The e-Open Sets in Neutrosophic Hypersoft Topological Spaces and Application in Covid-19 Diagnosis using Normalized Hamming Distance
Abstract
In this paper, we introduce a neutrosophic hypersoft e-open set which is the union of neutrosophic hypersoft δ-pre open sets and neutrosophic hypersoft δ-semi open sets in neutrosophic hypersoft topological spaces. Also, we discuss about the relations between neutrosophic hypersoft δ-pre open sets, neutrosophic hypersoft δ-semi open sets, neutrosophic hypersoft e-open sets and neutrosophic hypersoft e∗-open sets and their properties with the examples. Moreover, we investigate some of the basic properties of neutrosophic hypersoft e-interior and e-closure in a neutrosophic hypersoft topological space and proposed some examples for important results. Added to that, an application in Covid-19 diagnosis using normalized Hamming distance via neutrosophic hypersoft sets is discussed.
Full text article
References
Acikgoz, A. and Esenbel, F., Neutrosophic soft δ-topology and neutrosophic soft compactness, AIP Conference Proceedings, 2183 (2019), 030002.
Ajay, D. and Joseline Charisma, J., Neutrosophic hypersoft topological spaces, Neutrosophic Sets and Systems, 40 (2021), 178-194.
Ajay, D., Joseline Charisma, J., Boonsatit, N., Hammachukiattikul, P. and Rajchakit, G., Neutrosophic semiopen hypersoft sets with an application to MAGDM under the COVID-19 scenario, Hindawi Journal of Mathematics, 2021 (2021), 1-16.
Atanassov, K., Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87-96.
Bera, T. and Mahapatra, N. K., Introduction to neutrosophic soft topological space, Opsearch, 54 (2017), 841-867.
Chandrasekar, V., Sobana, D. and Vadivel, A., On Fuzzy e-open Sets, Fuzzy e-continuity and Fuzzy e-compactness in Intuitionistic Fuzzy Topological Spaces, Sahand Communications in Mathematical Analysis (SCMA), 12 (1) (2018), 131-153.
Chang, C. L., Fuzzy topological spaces, J. Math. Anal. Appl., 24 (1968), 182-190.
Coker, D., An introduction to intuitionistic fuzzy topological spaces, Fuzzy Sets and Systems, 88 (1997), 81-89.
Deli, I. and Broumi, S., Neutrosophic soft relations and some properties, Ann. Fuzzy Math. Inform., 9 (2015), 169-182.
Ekici, E., On e-open sets, DP⋆-sets and DPϵ⋆-sets and decomposition of continuity, The Arabian Journal for Science and Engineering, 33 (2A) (2008), 269-282.
Maji, P. K., Neutrosophic soft set, Ann. Fuzzy Math. Inform., 5 (2013), 157-168.
Molodtsov, D., Soft set theory-first results, Comput. Math. Appl., 37 (1999), 19-31.
Ozturk, T. Y. and Yolcu, A., On Neutrosophic hypersoft topological spaces, Theory and Application of Hypersoft Set, Pons Publishing House, Brussels, Chapter 12, (2021), 223-234.
Revathi, P., Chitirakala, K. and Vadivel, A., Soft e-separation axioms in neutrosophic soft topological spaces, Journal of Physics: Conference Series, 2070 (2021), 012028.
Revathi, P., Chitirakala, K. and Vadivel, A., Neutrosophic Soft e-Open Maps, Neutrosophic Soft e-Closed Maps and Neutrosophic Soft e-Homeomorphisms in Neutrosophic Soft Topological Spaces, Springer Proceedings in Mathematics and Statistics, 384 (2022), 47-58.
Saha, S., Fuzzy δ-continuous mappings, Journal of Mathematical Analysis and Applications, 126 (1987), 130-142.
Salama, A. A. and Alblowi, S. A., Neutrosophic set and neutrosophic topological spaces, IOSR Journal of Mathematics, 3 (4) (2012), 31-35.
Saqlain, M., Moin, S., Jafar, M.N., Saeed, M. and Smarandache, F., Aggregate operators of neutrosophic hypersoft set, Neutrosophic Sets and Systems, 32 (1) (2020), 294-306.
Saqlain, M., Riaz, M., Saleem, M.D. and Yang, M. S., Distance and similarity measures for neutrosophic hypersoft set (NHSS) with construction of NHSS-TOPSIS and applications, Neutrosophic Sets and Systems, 32 (2020), 317-329.
Seenivasan, V. and Kamala, K., Fuzzy e-continuity and fuzzy e-open sets, Annals of Fuzzy Mathematics and Informatics, 8 (2014), 141-148.
Shabir, M. and Naz, M., On soft topological spaces, Comput. Math. Appl., 61 (2011), 1786-1799.
Smarandache, F., A Unifying field in logics: neutrosophic logic. neutrosophy, neutrosophic set, neutrosophic probability, American Research Press, Rehoboth, NM, (1999).
Smarandache, F., Neutrosophic set: A generalization of the intuitionistic fuzzy sets, Inter. J. Pure Appl. Math., 24 (2005), 287-297.
Smarandache, F., Extension of soft set to hypersoft set, and then to plithogenic hypersoft set, Neutrosophic Sets and Systems, 22, (2018), 168-170.
Vadivel, A., Seenivasan, M. and John Sundar, C., An introduction to δ-open sets in a neutrosophic topological spaces, Journal of Physics: Conference series, 1724 (2021), 012011
Vadivel, A., Thangaraja, P. and John Sundar, C., Neutrosophic e-Continuous Maps and Neutrosophic e-Irresolute Maps, Turkish Journal of Computer and Mathematics Education, 12 (1S) (2021), 369-375.
Vadivel, A., Thangaraja, P. and John Sundar, C., Neutrosophic e-open maps, neutrosophic e-closed maps and neutrosophic e homeomorphisms in neutrosophic topological spaces, AIP Conference Proceedings, 2364 (2021), 020016.
Vadivel, A., Thangaraja, P. and John Sundar, C., Some Spaces in Neutrosophic e-Open Sets, Algebra, Analysis, and Associated Topics, Trends in Mathematics, (2022), 213-225.
Zadeh, L. A., Fuzzy sets, Information and Control, 8 (3) (1965), 338–353
Authors
Copyright (c) 2023 Journal of the Indonesian Mathematical Society
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Article Details
