Stronger and Weaker Forms of Homeomorphisms Mappings via Fermatean Fuzzy $ M $-open Sets
DOI:
https://doi.org/10.5269/bspm.82986Resumen
In this paper, we introduce the concept of Fermatean fuzzy $ M $ open and Fermatean fuzzy $ M $ closed mappings in Fermatean fuzzy topological spaces. Also, we study about Fermatean fuzzy $ M $ Homeomorphism, almost Fermatean fuzzy $ M $ totally mappings, almost Fermatean fuzzy $ M $ totally continuous mappings and super Fermatean fuzzy $ M $ clopen continuous functions and their properties in Fermatean fuzzy topological spaces.
Referencias
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%
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\bibitem{at5} K. Atanassov (2016), {\it Review and new results on intuitionistic fuzzy sets}, International Journal Bioautomation. {\bf 20}, S17-S26.
\bibitem{ch} C. L Chang, {\it Fuzzy topological spaces}, J. Math. Anal. Appl., {\bf 24} (1968), 182-190.
\bibitem{co} D. Coker, {\it An introduction to intuitionistic fuzzy topological spaces}, Fuzzy sets and systems, {\bf 88} (1997), 81-89.
\bibitem{m1} A. I. El-Maghrabi and M. A. Al-Juhani, {\it $ M$-open sets in topological spaces,} Pioneer J. Math. Sci., {\bf 4} (2) (2011), 213–230.
\bibitem{ha} Hariwan Z. Ibrahim(2022), {\it Fermatean fuzzy Topological Spaces}, J. Appl. Math. and Informatics. {\bf 40}, 85-98.
\bibitem{he} X. He, Y. Du and W. Liu (2016), {\it Pythagorean fuzzy power average operators}, Fuzzy Syst. Math. {\bf 30} (6), 116-124.
\bibitem{le} M. Lellis Thivagar, S. Jafari, V. Sutha Devi and V. Antonysamy, \textit{ A novel approach to nano topology via neutrosophic sets}, Neutrosophic Sets and Systems, {\bf 20} (2018), 86-94.
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\bibitem{pa} A. Padma, M. Saraswathi, A. Vadivel and G. Saravanakumar, {\it New Notions of Nano $ M $-open Sets}, Malaya Journal of Matematik, \textbf{S} (1) (2019), 656-660.
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\bibitem{ssa} S. Saha, \textit{Fuzzy $ \delta $-continuous mappings}, Journal of Mathematical Analysis and Applications, \textbf{126} (1987), 130-142.
\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{th} R. Thangammal, M. Saraswathi, A. Vadivel and C. John Sundar, {\it Fuzzy nano $Z$-open sets in fuzzy nano
topological spaces}, Journal of Linear and Topological Algebra, {\bf 11} (01) (2022), 27-38.
\bibitem{th1} R. Thangammal, M. Saraswathi, A. Vadivel, Samad Noeiaghdam, C. John Sundar, V. Govindan, Aiyared
Iampan, {\it Fuzzy nano $Z$-locally closed sets, extremally disconnected spaces, normal spaces, and their application}, Advances in Fuzzy Systems, (2022), 3364170.
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\bibitem{va1} A. Vadivel, C. John Sundar, K. Kirubadevi and S. Tamilselvan, {\it More on Neutrosophic Nano Open Sets},
International Journal of Neutrosophic Science (IJNS), {\bf 18} (4) (2022), 204-222.
\bibitem{va2} A. Vadivel, C. John Sundar, K. Saraswathi and S. Tamilselvan, {\it Neutrosophic Nano $M$ Open Sets},
International Journal of Neutrosophic Science, {\bf 19} (1) (2022), 132-147.
\bibitem{va} A. Vadivel, V. Sagunthaladevi and S. Priya (2025), {\it More on Open Sets in Fermatean Fuzzy Topological Spaces and its Application}, accepted in J. Appl. Math. $\&$ Informatics.
\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}, accepted in Communications on Applied Nonlinear Analysis.
\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}, accepted in Communications on Applied Nonlinear Analysis.
\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{ya1} R. R. Yager (2013), {\it Pythagorean fuzzy subsets}, In: Proceedings of the joint $IFSA$ world congress $NAFIPS$ annual meeting, 57-61.
\bibitem{ya2} R. R. Yager (2014), {\it Pythagorean membership grades in multicriteria decision making}, $IEEE$ Trans Fuzzy Syst. {\bf 22} (4), 958-965.
\bibitem{za} L. A. Zadeh (1965), {\it Fuzzy sets}, Inf. Control, {\bf 8}, 338-353.
\bibitem{zad} L. Zadeh (1965), {\it Fuzzy Sets and Systems}, in Proc. Symp. on Systems Theory, Polytechnic Institute of Brooklyn, New York.
\bibitem{at1} K. T. Atanassov (1986), {\it Intuitionistic fuzzy sets}, Fuzzy Sets Syst. {\bf 20}, 87-96.
%
\bibitem{at4} K. T. Atanassov (1989), {\it Geometrical interpretation of the elements of the intuitionistic fuzzy objects}, Preprint IM-MFAIS-1-89, Sofia.
\bibitem{at2} K. T. Atanassov (1999), {\it Intuitionistic fuzzy sets: theory and applications}, Physica, Heidelberg.
