1
Department of Mathematics, Annamalai University, Annamalainagar, TN, India
(kv.chinnaduraimaths@gmail.com )
2
Department of Mathematics, Karpagam College of Engineering, Coimbatore, TN, India
(sindhu.mp@kce.ac.in)
Abstract :
The set which describes the uncertainty incident with three levels of attributes is entitled as a neutrosophic set. The unique collection of open sets which contains all types of open sets is termed as fine-open sets. The current study introduces a topology on merging these two sets, called neutro-fine topological space. Additionally, the approach of separation axioms is implemented in such space. Furthermore, the real-life application is examined as a decision-making problem in this space. The problem is to make an unfavorable query into a favorable one by determining the complement and absolute complement of such issued neutro-fine open sets. This problem desires to find a positive solution. The solving stepwise mechanism reveals in the algorithm, also formulae provide to compute the outcome with explanatory examples.
Keywords :
Subset of neutrosophic sets , neutro-fine sets (NFSs) , neutro-fine topological space (NFTS) , neutro-fine open sets (NFOSs) , neutro-fine interior and closure , neutro-fine -spaces , absolute complement , decision making (DM).
References :
[1] Abdel, B. M., Mohamed, M., Smarandache, F., “Comment on a novel method for solving the fully neutrosophic linear programming problems: suggested modifications”, Neutrosophic Sets and Systems, Vol 31, pp.305-309, 2020.
[2] Abdel-Basset, M., El-hoseny, M., Gamal, A., Smarandache, F., “A novel model for evaluation hospital medical care systems based on plithogenic sets”, Artificial Intelligence in Medicine, Vol 100, pp.101710, 2019.
[3] Abdel-Basset, M., Mohamed, R., Zaied, A. E. N. H., Smarandache, F., “A hybrid plithogenic decision-making approach with quality function deployment for selecting supply chain sustainability metrics”, Symmetry, Vol 11 (7), pp.903, 2019.
[4] Abdel-Basset, M., Mohamed, M., Smarandache, F., “An extension of neutrosophic AHP–SWOT analysis for strategic planning and decision making”, Symmetry, Vol 10, pp.116, 2018.
[5] Abishek, G., Saurabh, S., Rakesh, K. B., “On parametric diverdence measure of neutrosophic sets with its application in decision-making models”, Neutrosophic Sets and Systems, Vol 29, pp.101-120, 2019.
[6] Atanassov, K., “Intuitionistic fuzzy sets”, Fuzzy Sets and Systems, Vol 20, pp.87-96, 1986.
[7] Chinnadurai, V., Sindhu, M. P., “A novel approach for pairwise separation axioms on bi-soft topology using neutrosophic sets and an output validation in real life application”, Neutrosophic Sets and Systems, Vol 35, pp.435-463, 2020.
[8] Chinnadurai, V., Sindhu, M. P., “A novel approach: neutro-spot topology and its supra topology with separation axioms and computing the impact on covid-19”, Neutrosophic Sets and Systems, 2020 (Submitted).
[9] Chinnadurai, V., Sindhu, M. P., “Generalization of level sets in neutrosophic soft sets and points: a new approach”, Tathapi, Vol 19 (50), pp.54-81, 2020.
[10] Chinnadurai, V., Smarandache, F., Bobin, A., “Multi-aspect decision-making process in equity investment using neutrosophic soft matrices”, Neutrosophic Sets and Systems, Vol 31, pp.224-241, 2020.
[11] Ibrahim, Y., Abeer, T., Abd El-Khalek, A. A., Ahmed, S., Salama, A. A., “COVID-X: novel health-fog framework based on neutrosophic classifier for confrontation covid-19”, Neutrosophic Sets and Systems, Vol 35, pp.1-21, 2020.
[12] Kalaiselvi, S., Sindhu, M. P., “ -fb-open sets in fine-bitopological spaces”, International Journal of Multidisciplinary Research and Modern Education, Vol 2 (2), pp.435-441, 2016.
[13] Nandhini, R., Amsaveni, D., “Fine fuzzy sp closed sets in fine fuzzy topological space”, International Journal of Engineering and Advanced Technology, Vol 9 (3), pp.1306-1313, 2020.
[14] Parimala, M., Karthika, M., Smarandache, F., Broumi, S., “On -closed sets and its connectedness in terms of neutrosophic topological spaces”, International Journal of Neutrosophic Science, Vol 2 (2), pp.82-88, 2020.
[15] Parimala, M., Karthika, M., Smarandache, F., “Review of fuzzy soft topological spaces, intuitionistic fuzzy soft topological spaces and neutrosophic soft topological spaces”, International Journal of Neutrosophic Science, Vol 10 (2), pp.96-104, 2020.
[16] Powar, P. I., Rajak, K., “Fine-irresolute mappings”, Journal of Advanced Studies in Topology, Vol 3 (4), pp.125-139, 2012.
