Some remarks on neutro-fine topology

Document Type: Research Paper

Authors

1 Department of Mathematics, Annamalai University, Chidambaram, Tamilnadu, India.

2 Department of Mathematics, Faculty of Karpagam College of Engineering, Coimbatore, Tamilnadu, India.

Abstract

The neutro-fine topological space is a space that contains a combination of neutrosophic and fine sets. In this study, the various types of open sets such as generalized open and semi-open sets are defined in such space. The concept of interior and closure on semi-open sets are defined and some of their basic properties are stated. These definitions extend the concept to generalized semi-open sets. Moreover, the minimal and maximal open sets are defined and some of their properties are studied in this space. As well as, discussed the complement of all these sets as its closed sets. The basic properties of the union and intersection of these open sets are stated in some theorems. Only a few sets satisfy this postulates, and others are disproved as shown in the counterexamples. The converse of some theorems is proved in probable examples.

Keywords

Main Subjects


[1]     Smarandache, F. (2020). Generalizations and alternatives of classical algebraic Structures to NeutroAlgebraic structures and antialgebraic structures. Journal of fuzzy extension & applications1(2), 85.
[2]     Kumar Das, S. (2020). Application of transportation problem under pentagonal Neutrosophic environment. Journal of fuzzy extension and applications1(1), 27-41.
[3]     Abdel-Basset, M., Mohamed, M., & Smarandache, F. (2020). Comment on" a novel method for solving the fully neutrosophic linear programming problems: suggested modifications”. Neutrosophic sets and systems31(1), 22.
[4]     Smarandache, F. (2020). Extension of HyperGraph to n-SuperHyperGraph and to Plithogenic n-SuperHyperGraph, and Extension of HyperAlgebra to n-ary (Classical-/Neutro-/Anti-) HyperAlgebra. Neutrosophic sets and systems, 33, 290-296.
[5]     Chinnadurai, V., Smarandache, F., & Bobin, A. (2020). Multi-aspect decision-making process in equity investment using neutrosophic soft matrices. Neutrosophic Sets and Systems31, 224-241.
[6]     Chinnadurai, V., & Sindhu, M. P. (2020). 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 Systems35, 435-463.
[7]     Chinnadurai, V., & Sindhu, M. P. (2020). A novel approach: neutro-spot topology and its supra topology with separation axioms and computing the impact on COVID-19. Neutrosophic sets and systems (Submitted).
[8]     Chinnadurai, V., & Sindhu, M. P. (2020). An introduction to neutro-fine topology with separation axioms and decision making. International journal of neutrosophic science (Submitted).
[9]     Riaz, M., Naeem, K., Zareef, i., & afzal, d. (2020). neutrosophic n-soft sets with topsis method for multiple Attribute Decision Making. Neutrosophic sets and systems32(1).
[10] Guleria, A., Srivastava, S., & Bajaj, R. K. (2019). On parametric divergence measure of neutrosophic sets with its application in decision-making models. Neutrosophic sets and systems29(1), 9.
[11] Yasser, I., Twakol, A., Abd El-Khalek, A. A., Samrah, A., & Salama, A. A. (2020). COVID-X: novel health-fog framework based on neutrosophic classifier for confrontation Covid-19. Neutrosophic Sets and Systems35(1), 1.
[12] Nabeeh, N. A., Abdel-Monem, A., & Abdelmouty, A. (2019). A Hybrid Approach of Neutrosophic with MULTIMOORA in Application of Personnel Selection. Neutrosophic Sets and Systems30(1), 1.
[13] Nogueira, Y. E. M., Ojeda, Y. E. A., Rivera, D. N., León, A. M., & Nogueira, D. M. (2019). design and application of a questionnaire for the development of the knowledge management audit using neutrosophic iadov technique. Neutrosophic sets and systems30(1).
[14] Altinirmak, S., Gul, Y., Okoth, B. O., & Karamasa, C. (2018). Performance evaluation of mutual funds via single valued neutrosophic set (svns) perspective: a case study in turkey. Neutrosophic sets and systems23(1), 10.
[15] Smarandache, F. (2018). Plithogenic Set, an extension of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets-revisited. Infinite study, 21, 153-166. 
