1
Department of Mathematics, Annamalai University, Annamalai Nagar - 608 002, India.
(surendrasarathi47@gmail.com)
2
Department of Mathematics, Annamalai University, Annamalai Nagar - 608 002, India; Department of Mathematics, Arignar Anna Government Arts College, Namakkal - 637 002, India
(chitrakalalaksana@gmail.com)
3
Department of Mathematics, Annamalai University, Annamalai Nagar - 608 002, India; Department of Mathematics, M.Kumarasamy College of Engineering, Karur - 639 113, India.
(avmaths@gmail.com)
Abstract :
In this article, the concept of fuzzy hypersoft δ (resp. semi, pre, δ semi & δ pre)-separation axioms in fuzzy hypersoft topological spaces are introduced by developing fuzzy hypersoft δ (resp. semi, pre, δ semi & δ pre)-neighbourhood with respect to fuzzy hypersoft points. Also, the properties and relations between fuzzy hypersoft δ (resp. semi, pre, δ semi & δ pre)- Ti- spaces (i = 0, 1, 2, 3, 4) are discussed.
Keywords :
FHyS δ (resp. semi , pre; δ semi & δ pre)-neighbourhood; FHyS δ (resp. semi , pre , δ semi & δ pre)-separation axioms; FHyS δ (resp. semi , pre , δ semi & δ pre)- Ti- space (i = 0 , 1 , 2 , 3 , 4).
References :
[1] A. Acikgoz and F. Esenbel, Neutrosophic soft δ-topology and neutrosophic soft compactness, AIP Conference Proceedings 2183, 030002, (2019).
[2] A. Acikgoz and F. Esenbel, An approach to pre-separation axioms in neutrosophic soft topological spaces, Commun.Fac.Sci.Univ.Ank.ser. AI Math. Stat., 69 (2), (2020), 1389-1404.
[3] M. Abbas, G. Murtaza and F. Smarandache, Basic operations on hypersoft sets and hypersoft point, Neutrosophic Sets and Systems, 35, (2020), 407-421.
[4] D. Ajay and J. Joseline Charisma, Neutrosophic hypersoft topological spaces, Neutrosophic Sets and Systems, 40, (2021), 178-194.
[5] D. Ajay, J. Joseline Charisma, N. Boonsatit, P. Hammachukiattikul and G. Rajchakit Neutrosophic semiopen hypersoft sets with an application to MAGDM under the COVID-19 scenario, Hindawi Journal of Mathematics, 2021, (2021), 1-16.
[6] C. G. Aras, T. Y. Ozturk and S. Bayramov, Separation axioms on neutrosophic soft topological spaces, Turkish Journal of Mathematics, 43 (2019), 498-510.
[7] C. L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl., 24 (1968), 182-190.
[8] C. Gunduz, TY. Ozturk, and S. Bayramov, Separation axioms on neutrosophic soft topological spaces, Turkish Journal of Mathematics, 43 (1), (2019), 498 - 510.
[9] A. M. Khattak, N. Hanif, F. Nadeem, M. Zamir, C. Park, G. Nordo and S. Jabeen, Soft b-separation axioms in neutrosophic soft topological structures, Annals of Fuzzy Mathematics and Informatics, 18 (1) (2019), 93-105.
[10] D. Molodtsov, Soft set theory-first results, Comput. Math. Appl., 37, (1999), 19-31.
[11] T. Y. Ozturk, Separation axioms on fuzzy hypersoft topological spaces, Journal of Interdisciplinary Mathematics, 43 (1), (2022), 1 - 11.
[12] P. Revathi, K. Chitirakala and A. Vadivel, Soft e-Separation Axioms in Neutrosophic soft Topological Spaces, Journal of Physics: Conference Series, 2070 (012028), (2021).
[13] S. Saha, Fuzzy δ-continuous mappings, Journal of Mathematical Analysis and Applications, 126 (1987), 130-142.
[14] M. Saqlain, S. Moin, M.N. Jafar, M. Saeed and F. Smarandache, Aggregate operators of neutrosophic hypersoft set, Neutrosophic Sets and Systems, 32 (1), (2020), 294-306.
[15] M. Shabir and M. Naz, On soft topological spaces, Comput. Math. Appl., 61, (2011), 1786-1799.
[16] F. Smarandache, A Unifying field in logics: neutrosophic logic. neutrosophy, neutrosophic set, neutrosophic probability, American Research Press, Rehoboth, NM, (1999).
[17] F. Smarandache, Neutrosophic set: A generalization of the intuitionistic fuzzy sets, Inter. J. Pure Appl. Math., 24 (2005), 287-297.
[18] F. Smarandache, Extension of soft set to hypersoft set, and then to plithogenic hypersoft set , Neutrosophic Sets and Systems, 22, (2018), 168-170.
[19] A. Vadivel, M. Seenivasan and C. John Sundar, An introduction to δ-open sets in a neutrosophic topological spaces, Journal of Physics: Conference series, 1724 (2021), 012011.
[20] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (3), (1965), 338–353.
Style | # |
---|---|
MLA | P. Surendra, A. Vadivel, K. Chitirakala. "δ-separation Axioms on Fuzzy Hypersoft Topological Spaces." International Journal of Neutrosophic Science, Vol. 23, No. 1, 2024 ,PP. 17-26 (Doi : https://doi.org/10.54216/IJNS.230102) |
APA | P. Surendra, A. Vadivel, K. Chitirakala. (2024). δ-separation Axioms on Fuzzy Hypersoft Topological Spaces. Journal of International Journal of Neutrosophic Science, 23 ( 1 ), 17-26 (Doi : https://doi.org/10.54216/IJNS.230102) |
Chicago | P. Surendra, A. Vadivel, K. Chitirakala. "δ-separation Axioms on Fuzzy Hypersoft Topological Spaces." Journal of International Journal of Neutrosophic Science, 23 no. 1 (2024): 17-26 (Doi : https://doi.org/10.54216/IJNS.230102) |
Harvard | P. Surendra, A. Vadivel, K. Chitirakala. (2024). δ-separation Axioms on Fuzzy Hypersoft Topological Spaces. Journal of International Journal of Neutrosophic Science, 23 ( 1 ), 17-26 (Doi : https://doi.org/10.54216/IJNS.230102) |
Vancouver | P. Surendra, A. Vadivel, K. Chitirakala. δ-separation Axioms on Fuzzy Hypersoft Topological Spaces. Journal of International Journal of Neutrosophic Science, (2024); 23 ( 1 ): 17-26 (Doi : https://doi.org/10.54216/IJNS.230102) |
IEEE | P. Surendra, A. Vadivel, K. Chitirakala, δ-separation Axioms on Fuzzy Hypersoft Topological Spaces, Journal of International Journal of Neutrosophic Science, Vol. 23 , No. 1 , (2024) : 17-26 (Doi : https://doi.org/10.54216/IJNS.230102) |