International Journal of Nonlinear Analysis and Applications

Pairwise connectedness in $\check{\text{C}}$ech fuzzy soft bi-closure spaces

Document Type : Research Paper

Authors

Department of Mathematics, Faculty of Education for Pure Sciences Ibn Al-Haitham, University of Baghdad, Baghdad, Iraq

Abstract

The concept of $\check{\text{C}}$ech fuzzy soft bi-closure space ($ \check{\text{C}} $fs bi-csp) $\left(\mathcal{U}, \mathcal{L}_{1}, \mathcal{L}_{2}, S\right)$ is initiated and studied by the authors in \cite{6}. The notion of pairwise fuzzy soft separated sets in $ \check{\text{C}} $fs bi-csp is defined in this study, and various features of this notion are proved. Then, we introduce and investigate the concept of connectedness in both $ \check{\text{C}} $fs bi-csps and its associated fuzzy soft bitopological spaces utilizing the concept of pairwise fuzzy soft separated sets. Furthermore, the concept of pairwise feebly connected is introduced, and the relationship between pairwise connected and pairwise feebly connected is discussed. Finally, we provide various instances to further explain our findings.

Keywords

[1] E. Cech, Topological spaces, Inter-Science Publishers, John Wiley and Sons, New York, 1966.
[2] K. Chandrasekha Rao and R. Gowri, On biclosure spaces, Bull. Pure Appl. Sci. 25E (2006), 171–175.
[3] C.L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl. 24 (1968), 182–190.[4] R.Gowri and G. Jegadeesan, On soft biCech closure spaces, Int. J. Math. Arch. 5 (2014), no. 11, 99–105.
[5] R. Gowri and G. Jegadeesan, On soft Cech closure spaces, Int. J. Math. Trends Technol. 9 (2014), no. 2, 122–127.
[6] M.Th. Hmood and R.N. Majeed, Cech fuzzy soft bi-closure spaces, IOP Conf. Ser. J. Phys.: Conf. Ser. 1879 (2021), 1–11.
[7] M.Th. Hmood and R.N. Majeed, On Cech fuzzy soft bi-closure spaces, AIP Conf. Proc. accepted.
[8] M.Th. Hmood and R.N. Majeed, “Pairwise Lower Separation Axioms in Cech Fuzzy Soft Bi-Closure Spaces, J. AL-Qadisiyah Comput. Sci. Math. 26 (2021), no. 4, 405–422.
[9] J. Krishnaveni and C. Sekar, Cech soft closure spaces, Int. J. Math. Trends Technol. 6 (2014), 123–135.
[10] R.N. Majeed and L.H. Maibed, Some structures of Cech fuzzy soft closure spaces, J. Engin. Appl. Sci. 13 (2018), no. 18, 7520–7526.
[11] R. N. Majeed, Cech fuzzy soft closure spaces, Int. J. Fuzzy Sys. Appl. 7 (2018), no. 2, 62–74.
[12] R.N. Majeed and L.H. Maibed, Lower separation axioms in Cech fuzzy soft closure spaces, Gazi Univ. J. Sci. 32 (2019), no. 4, 1254–1269.
[13] L. H. Maibed and R.N. Majeed, Connectedness in Cech fuzzy soft closure spaces, J. AL-Qadisiyah Comput. Sci. Math. 1 (2019), no. 11, 19–26.
[14] L.H. Maibed and R.N. Majeed, Some types of regularity and normality axioms in Cech fuzzy soft closure spaces, J. New Theory 24 (2018), 73–87.
[15] P.K. Maji, R. Biswas and A.R. Roy, Fuzzy soft sets, J. Fuzzy Math. 9 (2001), no. 3, 589–602.
[16] A.S. Mashhour and M.H. Ghanim, Fuzzy closure spaces, J. Math. Anal. Appl. 106 (1985), 154–170.
[17] D.A. Molodtsov, Soft set theory-first results, Comput. Math. Appl. 37 (1999), 19-31.
[18] P. Mukherjee and C. Park, On fuzzy soft bitopological spaces, Math. Comput. Sci. J. 10 (2015), no. 7, 2–9.
[19] S. Roy and T.K. Samanta, A note on fuzzy soft topological spaces, Ann. Fuzzy Math. Inf. 3 (2012), no. 2, 305–311.
[20] B. Tanay and M.B. Kandemir, Topological structures of fss’s, Comput. Math. Appl. 61 (2011), 412–418.
[21] U.D. Tapi and R. Navalakhe, Fuzzy biclosure spaces, Int. J. Math. Anal. 5 (2011), 789.
[22] B. P. Varol and H. Ayg¨un, Fuzzy soft topology, Hacettepe J. Math. Statist. 41 (2012), no. 2, 407–419.
[23] L.A. Zadeh, Fuzzy sets, Inf. Control 8 (1965), 338–353.
International Journal of Nonlinear Analysis and Applications
Volume 13, Issue 2
July 2022
Pages 2603-2610
  • Receive Date: 16 December 2021
  • Revise Date: 29 January 2022
  • Accept Date: 21 February 2022