Research Article
BibTex RIS Cite

BIPOLAR SOFT CONTINUITY ON BIPOLAR SOFT TOPOLOGICAL SPACES

Year 2023, , 11 - 23, 30.11.2023
https://doi.org/10.47087/mjm.1314428

Abstract

The striking idea of soft sets was frst claimed that by Molodtsov as a new mathematical tool for dealing with uncertainties which is free from the other theories limitations. After the advent of soft set theory, bipolar soft sets as a generalization of soft sets, a new model of uncertain information, were introduced by Shabir and Naz. The main purpose of this paper is to introduce and investigate the structures of bipolar soft continuity, bipolar soft openness, bipolar soft closedness and bipolar soft homeomorphism.

References

  • M.I. Ali, F. Feng, X. Liu, W.K. Min and M. Shabir, On some new operations in soft set theory, Comput. Math. Appl., 57 (2009), 1547-1553.
  • T.M. Al-Shami, Soft somewhere dense sets on soft topological spaces, Commun. Korean Math. Soc., 33(4) (2018), 1341-1356.
  • T.M. Al-Shami, M.E. El-Shafei, Partial belong relation on soft separation axioms and decision-making roblem, two birds with one stone, Soft Computing, 24(7) (2020), 5377-5387.
  • M Aslam, S. Abdullah and K. Ullah, Bipolar fuzzy soft sets and its applications in decision making problem, J. Intell. Fuzzy Systems, 27(2) (2014), 729-742.
  • S. Bayramov and C. Gunduz , Soft locally compact spaces and soft paracompact spaces, Journal of Math. and Sys. Sci. 3, (2013), 122-130.
  • S. Bayramov and C. Gunduz , A new approach to separability and compactness in soft topological spaces, TWMS Journal of Pure and Applied Mathematics, 9(1) (2018), 82-93.
  • A.Fadel, S.C.Dzul-Kii, Bipolar soft topological spaces, European Journal of Pure and Applied Mathematics, 13 (2020), 227-245.
  • A.Fadel, S.C.Dzul-Kii, Bipolar soft functions, AIMS Mathematics, 6(5) (2021), 4428-4446.
  • C. Gunduz Aras and S. Bayramov, On the Tietze extension theorem in soft topological spaces, Proc. of Inst.Math. and Mech., 43(1) (2017), 105-115.
  • C. Gunduz Aras, T.M. Al-Shami, A. Mhemdi, S. Bayramov, Local compactness and para- compactness on soft bipolar topological spaces, J. Intell. Fuzzy Systems, 43 (2022), 6755- 6763.
  • C. G. Aras, A.Sonmez, H.Cakallı, An approach to soft functions, J.Math.Anal., 8 (2017), 129-138.
  • C. G. Aras, C. Metin, A note on bipolar soft continuity, International Conference of Math-ematical Sciences, 2021.
  • H. Posul, C. G. Aras, Servet Kutukcu,Soft A-Metric Spaces, Journal of New Theory, 41 (2022) 70-81.
  • K. Hayat and T. Mahmood, Some applications of bipolar soft set: Characterizations of two isomorphic Hemi-rings via BSI-h-Ideals, British Journal of Mathematics and Computer Sciences, 13 (2015), 1-21.
  • F. Karaaslan and S. Karatas, A new approach to bipolar soft sets and its applications, Discrete Mathematics, Algorithms and Applications, 7(4) (2015), 14 pg.
  • P.K. Maji, R. Biswas, A.R. Roy, Soft set theory, Comput. Math. Appl., 45 (2003), 555-562.
  • P. Majumdar, S.K.Samanta, On soft mappings, Comput. Math. Appl., 60 (2010), 2666-2672.
  • D. A. Molodtsov, Soft set theory-rst results, Comput. Math. Appl., 37 (1999), 19-31.
  • T.Y Ozturk, On bipolar soft topological spaces, J. New Theory, 20 (2018), 64-75.
  • T.Y Ozturk, On bipolar soft points, TWMS J. App. and Eng. Math., 10(4) (2020), 877-885.
  • M. Shabir, M. Naz, On bipolar soft sets, Retrieved from https://arxiv.org/abs/1303.1344v1 (2013).
  • M. Naz and M. Shabir, On fuzzy bipolar soft sets, their algebraic structures and applications, J. Intell. Fuzzy Systems, 26(4) (2014), 1645-1656.
  • M. Shabir and A. Bakhtawar, Bipolar soft connected, bipolar soft disconnected and bipolar soft compact spaces, Songklanakarin Journal of Science and Technology, 39(3) (2017), 359-371.
Year 2023, , 11 - 23, 30.11.2023
https://doi.org/10.47087/mjm.1314428

