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On Certain Properties of Bipolar Fuzzy Supra Preopen Sets

Year 2022, Volume: 11 Issue: 4, 1152 - 1158, 31.12.2022
https://doi.org/10.17798/bitlisfen.1196754

Abstract

The goal of this paper is to investigate the certain properties of bipolar fuzzy supra preopen sets (BF supra preopen set). We introduce and study the concepts of bipolar fuzzy supra pre-interior (BF supra pre-interior) and bipolar fuzzy supra pre-closure (BF supra pre-closure) operators. Furthermore, we define new type of bipolar fuzzy supra continuous mapping based on the BF preopen sets.

References

  • [1] L. Zadeh, Fuzzy sets, Information and Control vol.8, pp.338–353, 1965.
  • [2] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy sets and Systems, vol.20, pp.87-96, 1986.
  • [3] L. Zadeh, The concept of a linguistic variable and its application to approximate reasoning-I, Inform. Sci. vol.8, pp.199–249, 1975.
  • [4] W.L. Gau and D.J. Buehrer, Vague sets, IEEE Transactions on Systems, Man and Cybernetics, vol. 23, no.2, pp. 610-614, 1993.
  • [5] W-R. Zhang, Bipolar fuzzy sets and relations: a computational framework for cognitive modeling 356 and multiagent decision analysis NAFIPS/IFIS/NASA'94, pp.305-309, 1994.
  • [6] K. M. Lee, “Bipolar-valued fuzzy sets and their operations”, Proc. Int. Conf. on Intelligent Technologies Bangkok Thailand, pp. 307-312, 2000.
  • [7] M. S. Anitha, K. L. Muruganantha and K. Arjunan, Notes on bipolar valued fuzzy subgroups of a group, The Bulletin of Society for Mathematical Services and Standards, vol.7, pp. 40-45, 2013.
  • [8] B. Pazar Varol, An approach to bipolar fuzzy submodules, TWMS J. App. and Eng. Math., vol.11, No.1, pp. 168-175, 2021.
  • [9] M. Azhagappan and M. Kamaraj, “Notes on bipolar valued fuzzy RW-closaed and bipolar valued fuzzy RW-open sets in bipolar valued fuzzy topological spaces”, International Journal 796 of Mathematical Archive vol.7, no. 3, pp. 30-36, 2016.
  • [10] J. Kim, S. K. Samanta, P. K. Lim, J. G. Lee, K. Hur, Bipolar fuzzy topological spaces, Annals of Fuzzy Mathematics and Informatics, vol.17, no. 3, pp. 205-229, 2019.
  • [11] A. S. Mashhour, A. A. Allam, F. S. Mahmoud and F.H. Khedr, “On Supra Topological spaces”, Indian J. Pure Appl. Math. vol. 14, no. 4, pp. 502-510, 1983.
  • [12] M. E. Abd El-Monsef and A. E. Ramadan A. E, “On Fuzzy Supra Topological Spaces”, Indian J. Pure Appl. Math., vol.18, no.4, pp.322-329, 1987.
  • [13] N. Turanlı, An overview of intuitionistic fuzzy supra topological spaces, Hacettepe Journal of Mathematics and Statistics, vol.32, pp. 17-26, 2003.
  • [14] H. Malkoç and B. Pazar Varol, “Bipolar Fuzzy Supra Topological Spaces”, Sakarya University Journal of Science, vol.26, no.1, pp. 156-168, 2022.
  • [15] A. S. Mashhour et al., “On precontinuous and weak precontinuous mappings”, Proc. Math. Phys. Soc. Egypt., vol. 53, pp.47– 53, 1982.
  • [16] M. K. Signal and Niti Rajvanshi, “Fuzzy preopen sets and preseparation axioms”, Fuzzy Sets and Systems, vol.44, pp. 273-281, 1991.
  • [17] O.R. Sayed, “Supra preopen sets and Supra precontinuity on topological spaces”, Scientific Studies and Research, Series Mathematics and Informatics, vol.20, no.2, pp.79-88, 2010.
  • [18] J. Srikiruthika and A. Kalichelvi, “Fuzzy Supra Preopen Sets”, Global Journal of Pure and Applied Mathematics, vol. 14, no.1, pp. 57-66, 2018.
  • [19] K. M. Lee, “Comparison of interval-valued fuzzy sets, intuitionistic fuzzy sets and bipolar- valued fuzzy sets”, J. Fuzzy Logic Intelligent Systems vol.14, pp.125-129, 2004.
Year 2022, Volume: 11 Issue: 4, 1152 - 1158, 31.12.2022
https://doi.org/10.17798/bitlisfen.1196754

