019), 6521-6536.
  • [31] A. Açıkgöz, N. Taş, Some new mixed soft sets, MSAEN, 2 (2014), 105-118.
  • [32] A. Açıkgöz, N. A. Taş, T. Noiri, A decomposition of some types of mixed soft continuity in soft topological spaces, Filomat, 30 2016, 379-385.
  • [33] A. Csaszar, Mixed constructions for generalized topologies, Acta Math. Hung., 122 (2009), 153-159.
  • [34] W. K. Min, Mixed q-continuity on generalized topological spaces, Math. Comput. Modelling, 54 (2011), 2597-2601.
  • [35] W. K. Min, Mixed weak continuity on generalized topological spaces, Acta Math. Hung., 132 (2011), 339-347.
  • [36] N. A. Taş, A. Açıkgöz, Some mixed soft operations and extremally soft disconnectedness via two soft topologies, Appl. Math. 5 (2014), 490-500.
  • [37] N. A. Taş, O. B. Özbakır, On some mixed types of continuity on generalized neighborhood systems, J. Adv. Stud. Topol., 5 (2014), 32-43.
  • [38] M. Anitha, R. Selvi, P. Thangavelu, Pasting lemmas for g-continuous functions, Missouri J. Math. Sci., 21 (2009), 28-33.
  • [39] K. Balachandran, P. Sundaram, H. Maki, On generalized continuous maps in topological spaces, Mem. Fac. Sci., Kochi Univ., Ser. A 12 (1991), 5-13.
  • [40] Y. Gnanambal, K. Balachandran, On gpr-continuous functions in topological spaces, Indian J. Pure Appl. Math., 30 (1999), 581-593.
  • [41] K. Kannan, K. C. Rao, Pasting lemmas for some continuous functions, Thai J. Math., 12 (2014), 245-249.
  • [42] D. Vidhya, R. Parimelazhagan, g b-continuous maps and pasting lemma in topological spaces, Int. J. Math. Anal., 6 (2012), 2307-2315.
  • [43] S. Hussain, B. Ahmad, Some properties of soft topological space, Comput. Math. Appl., 62 (2011), 4058-4067.
  • [44] A. Kharal, B. Ahmad, Mappings on soft classes, New Math. Nat. Comput., 7(03) (2011), 471-481.
There are 44 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Nihal Taş 0000-0002-4535-4019

Publication Date June 1, 2022
Submission Date November 9, 2021
Acceptance Date February 22, 2022
Published in Issue Year 2022 Volume: 5 Issue: 2

Cite

APA Taş, N. (2022). Two New Versions of the Pasting Lemma via Soft Mixed Structure. Fundamental Journal of Mathematics and Applications, 5(2), 67-80. https://doi.org/10.33401/fujma.1021120
AMA Taş N. Two New Versions of the Pasting Lemma via Soft Mixed Structure. Fundam. J. Math. Appl. June 2022;5(2):67-80. doi:10.33401/fujma.1021120
Chicago Taş, Nihal. “Two New Versions of the Pasting Lemma via Soft Mixed Structure”. Fundamental Journal of Mathematics and Applications 5, no. 2 (June 2022): 67-80. https://doi.org/10.33401/fujma.1021120.
EndNote Taş N (June 1, 2022) Two New Versions of the Pasting Lemma via Soft Mixed Structure. Fundamental Journal of Mathematics and Applications 5 2 67–80.
IEEE N. Taş, “Two New Versions of the Pasting Lemma via Soft Mixed Structure”, Fundam. J. Math. Appl., vol. 5, no. 2, pp. 67–80, 2022, doi: 10.33401/fujma.1021120.
ISNAD Taş, Nihal. “Two New Versions of the Pasting Lemma via Soft Mixed Structure”. Fundamental Journal of Mathematics and Applications 5/2 (June 2022), 67-80. https://doi.org/10.33401/fujma.1021120.
JAMA Taş N. Two New Versions of the Pasting Lemma via Soft Mixed Structure. Fundam. J. Math. Appl. 2022;5:67–80.
MLA Taş, Nihal. “Two New Versions of the Pasting Lemma via Soft Mixed Structure”. Fundamental Journal of Mathematics and Applications, vol. 5, no. 2, 2022, pp. 67-80, doi:10.33401/fujma.1021120.
Vancouver Taş N. Two New Versions of the Pasting Lemma via Soft Mixed Structure. Fundam. J. Math. Appl. 2022;5(2):67-80.
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