Separation axioms in q∗-rung orthopair neutrosophic topological spaces

Shyamaladevi, V.; Revathi, G. K.

doi:10.47974/JIM-2327

Open Access Research Article

Separation axioms in q∗-rung orthopair neutrosophic topological spaces

V. Shyamaladevishyamaths@gmail.comDepartment of MathematicsSchool of Advanced SciencesVellore Institute of Technology ChennaiChennai, Tamil Nadu, 127, IndiaView full profile → , ^*G. K. RevathiCorresponding authorgk_revathi@yahoo.co.inDepartment of MathematicsSchool of Advanced SciencesVellore Institute of Technology ChennaiChennai, Tamil Nadu, 127, India0000-0003-1899-7390View full profile →

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pp. 2687–2706Vol. 28Issue 7October 2025DOI: 10.47974/JIM-2327XML

Received:: 07 Jan 2025
Published Online:: 25 Sep 2025
Article type:: Research Article
Language:: EN
Article no.:: JIM-2327
Pages:: 2687–2706

Abstract

In the framework of q*-rung orthopair neutrosophic topological space(q*-RONTS), this study focuses on establishing and analyzing separation axioms, such as N*qn T0, N*qn T1 and N*qnT2. The paper explores the manifestation of these axioms within the broader framework of q*-rung orthopair neutrosophic (q*-RON) theory, taking into account the complex role of degrees of truth, falsehood, and indeterminacy. Additionally demonstrate how the unique structure of q*-RONTS influences the separation of sets and points using in-depth definitions, theorems, and examples. The analysis of the impact of separation qualities in q*-rung orthopair neutrosophic topoligical subspaces and how these properties are maintained or changed under continuous mappings is also included in this paper.

Keywords

q*-rung orthopair neutrosophic set (q*-RONS)q*-RONTS q*-rung orthopair neutrosophic point (q*-RONP)q*-rung orthopair neutrosophic continuous (q*-RONC)q*-RON N*qn Ti-spaces (i = 0 1 2)

