Bipolar Fuzzy Supra Topological Spaces

Year 2022, Volume: 26 Issue: 1, 156 - 168, 28.02.2022

Hami Malkoç Banu Pazar Varol

https://doi.org/10.16984/saufenbilder.987410

Cited By: 1

Abstract

In the present work, we introduce bipolar fuzzy supra topological space as a generalization of fuzzy supra topological space, investigate the basic properties, give the concepts of interior and closure and encouraged them by examples and counterexamples. Moreover, we study the concepts of bipolar fuzzy supra continuity and S^* bipolar fuzzy supra continuity and see that composition of two S^* bipolar fuzzy supra continuous functions may not be a S^* bipolar fuzzy supra continuous function. Also, we attempt to define the concept of compactness on bipolar fuzzy supra topology.

Keywords

Bipolar fuzzy set, bipolar fuzzy supra topology, bipolar fuzzy supra continuity, bipolar fuzzy supra compactness

References

• [1] L. Zadeh, “Fuzzy sets,” Information and Control, vol. 8, pp. 338–353, 1965.
• [2] L. Zadeh, “The concept of a linguistic variable and its application to approximate reasoning-I,” Inform. Sci., vol. 8, pp. 199–249, 1975.
• [3] K. T. Atanassov, “Intuitionistic fuzzy sets,” Fuzzy sets and Systems, vol. 20, pp. 87-96, 1986.
• [4] P.K Maji., R. Biswas and A. R. Roy, “Fuzzy soft sets,” J. Fuzzy Math., vol. 9, no. 3, pp. 589–602, 2001.
• [5] W-R. Zhang, “Bipolar fuzzy sets and relations: a computational framework for cognitive modeling and multiagent decision analysis,” NAFIPS/IFIS/NASA'94, pp. 305-309, 1994.
• [6] K. M. Lee, “Comparison of interval-valued fuzzy sets, intuitionistic fuzzy sets, and bipolarvalued fuzzy sets,” J. Fuzzy Logic Intelligent Systems, vol. 14, pp. 125-129, 2004.
• [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] S. P. Subbian and M. Kamaraj, “Bipolar-valued fuzzy ideals of ring and bipolar-valued fuzzy ideal extensions in subrings,” International Journal of Mathematics Trends and Technology, vol. 61, no. 3, pp. 155-163, 2018.
• [9] B. Pazar Varol, An approach to bipolar fuzzy submodules, TWMS J. App. and Eng. Math., 11 (1), 168-175, 2021.
• [10] 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 of Mathematical Archive, vol. 7, no. 3, pp. 30-36, 2016.
• [11] 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.
• [12] A. S. Mashhour, A. A. Allam, F. S. Mahmoud and F. H. Khedr, “On supratopological spaces,” Indian J. Pure Appl. Math., vol. 14, no 4, pp. 502-510, 1983.
• [13] M. E. Abd El-Monsef and A. E. Ramadan, “On Fuzzy Supra Topological Spaces,” Indian J. Pure Appl. Math., vol. 18, no. 4, pp. 322-329, 1987.
• [14] M. E. Abd El-Latif, “Some properties of fuzzy supra soft topological spaces,” Europen Journal of Pure and Applied Mathematics, vol. 12, no. 3, pp. 999-1017, 2019.
• [15] T. M. Al-Shami and M. E. Shafei, “On supra topological ordered spaces,” Arab Journal of Basic and Applied Science, vol. 26, no. 1, pp. 433-445, 2019.
• [16] T. M. Al-Shami and M. E. Shafei, “Two types of separation axioms on supra soft topological spaces,” Demonstratio Mathematica, vol. 52, pp. 147-165, 2019.
• [17] T. M. Al-Shami, “Paracompactness on supra topological spaces,” Journal of Linear and Topological Algebra, vol. 9, no. 2, pp. 121-127, 2020.
• [18] T. M. Al-Shami, M. Al Shumrani and C. Özel, “Another form of supra ordered separation axioms,” Journla of Mathematical Extension, vol. 15, no 1, pp. 105-125, 2021.
• [19] N. Turanlı, “An overview of intuitionistic fuzzy supratopological spaces,” Hacettepe Journal of Mathematics and Statistics, vol. 32, pp. 17-26, 2003.