\bibitem{at3} K. T. Atanassov (2012), {\it On intuitionistic fuzzy sets theory}, Springer, Berlin.
\bibitem{at5} K. Atanassov (2016), {\it Review and new results on intuitionistic fuzzy sets}, International Journal Bioautomation. {\bf 20}, S17-S26.
\bibitem{ch} C. L Chang, {\it Fuzzy topological spaces}, J. Math. Anal. Appl., {\bf 24} (1968), 182-190.
\bibitem{co} D. Coker, {\it An introduction to intuitionistic fuzzy topological spaces}, Fuzzy sets and systems, {\bf 88} (1997), 81-89.
\bibitem{m1} A. I. El-Maghrabi and M. A. Al-Juhani, {\it $ M$-open sets in topological spaces,} Pioneer J. Math. Sci., {\bf 4} (2) (2011), 213–230.
\bibitem{ha} Hariwan Z. Ibrahim(2022), {\it Fermatean fuzzy Topological Spaces}, J. Appl. Math. and Informatics. {\bf 40}, 85-98.
\bibitem{he} X. He, Y. Du and W. Liu (2016), {\it Pythagorean fuzzy power average operators}, Fuzzy Syst. Math. {\bf 30} (6), 116-124.
\bibitem{le} M. Lellis Thivagar, S. Jafari, V. Sutha Devi and V. Antonysamy, \textit{ A novel approach to nano topology via neutrosophic sets}, Neutrosophic Sets and Systems, {\bf 20} (2018), 86-94.
\bibitem{mu} Murat Olgun, Mehmet Unver and Seyhmus Yardimci (2019), {\it Pythagorean fuzzy topological spaces}, Complex $\&$ Intelligent Systems. https://doi.org/10.1007/s40747-019-0095-2.
\bibitem{pa} A. Padma, M. Saraswathi, A. Vadivel and G. Saravanakumar, {\it New Notions of Nano $ M $-open Sets}, Malaya Journal of Matematik, \textbf{S} (1) (2019), 656-660.
\bibitem{vp} V. Pankajam and K. Kavitha, {\it $ \delta $-open sets and $ \delta $-nano continuity in $ \delta $-nano topological spaces}, International Journal of Innovative Science and Research Technology, {\bf 2} (12) (2017), 110-118.
\bibitem{ssa} S. Saha, \textit{Fuzzy $ \delta $-continuous mappings}, Journal of Mathematical Analysis and Applications, \textbf{126} (1987), 130-142.
\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{th} R. Thangammal, M. Saraswathi, A. Vadivel and C. John Sundar, {\it Fuzzy nano $Z$-open sets in fuzzy nano
topological spaces}, Journal of Linear and Topological Algebra, {\bf 11} (01) (2022), 27-38.
\bibitem{th1} R. Thangammal, M. Saraswathi, A. Vadivel, Samad Noeiaghdam, C. John Sundar, V. Govindan, Aiyared
Iampan, {\it Fuzzy nano $Z$-locally closed sets, extremally disconnected spaces, normal spaces, and their application}, Advances in Fuzzy Systems, (2022), 3364170.
\bibitem{vj} A. Vadivel, M. Seenivasan and C. John Sundar, {\it An Introduction to $ \delta $-open sets in a Neutrosophic Topological Spaces}, Journal of Physics: Conference Series, 1724 (2021), 012011.
\bibitem{va1} A. Vadivel, C. John Sundar, K. Kirubadevi and S. Tamilselvan, {\it More on Neutrosophic Nano Open Sets},
International Journal of Neutrosophic Science (IJNS), {\bf 18} (4) (2022), 204-222.
\bibitem{va2} A. Vadivel, C. John Sundar, K. Saraswathi and S. Tamilselvan, {\it Neutrosophic Nano $M$ Open Sets},
International Journal of Neutrosophic Science, {\bf 19} (1) (2022), 132-147.
\bibitem{va} A. Vadivel, V. Sagunthaladevi and S. Priya (2025), {\it More on Open Sets in Fermatean Fuzzy Topological Spaces and its Application}, accepted in J. Appl. Math. $\&$ Informatics.
\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}, accepted in Communications on Applied Nonlinear Analysis.
\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}, accepted in Communications on Applied Nonlinear Analysis.
\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{ya1} R. R. Yager (2013), {\it Pythagorean fuzzy subsets}, In: Proceedings of the joint $IFSA$ world congress $NAFIPS$ annual meeting, 57-61.
\bibitem{ya2} R. R. Yager (2014), {\it Pythagorean membership grades in multicriteria decision making}, $IEEE$ Trans Fuzzy Syst. {\bf 22} (4), 958-965.
\bibitem{za} L. A. Zadeh (1965), {\it Fuzzy sets}, Inf. Control, {\bf 8}, 338-353.
\bibitem{zad} L. Zadeh (1965), {\it Fuzzy Sets and Systems}, in Proc. Symp. on Systems Theory, Polytechnic Institute of Brooklyn, New York.
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Publicado
2026-06-03
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Conf. Issue: Mathematics and Computing - Innovations and Applications
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Derechos de autor 2026 Boletim da Sociedade Paranaense de Matemática
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