[17] Powar, P. I., Rajak, K., “Ultra separation axioms in generalized topological space”, International Journal for Electro Computational world Knowledge Interface, Vol 1 (4), pp.34-40, 2011.
[18] Prem, K. S., “Plithogenic set for multi-variable data analysis”, International Journal of Neutrosophic Science, Vol 1 (2), pp.81-89, 2020.
[19] Rajak, K., “Fine-minimal separation axioms in fine topological spaces”, International Journal of Advanced Research, Vol 2 (9), pp.40-43, 2014.
[20] Riad K. Al-Hamido, “On neutrosophic crisp supra bi-topological spaces”, International Journal of Neutrosophic Science, Vol 4 (1), pp.36-46, 2020.
[21] Riaz, M., Nazeem, K., Zareef, I., Afzal, D., “Neutrosophic N-soft sets with TOPSIS method for mutiple attribute decision making”, Neutrosophic Sets and Systems, Vol 32, pp.146-170, 2020.
[22] Rowthri, M., Amudhambigai, B., “A view on fuzzy fine topological group structures spaces”, International Journal of Computational and Applied Mathematics, Vol 12 (1), pp.412-422, 2017.
[23] Salma, A. A., Alblowi, S. A., “Neutrosophic set and neutrosophic topological spaces”, IOSR Journal of Applied Mathematics, Vol 3, pp.31-35, 2012.
[24] Salma, A. A., Alblowi, S. A., “Generalized neutrosophic set and generalized neutrosophic topological spaces”, Journal on Computer Science and Engineering, Vol 2 (7), pp.12-23, 2012.
[25] Sankar, C., Sujatha, R., Nagarajan, D., “TOPSIS by using plithogenic set in covid-19 decision making”, International Journal of Neutrosophic Science, Vol 10 (2), pp.116-125, 2020.
[26] Smarandache, F., “Neutrosophy, neutrosophic probability, set and logic”, American Research Press, Rehoboth, USA, pp.105, 1998.
[27] Smarandache, F., “Neutrosophic set, a generalisation of the intuitionistic fuzzy sets”, International Journal of Pure and Applied Mathematics, Vol 24, pp.287-297, 2005.
[28] Smarandache, F., “Plithogeny, plithogenic set, logic, probability, and statistics”, Infinity Study, pp.141, 2017.
[29] Smarandache, F., “Plithogenic set, an extension of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets –revisited”, Neutrosophic Sets and Systems, Vol 21, pp.153-166, 2018.
[30] Taha, Y. O., Cigdem, G. A., Sadi, B., “A new approach to operations on neutrosophic soft sets and to neutrosophic soft topological spaces”, Communications in Mathematics and Applications, Vol 10 (3), pp.481-493, 2019.
[31] Taha, Y. O., Cigdem, G.A., Sadi. B., “Separation axioms on neutrosophic soft topological spaces”, Turkish Journal of Mathematics, Vol 43, pp.498-510, 2019.
[32] Zadeh, L. A., “Fuzzy sets”, Information and Control, Vol 8, pp.338-353, 1965.
| Style | # |
|---|---|
| MLA | V. Chinnadurai, M. P. Sindhu. "An Introduction to Neutro-Fine Topology with Separation Axioms and Decision Making." International Journal of Neutrosophic Science, Vol. 12, No. 1, 2020 ,PP. 13-28 (Doi : https://doi.org/10.54216/IJNS.120103) |
| APA | V. Chinnadurai, M. P. Sindhu. (2020). An Introduction to Neutro-Fine Topology with Separation Axioms and Decision Making. Journal of International Journal of Neutrosophic Science, 12 ( 1 ), 13-28 (Doi : https://doi.org/10.54216/IJNS.120103) |
| Chicago | V. Chinnadurai, M. P. Sindhu. "An Introduction to Neutro-Fine Topology with Separation Axioms and Decision Making." Journal of International Journal of Neutrosophic Science, 12 no. 1 (2020): 13-28 (Doi : https://doi.org/10.54216/IJNS.120103) |
| Harvard | V. Chinnadurai, M. P. Sindhu. (2020). An Introduction to Neutro-Fine Topology with Separation Axioms and Decision Making. Journal of International Journal of Neutrosophic Science, 12 ( 1 ), 13-28 (Doi : https://doi.org/10.54216/IJNS.120103) |
| Vancouver | V. Chinnadurai, M. P. Sindhu. An Introduction to Neutro-Fine Topology with Separation Axioms and Decision Making. Journal of International Journal of Neutrosophic Science, (2020); 12 ( 1 ): 13-28 (Doi : https://doi.org/10.54216/IJNS.120103) |
| IEEE | V. Chinnadurai, M. P. Sindhu, An Introduction to Neutro-Fine Topology with Separation Axioms and Decision Making, Journal of International Journal of Neutrosophic Science, Vol. 12 , No. 1 , (2020) : 13-28 (Doi : https://doi.org/10.54216/IJNS.120103) |