Intuitionistic fine space

Year 2024, Volume: 73 Issue: 2, 410 - 419, 21.06.2024

Ayyakanupillai Gnanaudhayam Rose Venish , Lakshmanadas Vidyarani , Vigneshwaran M

https://doi.org/10.31801/cfsuasmas.1286719

Abstract

In the exploration of intuitionistic fine spaces, this article introduces a novel concept known as intuitionistic fine open sets (IfOS). Delving into the properties of these sets, the study analyzes both intuitionistic fine open and closed sets within the context of intuitionistic fine spaces. The article establishes fundamental definitions, accompanied by illustrative real time example, to provide a comprehensive understanding of the newly introduced sets. Furthermore, the exploration extends to defining and examining key concepts such as intuitionistic fine continuity, intuitionistic fine irresoluteness, and intuitionistic fine irresolute homeomorphism. This progression aims to contribute to the broader comprehension and application of intuitionistic fine spaces in topological contexts.

Keywords

IfOS, intuitionistic fine continuous, intuitionistic fine irresolute, intuitionistic fine irresolute homeomorphism

References

• Bouchet, A., Montes, S., Diaz, I., Intuitionistic fuzzy sets applied to color image processing, CEUR Workshop Proceedings, 3074 (2021), 1-9.
• Coker, D., A note on intutionistic sets and intuitionistic points, Turk. J. Math., 20(3) (1996), 343-351.
• Coker, D., An introduction to intuitionistic fuzzy topological spaces, Fuzzy Sets and Syst., 88 (1997), 81-89. https://doi.org/10.1016/S0165-0114(96)00076-0
• Erdal, C., Coker, D., On neighborhood structures in intuitionistic topological spaces, Math. Balk., 12 (1998), 283-293.
• Girija, S., Gnanambal, I., Some more results on intuitionistic semi open sets, Int J Eng Res Appl., 4(11) (2014), 70-74.
• Bredon, G. E., Topology and Geometry, Springer, New York, (1993). https://doi.org/10.1007/978-1-4757-6848-0
• Gnanambal, I., Selvanayaki, S., IGPR-continuity and compactness in intuitionistic topological spaces, British Journal of Mathematicas and Computer Science, 11(2) (2015), 1-8. 10.9734/BJMCS/2015/19568
• Valachos, I. K., Serigiadis, G. D., Intuitionistic fuzzy information-Applications to pattern recognition, Pattern Recognit. Lett., 28 (2007), 197–206. 10.1016/j.patrec.2006.07.004
• Levine, N., Semi-open sets and semi-continuity in topological spaces, Am Math Mon., 70(1) (1963), 36-41. https://doi.org/10.2307/2312781
• Li, Y., Li, T., Zhao, Q., Remote sensing image intuitionistic fuzzy set segmentation method, Acta Geodaetica et Cartographica Sinica, 52(3) (2023), 405-418. DOI:10.11947/j.AGCS.2023.20210419
• Munkres, J. R.,Topology, Pearson, (2003).
• Olgun, M., Unver, M., Yardimci, S., Pythagorean fuzzy points and applications in pattern recognition and Pythagorean fuzzy topologies, Methodologies and Application, 25 (2021), 5225-5232. DOI: 10.1007/s00500-020-05522-2
• Olav, N., On some classes of nearly open sets, Pac J Math., 15(3) (1963), 961-970. DOI:10.2140/PJM.1965.15.961
• Powar, P. L., Prathibha, D., A concise form of continuity in fine topological space, Adv. Comput. Sci. Technol., 10(6) (2017), 1785-1805.
• Powar, P. L., Rajak, K., Fine irresolute mappings, J. Adv. Stud. Topol., 3(4) (2012), 125-139. DOI:10.20454/JAST.2012.428
• Powar, P. L., Baravan A. A., Rajak, K., Kushwaha, R., Operations on fine topology, Eur. J. Appl. Math, 8 (1965), 338-353. DOI:10.29020/nybg.ejpam.v12i3.3449
• Senthilkumar, P., Algorithms for solving the opyimization problems using fuzzy and intutionistic fuzzy set, Int. J. Syst. Assur., 11 (2020), 189-222. https://doi.org/10.1007/s13198-019-00941-3
• Supriya, K. D., Ranjith, B., Akil, R. R., An application of intuitionistic fuzzy sets in medical diagnosis, Fuzzy Sets and Syst., 117 (2001), 209-213. DOI:10.1016/S0165-0114(98)00235-8
• Chaira, T., Intuitionistic fuzzy set approach for color region extraction, Journal of Scientific and Industrial Research , 69 (2010), 426-432.
• Vidyarani, L., Vigneshwaran, M., On some intutionistic supra closed sets on intuitionistic supra topological spaces, Bulletin of Mathematics and Statistics Research, 3(3) (2015), 1-9.
• Kovalevsky, V., Digital geometry based on the topology of abstract cell complexes, Proceedings of the Colloquium Discrete Geometry for Computer Imagery, (1993), 259-284.
• Zadeh, L. A., Fuzzy sets, Inf. Control., 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X