Abstract

References

  • M.I. Ali, F. Feng, X. Liu, W.K. Min and M. Shabir, On some new operations in soft set theory, Comput. Math. Appl., 57 (2009), 1547-1553.
  • T.M. Al-Shami, Soft somewhere dense sets on soft topological spaces, Commun. Korean Math. Soc., 33(4) (2018), 1341-1356.
  • T.M. Al-Shami, M.E. El-Shafei, Partial belong relation on soft separation axioms and decision-making roblem, two birds with one stone, Soft Computing, 24(7) (2020), 5377-5387.
  • M Aslam, S. Abdullah and K. Ullah, Bipolar fuzzy soft sets and its applications in decision making problem, J. Intell. Fuzzy Systems, 27(2) (2014), 729-742.
  • S. Bayramov and C. Gunduz , Soft locally compact spaces and soft paracompact spaces, Journal of Math. and Sys. Sci. 3, (2013), 122-130.
  • S. Bayramov and C. Gunduz , A new approach to separability and compactness in soft topological spaces, TWMS Journal of Pure and Applied Mathematics, 9(1) (2018), 82-93.
  • A.Fadel, S.C.Dzul-Kii, Bipolar soft topological spaces, European Journal of Pure and Applied Mathematics, 13 (2020), 227-245.
  • A.Fadel, S.C.Dzul-Kii, Bipolar soft functions, AIMS Mathematics, 6(5) (2021), 4428-4446.
  • C. Gunduz Aras and S. Bayramov, On the Tietze extension theorem in soft topological spaces, Proc. of Inst.Math. and Mech., 43(1) (2017), 105-115.
  • C. Gunduz Aras, T.M. Al-Shami, A. Mhemdi, S. Bayramov, Local compactness and para- compactness on soft bipolar topological spaces, J. Intell. Fuzzy Systems, 43 (2022), 6755- 6763.
  • C. G. Aras, A.Sonmez, H.Cakallı, An approach to soft functions, J.Math.Anal., 8 (2017), 129-138.
  • C. G. Aras, C. Metin, A note on bipolar soft continuity, International Conference of Math-ematical Sciences, 2021.
  • H. Posul, C. G. Aras, Servet Kutukcu,Soft A-Metric Spaces, Journal of New Theory, 41 (2022) 70-81.
  • K. Hayat and T. Mahmood, Some applications of bipolar soft set: Characterizations of two isomorphic Hemi-rings via BSI-h-Ideals, British Journal of Mathematics and Computer Sciences, 13 (2015), 1-21.
  • F. Karaaslan and S. Karatas, A new approach to bipolar soft sets and its applications, Discrete Mathematics, Algorithms and Applications, 7(4) (2015), 14 pg.
  • P.K. Maji, R. Biswas, A.R. Roy, Soft set theory, Comput. Math. Appl., 45 (2003), 555-562.
  • P. Majumdar, S.K.Samanta, On soft mappings, Comput. Math. Appl., 60 (2010), 2666-2672.
  • D. A. Molodtsov, Soft set theory-rst results, Comput. Math. Appl., 37 (1999), 19-31.
  • T.Y Ozturk, On bipolar soft topological spaces, J. New Theory, 20 (2018), 64-75.
  • T.Y Ozturk, On bipolar soft points, TWMS J. App. and Eng. Math., 10(4) (2020), 877-885.
  • M. Shabir, M. Naz, On bipolar soft sets, Retrieved from https://arxiv.org/abs/1303.1344v1 (2013).
  • M. Naz and M. Shabir, On fuzzy bipolar soft sets, their algebraic structures and applications, J. Intell. Fuzzy Systems, 26(4) (2014), 1645-1656.
  • M. Shabir and A. Bakhtawar, Bipolar soft connected, bipolar soft disconnected and bipolar soft compact spaces, Songklanakarin Journal of Science and Technology, 39(3) (2017), 359-371.
There are 23 citations in total.

Details

Primary Language English
Subjects Mathematical Methods and Special Functions
Journal Section Articles
Authors

Çiğdem Gündüz 0000-0002-3033-9772

Can Metin This is me 0000-0003-4607-8519

Early Pub Date September 19, 2023
Publication Date November 30, 2023
Acceptance Date July 1, 2023
Published in Issue Year 2023

Cite

APA Gündüz, Ç., & Metin, C. (2023). BIPOLAR SOFT CONTINUITY ON BIPOLAR SOFT TOPOLOGICAL SPACES. Maltepe Journal of Mathematics, 5(2), 11-23. https://doi.org/10.47087/mjm.1314428
AMA Gündüz Ç, Metin C. BIPOLAR SOFT CONTINUITY ON BIPOLAR SOFT TOPOLOGICAL SPACES. Maltepe Journal of Mathematics. November 2023;5(2):11-23. doi:10.47087/mjm.1314428
Chicago Gündüz, Çiğdem, and Can Metin. “BIPOLAR SOFT CONTINUITY ON BIPOLAR SOFT TOPOLOGICAL SPACES”. Maltepe Journal of Mathematics 5, no. 2 (November 2023): 11-23. https://doi.org/10.47087/mjm.1314428.
EndNote Gündüz Ç, Metin C (November 1, 2023) BIPOLAR SOFT CONTINUITY ON BIPOLAR SOFT TOPOLOGICAL SPACES. Maltepe Journal of Mathematics 5 2 11–23.
IEEE Ç. Gündüz and C. Metin, “BIPOLAR SOFT CONTINUITY ON BIPOLAR SOFT TOPOLOGICAL SPACES”, Maltepe Journal of Mathematics, vol. 5, no. 2, pp. 11–23, 2023, doi: 10.47087/mjm.1314428.
ISNAD Gündüz, Çiğdem - Metin, Can. “BIPOLAR SOFT CONTINUITY ON BIPOLAR SOFT TOPOLOGICAL SPACES”. Maltepe Journal of Mathematics 5/2 (November 2023), 11-23. https://doi.org/10.47087/mjm.1314428.
JAMA Gündüz Ç, Metin C. BIPOLAR SOFT CONTINUITY ON BIPOLAR SOFT TOPOLOGICAL SPACES. Maltepe Journal of Mathematics. 2023;5:11–23.
MLA Gündüz, Çiğdem and Can Metin. “BIPOLAR SOFT CONTINUITY ON BIPOLAR SOFT TOPOLOGICAL SPACES”. Maltepe Journal of Mathematics, vol. 5, no. 2, 2023, pp. 11-23, doi:10.47087/mjm.1314428.
Vancouver Gündüz Ç, Metin C. BIPOLAR SOFT CONTINUITY ON BIPOLAR SOFT TOPOLOGICAL SPACES. Maltepe Journal of Mathematics. 2023;5(2):11-23.

Creative Commons License
The published articles in MJM are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

ISSN 2667-7660