Fermatean Picture Fuzzy Connectedness and Its 
Compactness

V. Chitra; B. Maheswari

doi:https://doi.org/10.14445/22315373/IJMTT-V71I2P102

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 71 | Issue 2 | Year 2025 | Article Id. IJMTT-V71I2P102 | DOI : https://doi.org/10.14445/22315373/IJMTT-V71I2P102

Fermatean Picture Fuzzy Connectedness and Its Compactness

V. Chitra, B. Maheswari

Received	Revised	Accepted	Published
18 Dec 2024	21 Jan 2025	05 Feb 2025	19 Feb 2025

Abstract

This paper aims to introduce and explore the concepts of connectedness and compactness within Fermatean Picture fuzzy topological spaces. We will examine some fundamental properties and provide characterization theorems for these newly defined notions of connectedness and compactness in this specific type of topological space.

Keywords

Fermatean Picture fuzzy set (FPF), Fermatean Picture fuzzy topological spaces (FPFTS), FPF-continuous, FPF connectedness.

References

[1] Krassimir T. Atanassov, Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems, vol. 20, no. 1, pp. 87-96, 1986.
[CrossRef] [Google Scholar] [Publisher Link]
[2] Krassimir T. Atanassov, Intuitionistic Fuzzy Sets: Theory and Applications, Heidelberg: Physica-Verlag, 1999.
[CrossRef] [Google Scholar] [Publisher Link]
[3] K. Atanassov, and G. Gargov, “Interval-Valued Intuitionistic Fuzzy Sets,” Fuzzy Sets and Systems, vol. 31, no. 3, pp. 343-349, 1989.
[CrossRef] [Google Scholar] [Publisher Link]
[4] Said Broumi, and Florentin Smarandache, “Correlation Coefficient of Interval Neutrosophic Set,” Proceedings of the International Conference ICMERA, Bucharest, vol. 436, pp. 511-517, 2013.
[CrossRef] [Google Scholar] [Publisher Link]
[5] Said Broumi, and Florentin Smarandache, “Several Similarity Measures of Neutrosophic Sets,” Neutrosophic Sets and Systems, vol. 1, pp. 54-62, 2013.
[Google Scholar] [Publisher Link]
[6] Bui Cong Cuong, and Vladik Kreinovich, “Picture Fuzzy Sets - A New Concept for Computational Intelligence Problems,” Third World Congress on Information and Communication Technologies, Hanoi, Vietnam, pp. 1-6, 2013.
[CrossRef] [Google Scholar] [Publisher Link]
[7] Bùi Công Cường, “Picture Fuzzy Sets,” Journal of Computer Science and Cybernetics, vol. 30, no. 4, pp. 409-420, 2014.
[CrossRef] [Google Scholar] [Publisher Link]
[8] Bui Cong Cuong, “Pythagorean Picture Fuzzy Sets, Part 1- Basic Notions,” Journal of Computer Science and Cybernetics, vol. 35, no. 4, pp. 293-304, 2019.
[CrossRef] [Google Scholar] [Publisher Link]
[9] Hariwan Z. Ibrahim, “Fermatean Fuzzy Topological Spaces,” Journal of Applied Mathematics & Informatics, vol. 40, no. 1, pp. 85-98, 2022.
[CrossRef] [Google Scholar] [Publisher Link]
[10] Hariwan Z. Ibrahim, Tareq M. Al-shami, and O. G. Elbarbary, “(3,2) - Fuzzy Sets and Their Applications to Topology and Optimal Choices,” Computational Intelligence and Neuroscience, pp. 1-14, 2021.
[CrossRef] [Google Scholar] [Publisher Link]
[11] Young Bae Jun, and Kyoung Ja Lee, “Closed Cubic Ideals and Cubic Subalgebras in BCK/BCI Algebras,” Appied Mathematical Sciences, vol. 4, no. 68, pp. 3395-3402, 2010.
[Google Scholar] [Publisher Link]
[12] Young Bae Jun, Kyoung Ja Lee, and Min Su Kang, “Cubic Structures Applied to Ideals of BCI Algebras,” Computers & Mathematics with Applications, vol. 62, no. 9, pp. 3334-3342, 2011.
[CrossRef] [Google Scholar] [Publisher Link]
[13] V. Chitra, and B. Maheswari, “Fermatean Picture Fuzzy Sets,” Advances in Nonlinear Variational Inequalities, vol. 28, pp. 390-399, 2024.
[CrossRef] [Google Scholar] [Publisher Link]
[14] V. Chitra, and B. Maheswari, “Fermatean Picture Fuzzy Continuity in Fermatean Picture Fuzzy Topological Spaces,” Communications in Mathematics and Applications, Communicated.
[15] Haibin Wang, and Rajshekhar Sunderraman, Interval Neutrosophic Sets and Logic: Theory and Applications in Computing, Hexis, 2005.
[Google Scholar] [Publisher Link]
[16] Xindong Peng, and Yong Yang, “Some Results for Pythagorean Fuzzy Sets,” International Journal of Intelligent Systems, pp. 1133-1160, 2015.
[CrossRef] [Google Scholar] [Publisher Link]
[17] Ronald R. Yager, “Pythagorean Fuzzy Subsets,” IFSA World Congress and NAFIPS Annual Meeting, Edmonton, Canada, Edmonton, AB, Canada, pp. 57-61, 2013.
[CrossRef] [Google Scholar] [Publisher Link]
[18] Young Bae Jun, Florentin Smarandache, and Chang Su Kim, “Neutrosophic Cubic Sets,” New Mathematics and Natural Computation, vol. 13, no. 1, pp. 41-54, 2017.
[CrossRef] [Google Scholar] [Publisher Link]
[19] Yongwei Yang, and Jibo Li, “Arithmetic Aggregation Operators on Type-2 Picture Fuzzy Sets and Their Application in Decision Making,” Engineering Letters, vol. 31, no. 4, pp. 1-10, 2023.
[Google Scholar] [Publisher Link]
[20] L.A. Zadeh, “Fuzzy Sets,” Information and Control, vol. 8, no. 3, pp. 338-353, 1965.
[CrossRef] [Google Scholar] [Publisher Link]

Citation :

V. Chitra, B. Maheswari, "Fermatean Picture Fuzzy Connectedness and Its Compactness," International Journal of Mathematics Trends and Technology (IJMTT), vol. 71, no. 2, pp. 7-14, 2025. Crossref, https://doi.org/10.14445/22315373/IJMTT-V71I2P102