[16] Abdel-Basset, M., El-hoseny, M., Gamal, A., & Smarandache, F. (2019). A novel model for evaluation Hospital medical care systems based on plithogenic sets. Artificial intelligence in medicine100, 101710.
[17] Abdel-Basset, M., Mohamed, R., Zaied, A. E. N. H., & Smarandache, F. (2019). A hybrid plithogenic decision-making approach with quality function deployment for selecting supply chain sustainability metrics. Symmetry11(7), 903.
[18] Abdel-Basset, M., Nabeeh, N. A., El-Ghareeb, H. A., & Aboelfetouh, A. (2019). Utilising neutrosophic theory to solve transition difficulties of IoT-based enterprises. Enterprise information systems, 1-21.
[19] Abdel-Baset, M., Chang, V., & Gamal, A. (2019). Evaluation of the green supply chain management practices: A novel neutrosophic approach. Computers in industry108, 210-220.
[20] Abdel-Basset, M., Mohamed, M., & Smarandache, F. (2018). An extension of neutrosophic AHP–SWOT analysis for strategic planning and decision-making. Symmetry10(4), 116.
[21] Smarandache, F. (1998). Neutrosophy: neutrosophic probability, set, and logic: analytic synthesis & synthetic analysis. https://philpapers.org/rec/SMANNP American Research Press, Rehoboth, USA, 105.
[22] Smarandache, F. (2005). Neutrosophic set-a generalization of the intuitionistic fuzzy set. International journal of pure and applied mathematics24(3), 287. 287-297
[23] Smarandache, F. (2017). Plithogeny, plithogenic set, logic, probability, and statistics. Infinity study, 141.
[24] Chinnadurai, V., & Sindhu, M. P. (2020). Generalization of level sets in neutrosophic soft sets and points: a new approach. Tathapi, 19(50), 54-81.
[25] Kalaiselvi, S., & Sindhu, M. P. (2016). -fb-open sets in fine-bitopological spaces. International journal of multidisciplinary research and modern education, 2(2), 435-441.
[26] Nandhini, R., & Amsaveni, D. (2020). Fine fuzzy sp closed sets in fine fuzzy topological space. International journal of engineering and advanced technology, 9(3), 1306-1313.
[27] Pushpalatha, A., & Nandhini, T. (1965). Generalized closed sets via neutrosophic topological Spaces. Infinite Study.
[28] Iswarya, P., & Bageerathi, K. (2019). A study on neutrosophic generalized semi-closed sets in neutrosophic topological spaces. Journal of emerging technologies and innovative research, 6(2), 452-457.
[29] Ozturk, T. Y., Aras, C. G., & Bayramov, S. (2019). A new approach to operations on neutrosophic soft sets and to neutrosophic soft topological spaces. Infinite Study.
[30] Rowthri, M., & Amudhambigai, B. (2017). A view on fuzzy fine topological group structures spaces. International journal of computational and applied mathematics, 12(1), 412-422.
[31] Iswarya, P., & Bageerathi, K. (2016). On neutrosophic semi-open sets in neutrosophic topological spaces. Infinite Study. International journal of mathematics trends and technology, 37(3), 214-223.
[32] Rajak, K. (2015). semi-closed sets in fine-topological spaces. International journal of mathamatical sciences and applications, 5(2), 329-331.
[33] Salama, A. A., & Alblowi, S. A. (2012). Neutrosophic set and neutrosophic topological spaces. IOSR journal of mathematics3(4), 31-35.
[34] Salama, A. A., & Alblowi, S. A. (2012). Generalized neutrosophic set and generalized neutrosophic topological spaces. Infinite Study. Journal on computer science and engineering, 2(7), 12-23.
[35] Powar, P. L., & Rajak, K. (2012). Fine-irresolute mappings. Journal of advance studies in topology3(4), 125-139.
[36] Nakaoko, F., & Oda, N. (2003). On minimal closed sets. Proceeding of topological Spaces Theory and its Applications, 5, 19-21.
[37] Nakaoka, F., & Oda, N. (2003). Some properties of maximal open sets. International journal of mathematics and mathematical sciences, 21, 1331-1340.
[38] Nakaoka, F., & Oda, N. (2001). Some applications of minimal open sets. International journal of mathematics and mathematical sciences, 27 (8), 471-476.
[39] Atanassov, K. T. (1999). Intuitionistic fuzzy sets. In intuitionistic fuzzy sets (pp. 1-137). Physica, Heidelberg.
[40] Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8, 338-353.