Abstract

References

  • [1] L. Zadeh, Fuzzy sets, Information and Control vol.8, pp.338–353, 1965.
  • [2] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy sets and Systems, vol.20, pp.87-96, 1986.
  • [3] L. Zadeh, The concept of a linguistic variable and its application to approximate reasoning-I, Inform. Sci. vol.8, pp.199–249, 1975.
  • [4] W.L. Gau and D.J. Buehrer, Vague sets, IEEE Transactions on Systems, Man and Cybernetics, vol. 23, no.2, pp. 610-614, 1993.
  • [5] W-R. Zhang, Bipolar fuzzy sets and relations: a computational framework for cognitive modeling 356 and multiagent decision analysis NAFIPS/IFIS/NASA'94, pp.305-309, 1994.
  • [6] K. M. Lee, “Bipolar-valued fuzzy sets and their operations”, Proc. Int. Conf. on Intelligent Technologies Bangkok Thailand, pp. 307-312, 2000.
  • [7] M. S. Anitha, K. L. Muruganantha and K. Arjunan, Notes on bipolar valued fuzzy subgroups of a group, The Bulletin of Society for Mathematical Services and Standards, vol.7, pp. 40-45, 2013.
  • [8] B. Pazar Varol, An approach to bipolar fuzzy submodules, TWMS J. App. and Eng. Math., vol.11, No.1, pp. 168-175, 2021.
  • [9] M. Azhagappan and M. Kamaraj, “Notes on bipolar valued fuzzy RW-closaed and bipolar valued fuzzy RW-open sets in bipolar valued fuzzy topological spaces”, International Journal 796 of Mathematical Archive vol.7, no. 3, pp. 30-36, 2016.
  • [10] J. Kim, S. K. Samanta, P. K. Lim, J. G. Lee, K. Hur, Bipolar fuzzy topological spaces, Annals of Fuzzy Mathematics and Informatics, vol.17, no. 3, pp. 205-229, 2019.
  • [11] A. S. Mashhour, A. A. Allam, F. S. Mahmoud and F.H. Khedr, “On Supra Topological spaces”, Indian J. Pure Appl. Math. vol. 14, no. 4, pp. 502-510, 1983.
  • [12] M. E. Abd El-Monsef and A. E. Ramadan A. E, “On Fuzzy Supra Topological Spaces”, Indian J. Pure Appl. Math., vol.18, no.4, pp.322-329, 1987.
  • [13] N. Turanlı, An overview of intuitionistic fuzzy supra topological spaces, Hacettepe Journal of Mathematics and Statistics, vol.32, pp. 17-26, 2003.
  • [14] H. Malkoç and B. Pazar Varol, “Bipolar Fuzzy Supra Topological Spaces”, Sakarya University Journal of Science, vol.26, no.1, pp. 156-168, 2022.
  • [15] A. S. Mashhour et al., “On precontinuous and weak precontinuous mappings”, Proc. Math. Phys. Soc. Egypt., vol. 53, pp.47– 53, 1982.
  • [16] M. K. Signal and Niti Rajvanshi, “Fuzzy preopen sets and preseparation axioms”, Fuzzy Sets and Systems, vol.44, pp. 273-281, 1991.
  • [17] O.R. Sayed, “Supra preopen sets and Supra precontinuity on topological spaces”, Scientific Studies and Research, Series Mathematics and Informatics, vol.20, no.2, pp.79-88, 2010.
  • [18] J. Srikiruthika and A. Kalichelvi, “Fuzzy Supra Preopen Sets”, Global Journal of Pure and Applied Mathematics, vol. 14, no.1, pp. 57-66, 2018.
  • [19] K. M. Lee, “Comparison of interval-valued fuzzy sets, intuitionistic fuzzy sets and bipolar- valued fuzzy sets”, J. Fuzzy Logic Intelligent Systems vol.14, pp.125-129, 2004.
There are 19 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Araştırma Makalesi
Authors

Banu Pazar Varol 0000-0002-8627-7910

Early Pub Date December 31, 1899
Publication Date December 31, 2022
Submission Date October 31, 2022
Acceptance Date December 19, 2022
Published in Issue Year 2022 Volume: 11 Issue: 4

Cite

IEEE B. Pazar Varol, “On Certain Properties of Bipolar Fuzzy Supra Preopen Sets”, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, vol. 11, no. 4, pp. 1152–1158, 2022, doi: 10.17798/bitlisfen.1196754.

Bitlis Eren University
Journal of Science Editor
Bitlis Eren University Graduate Institute
Bes Minare Mah. Ahmet Eren Bulvari, Merkez Kampus, 13000 BITLIS