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Intuitionistic fine space

Yıl 2024, Cilt: 73 Sayı: 2, 410 - 419, 21.06.2024

Ayyakanupillai Gnanaudhayam Rose Venish , Lakshmanadas Vidyarani , Vigneshwaran M

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

Öz

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.

Anahtar Kelimeler

IfOS intuitionistic fine continuous intuitionistic fine irresolute intuitionistic fine irresolute homeomorphism

Kaynakça

  • 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

Yıl 2024, Cilt: 73 Sayı: 2, 410 - 419, 21.06.2024

Ayyakanupillai Gnanaudhayam Rose Venish , Lakshmanadas Vidyarani , Vigneshwaran M

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

Öz

Kaynakça

  • 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
Toplam 22 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Research Article
Yazarlar

Ayyakanupillai Gnanaudhayam Rose Venish 0000-0002-3710-997X

Lakshmanadas Vidyarani 0000-0002-2244-7140

Vigneshwaran M 0000-0003-1845-6877

Yayımlanma Tarihi 21 Haziran 2024
Gönderilme Tarihi 25 Nisan 2023
Kabul Tarihi 13 Şubat 2024
Yayımlandığı Sayı Yıl 2024 Cilt: 73 Sayı: 2

Kaynak Göster

APA Rose Venish, A. G., Vidyarani, L., & M, V. (2024). Intuitionistic fine space. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 73(2), 410-419. https://doi.org/10.31801/cfsuasmas.1286719
AMA Rose Venish AG, Vidyarani L, M V. Intuitionistic fine space. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Haziran 2024;73(2):410-419. doi:10.31801/cfsuasmas.1286719
Chicago Rose Venish, Ayyakanupillai Gnanaudhayam, Lakshmanadas Vidyarani, ve Vigneshwaran M. “Intuitionistic Fine Space”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73, sy. 2 (Haziran 2024): 410-19. https://doi.org/10.31801/cfsuasmas.1286719.
EndNote Rose Venish AG, Vidyarani L, M V (01 Haziran 2024) Intuitionistic fine space. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73 2 410–419.
IEEE A. G. Rose Venish, L. Vidyarani, ve V. M, “Intuitionistic fine space”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 73, sy. 2, ss. 410–419, 2024, doi: 10.31801/cfsuasmas.1286719.
ISNAD Rose Venish, Ayyakanupillai Gnanaudhayam vd. “Intuitionistic Fine Space”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73/2 (Haziran 2024), 410-419. https://doi.org/10.31801/cfsuasmas.1286719.
JAMA Rose Venish AG, Vidyarani L, M V. Intuitionistic fine space. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2024;73:410–419.
MLA Rose Venish, Ayyakanupillai Gnanaudhayam vd. “Intuitionistic Fine Space”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 73, sy. 2, 2024, ss. 410-9, doi:10.31801/cfsuasmas.1286719.
Vancouver Rose Venish AG, Vidyarani L, M V. Intuitionistic fine space. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2024;73(2):410-9.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics

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