Generalized $M$-Closed Functions and Homeomorphisms in Fermatean Neutrosophic Topological Spaces
DOI:
https://doi.org/10.5269/bspm.82922Resumo
In this paper, we undertake a detail study of Fermatean Neutrosophic generalized $M$-closed functions and Fermatean Neutrosophic generalized $M$-homeomorphisms by employing the framework of Fermatean Neutrosophic generalized $M$-open sets within Fermatean Neutrosophic topological spaces. The investigation not only introduces and formalizes these notions but also explores their fundamental characteristics, interrelationships, and behavior under various topological operations. Furthermore, several essential properties, illustrative examples, and potential applications of these functions and mappings are presented to highlight their significance in the broader development of Fermatean Neutrosophic topology.
Referências
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\bibitem{SS} A. A. Salama and F. Smarandache (2015), {\it Neutrosophic crisp set theory}, Educational Publisher, Columbus, Ohio, USA.
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\bibitem{mv1} A. Vadivel, C. John Sundar, K. Saraswathi and S. Tamilselvan (2022), {\it Neutrosophic nano $M$-open sets}, International Journal of Neutrosophic Science (IJNS), {\bf 19} (1), 132-147.
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https://doi.org/10.1063/5.0208371
\bibitem{va} A. Vadivel, V. Sagunthaladevi and S. Priya (2025), {\it More on open sets in Fermatean fuzzy topological spaces and its application}, J. Appl. Math. $\&$ Informatics, {\bf 43} (3), 839-852.
\bibitem{va3} A. Vadivel, V. Sagunthaladevi and S. Priya (2025), {\it Continuous and Irresolute Maps Via $\delta$-open Sets in Fermatean Fuzzy Topological Spaces And Application of MCDM Techniques}, Communications on Applied Nonlinear Analysis, {\bf 32} (10s), 1909-1924.
\bibitem{va4} A. Vadivel, V. Sagunthaladevi and S. Priya (2025), {\it Homeomorphism via $\delta\beta$-open Sets in Fermatean Fuzzy Topological Spaces and Application in Entropy Measure}, Communications on Applied Nonlinear Analysis, {\bf 32} (10s), 1895-1908.
\bibitem{va5} A. Vadivel, P. Thamilarasi, S. Priya and P. Periyasamy (2025), {\it $e$-open Maps and Homeomorphisms in Fermatean Neutrosophic Topological Spaces with Applications to Entropy Measures}, accepted in Neutrosophic Sets and Systems.
\bibitem{ya} R. R. Yager (2013), {\it Pythagorean membership grades in multicriteria decision making}, In: Technical report $MII$-3301. Machine Intelligence Institute, Iona College, New Rochelle.
\bibitem{za} L. A. Zadeh (1965), {\it Fuzzy sets}, Inf. Control, {\bf 8}, 338-353.
\bibitem{bi} N. G. Bilgin (2022), {\it $\Delta$-statistical convergence for Neutrosophic normed space}, J. Math., {\bf 2022}, 3890308.
\bibitem{VDA} V. Chandrasekar, D. Sobana and A. Vadivel (2018), {\it On Fuzzy $ e $-open Sets, Fuzzy $ e $-continuity and Fuzzy $ e $-compactness in Intuitionistic Fuzzy Topological Spaces}, Sahand Communications in Mathematical Analysis (SCMA), {\bf 12} (1), 131-153.
\bibitem{EE} Erdal Ekici (2008), {\it On $ e $-open sets, $ \mathcal{DP^\star} $-sets and $ \mathcal{DP \epsilon ^\star} $-sets and decomposition of continuity}, The Arabian Journal for Science and Engineering, {\bf 33} (2A), 269-282.
\bibitem{na} Nazmiye Gonul Bilgin, Dragan Pamucar and Muhammad Riaz (2022), {\it Fermatean neutrosophic topological spaces and an application of neutrosophic Kano Method}, Symmetry, {\bf 2022} (14), 2442. https://doi.org/10.3390/sym14112442
\bibitem{SA} A. A. Salama and S. A. Alblowi (2012), {\it Neutrosophic set and neutrosophic topological spaces}, IOSR Journal of Mathematics, {\bf 3} (4), 31-35.
\bibitem{SS} A. A. Salama and F. Smarandache (2015), {\it Neutrosophic crisp set theory}, Educational Publisher, Columbus, Ohio, USA.
\bibitem{VSKK} V. Seenivasan and K. Kamala (2014), {\it Fuzzy $ e $-continuity and fuzzy $ e $-open sets}, Annals of Fuzzy Mathematics and Informatics, {\bf 8}, 141-148.
\bibitem{sp} T. Senapati and R.R. Yager (2020), {\it Fermatean Fuzzy Sets}, Journal of Ambient Intelligence and Humanized Computing {\bf 11}, 663-674.
\bibitem{Sm1} F. Smarandache (1999), {\it A Unifying field in logics: neutrosophic logic. neutrosophy, neutrosophic set, neutrosophic probability}, American Research Press, Rehoboth, NM.
\bibitem{sw} C. A. C. Sweety and R. Jansi (2021), {\it Fermatean Neutrosophic Sets}, International Journal of Advanced Research in Computer and Communication Engineering, {\bf 10}, 24-27.
\bibitem{VJ4} A. Vadivel, M. Seenivasan and C. John Sundar (2021), {\it An introduction to $ \delta $-open sets in a neutrosophic topological spaces}, Journal of Physics: Conference Series, {\bf 1724}, 012011.
\bibitem{mv1} A. Vadivel, C. John Sundar, K. Saraswathi and S. Tamilselvan (2022), {\it Neutrosophic nano $M$-open sets}, International Journal of Neutrosophic Science (IJNS), {\bf 19} (1), 132-147.
\bibitem{mv2} D. Jeeva, A. Vadivel and D. Sivakumar (2024), {\it $M$-open sets in neutrosophic soft topological spaces}, AIP Conf. Proc. 2850, 020006 (2024)
https://doi.org/10.1063/5.0208371
\bibitem{va} A. Vadivel, V. Sagunthaladevi and S. Priya (2025), {\it More on open sets in Fermatean fuzzy topological spaces and its application}, J. Appl. Math. $\&$ Informatics, {\bf 43} (3), 839-852.
\bibitem{va3} A. Vadivel, V. Sagunthaladevi and S. Priya (2025), {\it Continuous and Irresolute Maps Via $\delta$-open Sets in Fermatean Fuzzy Topological Spaces And Application of MCDM Techniques}, Communications on Applied Nonlinear Analysis, {\bf 32} (10s), 1909-1924.
\bibitem{va4} A. Vadivel, V. Sagunthaladevi and S. Priya (2025), {\it Homeomorphism via $\delta\beta$-open Sets in Fermatean Fuzzy Topological Spaces and Application in Entropy Measure}, Communications on Applied Nonlinear Analysis, {\bf 32} (10s), 1895-1908.
\bibitem{va5} A. Vadivel, P. Thamilarasi, S. Priya and P. Periyasamy (2025), {\it $e$-open Maps and Homeomorphisms in Fermatean Neutrosophic Topological Spaces with Applications to Entropy Measures}, accepted in Neutrosophic Sets and Systems.
\bibitem{ya} R. R. Yager (2013), {\it Pythagorean membership grades in multicriteria decision making}, In: Technical report $MII$-3301. Machine Intelligence Institute, Iona College, New Rochelle.
\bibitem{za} L. A. Zadeh (1965), {\it Fuzzy sets}, Inf. Control, {\bf 8}, 338-353.
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Publicado
2026-06-03
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Conf. Issue: Mathematics and Computing - Innovations and Applications
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