On some weaker hesitant fuzzy open sets

Year 2021, Volume: 70 Issue: 2, 888 - 899, 31.12.2021

Hariwan Ibrahim

https://doi.org/10.31801/cfsuasmas.867250

Abstract

The purpose of this paper is to define and study some new types of hesitant fuzzy open sets namely, hesitant fuzzy $\alpha$-open, hesitant fuzzy preopen, hesitant fuzzy semiopen, hesitant fuzzy b-open and hesitant fuzzy $\beta$-open in hesitant fuzzy topological space. Some properties and the relationships between these hesitant fuzzy sets are investigated. Furthermore, some relationships between them in hesitant fuzzy subspace are introduced.

Keywords

hesitant fuzzy sets, hesitant fuzzy topology, hesitant fuzzy interior, hesitant fuzzy closure, hesitant fuzzy subspaces

References

• Abd El-Monsef, M. E., El-Deeb, S. N., Mahmoud, R. A., β-open sets and β-continuous mappings, Bull. Fac. Sci. Assuit Univ., 12 (1983), 77-90.
• Andrijevic, D., On b-open sets, Mat. Vesnik, 48 (1996), 59-64.
• Chang, C. L., Fuzzy topological spaces, J. Math. Anal. Appl., 24(1) (1968), 182-190.
• Divakaran, D., John, S. J., Hesitant fuzzy rough sets through hesitant fuzzy relations, Ann. Fuzzy Math. Inform., 8 (2014), 33-46.
• Jun, Y. B., Lee, K. J., Song, S. Z., Hesitant fuzzy bi-ideals in semigroups, Commun. Korean Math. Soc., 30(3) (2015), 143-154. http://dx.doi.org/10.4134/CKMS.2015.30.3.143
• Jun, Y. B., Ahn, S. S., Hesitant fuzzy sets theory applied to BCK/BCI-algebras, J. Comput. Anal. Appl., 20 (2016), 635-646.
• Kim, J., Lim, P. K., Lee, J. G., Hur, K., Hesitant fuzzy sets applied to BCK/BCI-algebras, Ann. Fuzzy Math. Inform., 18(3) (2019), 209-231. https://doi.org/10.30948/afmi.2019.18.3.209
• Kim, J., Jun, Y. B., Lim, P. K., Lee, J. G., Hur, K., The category of hesitant H-fuzzy sets, Ann. Fuzzy Math. Inform., 18(1) (2019), 57-74. https://doi.org/10.30948/afmi.2019.18.1.57
• Kim, J., Lim, P. K., Lee, J. G., Hur, K., Hesitant fuzzy subgroups and subrings, Ann. Fuzzy Math. Inform., 18(2) (2019), 105-122. https://doi.org/10.30948/afmi.2019.18.2.105
• Lee, J.-G., Hur, K., Hesitant fuzzy topological spaces, Mathematics, 8(2) (2020), 1-21. https://doi.org/10.3390/math8020188
• Levine, N., Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70 (1) (1963), 34-41.
• Mashhour, A. S., Abd El-Monsef, M. E., El-Deeb, S. N., On precontinuous and weak precontinuous functions, Proc. Math. Phys. Soc. Egypt, 51 (1982), 47-53.
• Njstad, O., On some classes of nearly open sets, Pacıfic J. Math., 15 (1965), 961-970.
• Torra, V., Hesitant fuzzy sets, Int. J. Intell. Syst., 25(6) (2010), 529-539. https://doi.org/10.1002/int.20418
• Xia, M., Xu, Z., Hesitant fuzzy information aggregation in decision making, Int. J. Approx. Reason., 52(3) (2011), 395-407. https://doi.org/10.1016/j.ijar.2010.09.002
• Zadeh, L. A., Fuzzy sets, Inf. Control., 8(3) (1965), 338-353.