Subject Classifications

54A0594D0554A40

References

[1] F. Smarandache, A unifying eld in logics: neutrosophic logic. Neutrosophy, neutrosophic set, neutrosophic probability: neutrsophic logic. Neutrosophy, neutrosophic set, neutrosophic probability. Innite Study (2005).
[2] A. Salama and S. Alblowi, “Neutrosophic set and neutrosophic topological spaces,” (2012).
[3] V. I. Bogachev, “Measures on topological spaces,” Journal of Mathematical Sciences, vol. 91, no. 4, pp. 30333156 (1998).
[4] P. Y. Lum, G. Singh, A. Lehman, T. Ishkanov, M. Vejdemo-Johansson, M. Alagappan, J. Carlsson, and G. Carlsson, “Extracting insights from the shape of complex data using topology,” Scientic reports, vol. 3, no. 1, pp. 1236 (2013).
[5] N. Bourbaki, General Topology: Chapters 14. Springer Science & Business Media, vol. 18 (2013).
[6] M. E. Sardiu, J. M. Gilmore, B. Groppe, L. Florens, and M. P.Washburn, “Identication of topological network modules in perturbed protein interaction networks,” Scientic reports, vol. 7, no. 1, pp. 43845 (2017).
[7] B. M. Stadler and P. F. Stadler, “Generalized topological spaces in evolutionary theory and combinatorial chemistry,” Journal of chemical information and computer sciences, vol. 42, no. 3, pp. 577585 (2002).
[8] L. A. Zadeh, “Fuzzy sets,” Information and control, vol. 8, no. 3, pp. 338353 (1965).
[9] K. T. Atanassov and S. Stoeva, “Intuitionistic fuzzy sets,” Fuzzy sets and Systems, vol. 20, no. 1, pp. 8796 (1986).
[10] G. Revathi, E. Roja, and M. Uma, “Ordered (r, s) intuitionistic fuzzy quasi uniform regular gδ extremally disconnected spaces,” Annals of Fuzzy Mathematics and Informatics, vol. 6, no. 1, pp. 3345 (2013).
[11] -----, “regular gδ continuous mapping,” Annals of Fuzzy Mathematics and Informatics, vol. 8, no. 1, pp. 5571 (2014).
[12] R. R. Yager, “Pythagorean fuzzy subsets,” in 2013 joint IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS). IEEE, pp. 5761 (2013).
[13] R. Yager, “Generalized orthopair fuzzy sets,” IEEE transactions on fuzzy systems, vol. 25, no. 5, pp. 12221230 (2016).
[14] B. C. Cuong and V. Kreinovich, “Picture fuzzy sets,” Journal of computer science and cybernetics, vol. 30, no. 4, pp. 409420 (2014).
[15] S. Ashraf, S. Abdullah, T. Mahmood, F. Ghani, and T. Mahmood, “Spherical fuzzy sets and their applications in multi-attribute decision making problems,” Journal of Intelligent & Fuzzy Systems, vol. 36, no. 3, pp. 28292844 (2019).
[16] F. Kutlu Gündoğdu and C. Kahraman, “Spherical fuzzy sets and spherical fuzzy topsis method,” Journal of intelligent & fuzzy systems, vol. 36, no. 1, pp. 337352 (2019).
[17] L. Li, R. Zhang, J. Wang, X. Shang, and K. Bai, “A novel approach to multi-attribute group decision-making with q-rung picture linguistic information,” Symmetry, vol. 10, no. 5, pp. 172 (2018).
[18] M. Olgun, M. Üver, and Ş. Yardımcı, “Pythagorean fuzzy points and applications in pattern recognition and pythagorean fuzzy topologies,” Soft Computing, vol. 25, no. 7, pp. 52255232 (2021).
[19] J. Ye, “Similarity measures based on the generalized distance of neutrosophic z-number sets and their multi-attribute decision making method,” Soft Computing, vol. 25, no. 22, pp. 13 97513 985 (2021).
[20] K. T. Atanassov and S. Stoeva, “Intuitionistic fuzzy sets,” Fuzzy sets and Systems, vol. 20, no. 1, pp. 8796 (1986).
[21] B. Coung, “Picture fuzzy sets-rst results part 1,” in Seminar neuro-fuzzy systems with applications, vol. 4, pp. 2013 (2013).
[22] F. Smarandache, “Neutrosophic set is a generalization of intuitionistic fuzzy set, inconsistent intuitionistic fuzzy set (picture fuzzy set, ternary fuzzy set), pythagorean fuzzy set, spherical fuzzy set, and q-rung orthopair fuzzy set, while neutrosophication is a generalization of regret theory, grey system theory, and three-ways decision (revisited),” Journal of New Theory, no. 29, pp. 131 (2019).
[23] N. Gonul Bilgin, D. Pamučar, and M. Riaz, “Fermatean neutrosophic topological spaces and an application of neutrosophic kano method,” Symmetry, vol. 14, no. 11, pp. 2442 (2022).
[24] H. Cheng-Ming, “Fuzzy topological spaces,” Journal of mathematical analysis and applications, vol. 110, no. 1, pp. 141178 (1985).
[25] R. Lowen, “Fuzzy topological spaces and fuzzy compactness,” Journal of Mathematical analysis and applications, vol. 56, no. 3, pp. 621633 (1976).
[26] D. Coker, “An introduction to intuitionistic fuzzy topological spaces,” Fuzzy sets and systems, vol. 88, no. 1, pp. 8189 (1997).
[27] N. Turanli and D. Coker, “Fuzzy connectedness in intuitionistic fuzzy topological spaces,” Fuzzy sets and systems, vol. 116, no. 3, pp. 369375 (2000).
[28] M. Olgun, M. Ünver, and S. Yardımcı, “Pythagorean fuzzy topological spaces,” Complex & Intelligent Systems, vol. 5, no. 2, pp. 177183 (2019).
[29] E. Türkarslan, M. Ünver, and M. Olgun, “-rung orthopair fuzzy topological spaces,” Lobachevskii Journal of Mathematics, vol. 42, no. 2, pp. 470478 (2021).
[30] A. Razaq, I. Masmali, H. Garg, and U. Shuaib, “Picture fuzzy topological spaces and associated continuous functions,” AIMS Mathematics, vol. 7, no. 8, pp. 14 84014 861 (2022).
[31] F. Smarandache, “Neutrosophy: neutrosophic probability, set, and logic: analytic synthesis & synthetic analysis” (1998).
[32] V. Shyamaladevi and G. Revathi, “An overview of neutrosophic topological spaces and its applications”. Journal of Engineering Science & Technology Review, vol. 17, no. 3 (2024).
[33] J. Shen, “Separation axiom in fuzzifying topology,” Fuzzy Sets and Systems, vol. 57, no. 1, pp. 111123 (1993).
[34] S. Bayhan and D. Coker, “On separation axioms in intuitionistic topological spaces,” International Journal of Mathematics and Mathematical Sciences, vol. 27, no. 10, pp. 621630 (2001).
[35] F. G. Lupianez, “Hausdorness in intuitionistic fuzzy topological spaces,” Journal of Fuzzy Mathematics, vol. 12, no. 3, pp. 521526 (2004).
[36] T. H. Jasim, H. I. Lafta, and S. M. Abdullah, “Some types of separation axioms for (k, m)-generalized fuzzy-(resp., fuzzy)-closed sets in dfts,” Journal of Interdisciplinary Mathematics, vol. 24, no. 7, pp. 17871798 (2021).
[37] R. D. Ali, L. A. Al-Swidi, and M. H. Hadi, “On fuzzy intense separation axioms in fuzzy ideal topological space,” Journal of Interdisciplinary Mathematics, vol. 25, no. 5, pp. 13571363 (2022).
[38] T. Y. Öztürk, “Separation axioms on fuzzy hypersoft topological spaces,” Journal of Interdisciplinary Mathematics, vol. 25, no. 8, pp. 25912601 (2022).
[39] S. Vaiyanan and R. Govindasamy Krishnamoorthy, “Enhanced control techniques for automated vehicles using q* ε-rung orthopair neutrosophic continuous functions,” Research in Mathematics, vol. 12, no. 1, pp. 2448378 (2025).
[40] S. Dey and G. C. Ray, “Separation axioms in neutrosophic topological spaces,” Neutrosophic Systems with Applications, vol. 2, pp. 3854 (2023).
[41] H. Garg, q-Rung Orthopair Fuzzy Sets. Springer (2022).
[42] M. G. Voskoglou, F. Smarandache, and M. Mohamed, q-Rung Neutrosophic Sets and Topological Spaces. Innite Study (2024).

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