NORMALITY AND REGULARITY OF PYTHAGOREAN FUZZY CELLULAR SPACES

Year 2025, Volume: 15 Issue: 10, 2543 - 2555, 01.10.2025

Gnanachristy N B , Revathi G K , William Obeng-denteh

Abstract

Normality and regularity are key separation axioms that helps to classify and understand the structure of topological spaces. This research article investigates the properties of normality and regularity within the context of Pythagorean fuzzy cellular spaces. Pythagorean fuzzy cellular space integrates Pythagorean fuzzy sets with cellular spaces, provide a robust framework for modeling and analyzing complex systems characterized by uncertainty and imprecision. In the the concepts of normality and regularity is defined formally in the context of Pythagorean fuzzy cellular space and explore their implications. This study establishes the theoretical foundations for analyzing normality and regularity in Pythagorean fuzzy cellular space, extending classical topological concepts to the fuzzy environment. In addition to it $ PF_{cel} \mathfrak{q} $-normal, $ PF_{cel} $ ultra normal, $ PF_{cel} $ completely ultra normal, $ PF_{cel} $ quasi normal is defined in Pythagorean fuzzy cellular space and interrelations are explored.

Keywords

Pythagorean fuzzy cellular space , Pythagorean fuzzy cellular $ \mathfrak{q} $ normal , $ PF_{cel} $ ultra normal , $ PF_{cel} $ quasi normal and $ PF_{cel} $ regular space

References

• Reference1 Al-Qubati, A. A., (2017), On b-Regularity and Normality in Intuitionistic Fuzzy Topological Spaces, Journal of Informatics and Mathematical Sciences, 9(1), pp. 89.
• Reference2 Al-Qubati, A. A. and Al-Qahtani, H. F., (2022), On Intuitionistic Fuzzy $ \beta $ Generalized $ \alpha $ Normal Spaces, International Journal of Analysis and Applications, 20, pp. 37-37.
• Reference3 Balasubramaniyan, K., Sriram, S. and Ravi, O., (2013), Mildly fuzzy normal spaces and some functions, J. Math. Comput. Sci., 3(4), pp. 1094-1107.
• Reference4 Ghareeb, A., (2011), Normality of double fuzzy topological spaces, Applied mathematics letters, 24(4), pp. 533-540.
• Reference5 Gnanachristy, N. B. and Revathi, G. K., (2024). An investigation on the recurrent function of the Pythagorean fuzzy cellular topological dynamical system, Heliyon, 10(13), pp. 1-12.
• Reference6 Hutton, B., (1975), Normality in fuzzy topological spaces, Journal of Mathematical Analysis and Applications, 50(1), pp. 74-79.
• Reference7 Karthika, A. and Prathiba., (2020), S. R., Fuzzy Ggp normal and regular spaces, Malaya Journal of Matematik, S(2), pp.1438-1442.
• Reference8 Liang, C. (2022). Regularity and normality of (L, M)-fuzzy topological spaces using residual implication. Fuzzy Sets and Systems, 444, pp 10-29. Reference9 Olgun, M.,Unver, M. and Yardimci S. , (2019), Pythagorean fuzzy topological spaces, Complex and Intelligent Systems, 5(2), pp. 177-183.
• Reference10 Ray, G. C. and Chetri, H. P., (2021), Separation Axioms in Mixed Fuzzy Topological Spaces, International Journal of Fuzzy Logic and Intelligent Systems, 21(4), pp. 423-430.
• Reference11 Saleh, S. A. M. and Al-Mufarrij, J., (2023), On g-regularity and g-normality in Fuzzy Soft Topological Spaces, European Journal of Pure and Applied Mathematics, 16(1), pp. 180-191.
• Reference12 Sivasangari, S. and Saravanakumar, G. (2021) . On e-Regularity and e- Normality in Intuitionisitic fuzzy topological spaces. Annals of Communications in Mathematics, 4(2), pp. 172.
• Reference13 Stephen M, G., Moses N, G., Paul A, O. and Hezron S, W., (2013), Normality and Its Variants on Fuzzy Isotone Spaces, Advances in Pure Mathematics, DOI:10.4236/apm.2013.37084.
• Reference14 Thabit, S. A. S., (2013), $ \Pi $-Normality in topological spaces and its generalization (Doctoral dissertation, Ph. D Thesis, School of Mathematical Sciences, Universiti Sains Malaysia, USM, Malaysia).
• Reference15 Vivek, S. and Mathew, S. C., (2022), Regularity of the extensions of a double fuzzy topological space, Proyecciones (Antofagasta), 41(1), pp. 163-176.
• Reference16 Yager, R. R., (2013), June, Pythagorean fuzzy subsets, In 2013 joint IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS), IEEE, pp. 57-61.
• Reference17 Zadeh, L. A., (1965), Fuzzy sets, Information and Control, 8 (3), pp. 338-353.