On Topological Properties of Fuzzy Sequence Space through Orlicz Function
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10.58578/mjaei.v1i3.3810
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Abstract
In this study, a new class of fuzzy number sequences is defined using Orlicz functions, and various useful classes with a variety of structures have been imposed. The behavior of these new classes has been examined as well as their topological properties and relationship to other fuzzy sequences.
Keywords:
Fuzzy Sets; Sequence Spaces; Functional Analysis; Fuzzy Topology; Mathematical Analysis
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Paudel, G. P., Rana, K. S., Shahi, N. K., & Baral, A. (2024). On Topological Properties of Fuzzy Sequence Space through Orlicz Function. Mikailalsys Journal of Advanced Engineering International, 1(3), 132-144. https://doi.org/10.58578/mjaei.v1i3.3810
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References
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2. Başarir, M., & Mursaleen, M. (2004). Some difference sequence spaces of fuzzy number. J. Fuzzy Math, 12(1), 1-6.
3. Dabbas, A. F., & Battor, A. H.: Convergent double sequence of fuzzy real numbers defined by double Orilz function, International Journal of Academic and Applied Research, 4(6) (2020),22-31.
4. Hardy, G. H. (1904). On the Convergence of Certain Multiple Series Proc. London Math. Soc, 1, 124-128.
5. Mansoor, M. M., &Battor, A. H. (2021, March). Some New Double Sequence Spaces of Fuzzy Numbers Defined by Double Orlicz Functions Using A Fuzzy Metric. In Journal of Physics: Conference Series (Vol. 1818, No. 1, p. 012092). IOP Publishing.
6. Matloka, M. (1986) Sequence of fuzzy numbers, Busefal, 28: 28-37
7. Mursaleen, M., Mohiuddine, S. A., & Edely, O. H. (2010). On the ideal convergence of double sequences in intuitionistic fuzzy normed spaces, Computers & mathematics with applications, 59(2), 603-611.
8. Nanda, S. (1989).On sequences of fuzzy numbers. Fuzzy Sets and System, 33; 123-126.
9. Pahari, N. P. (2014). On normed space valued total paranormed Orlicz space of null sequences and its topological structures, International Journal of Mathematics Trends and Technology, 6, 105-112.
10. Paudel, G. P., Pahari, N. P., & Kumar, S. : Application of fuzzy logic through the Bellmen-Zadeh maximin method, Journal of Nepal Mathematical Society, 5(1) (2022), 41-47.
11. Paudel, G. P., Pahari, N. P., & Kumar, S. (2022). Double sequence space of Fuzzy real numbers defined by Orlicz function. The Nepali Mathematical Sciences Report, 39(2), 85-94.
12. Paudel, G. P., Pahari, N. P., & Kumar, S. (2022). Generalized form of p-bounded variation of sequences of fuzzy real numbers. Pure and Applied Mathematics journal, 11(3), 47-50.
13. Paudel, G. P., Sahani, S. K., & Pahari, N. P. (2022). On Generalized Form of Difference Sequence Space of Fuzzy Real Numbers Defined by Orlicz Function. Nepal Journal of Mathematical Sciences, 3(2), 31-38.
14. Paudel, G. P., Sahani, S. K., & Pahari, N. P. (2022). Generalized Form of Difference Sequence Space of Fuzzy Real Numbers Defined by Orlicz Function. Nepal Journal of Mathematical Sciences, 3(2).
15. Paudel, G. P., Pahari, N. P., & Kuimar, S. (2023). Topological Properties of Difference Sequence Space Through Orlicz-Paranorm function, Advances and Applications in Mathematical Sciences, 22(8), 1689-1703.
16. Paudel, G. P., Pahari, N. P., & Kumar, S. (2022): On sequence space of fuzzy real numbers defined by Orlicz functioin and paranorm, Jilin Daxue Xuebao (Gongxueban)/Journal of Jilin University (Engineering and Technology Edition), 42(2-2023)(2023), 494-509.
17. Paudel, G. P., Upadhyay, P. K., & Baral, A. : Fuzzy arithmetic–based algorithm for identifying medical conditions for better treatment, Mikailalsys Journal of Mathematics and Statistics, 1(1), 35-46, 2023.
18. Savas, E., & Patterson, R. F. (2007). Double sequence spaces are defined by Orlicz functions. Iranian Journal of Science and Technology (Sciences), 31(2), 183-188.
19. Tripathy, B.C. and Sharma B. (2008). Sequences of fuzzy numbers defined by orlicz function. MathematicSlovaca,58,621-628
20. Zadeh, L. A. (2008). Is there a need for fuzzy logic? .Information Sciences, 178(13), 2751-2779.
2. Başarir, M., & Mursaleen, M. (2004). Some difference sequence spaces of fuzzy number. J. Fuzzy Math, 12(1), 1-6.
3. Dabbas, A. F., & Battor, A. H.: Convergent double sequence of fuzzy real numbers defined by double Orilz function, International Journal of Academic and Applied Research, 4(6) (2020),22-31.
4. Hardy, G. H. (1904). On the Convergence of Certain Multiple Series Proc. London Math. Soc, 1, 124-128.
5. Mansoor, M. M., &Battor, A. H. (2021, March). Some New Double Sequence Spaces of Fuzzy Numbers Defined by Double Orlicz Functions Using A Fuzzy Metric. In Journal of Physics: Conference Series (Vol. 1818, No. 1, p. 012092). IOP Publishing.
6. Matloka, M. (1986) Sequence of fuzzy numbers, Busefal, 28: 28-37
7. Mursaleen, M., Mohiuddine, S. A., & Edely, O. H. (2010). On the ideal convergence of double sequences in intuitionistic fuzzy normed spaces, Computers & mathematics with applications, 59(2), 603-611.
8. Nanda, S. (1989).On sequences of fuzzy numbers. Fuzzy Sets and System, 33; 123-126.
9. Pahari, N. P. (2014). On normed space valued total paranormed Orlicz space of null sequences and its topological structures, International Journal of Mathematics Trends and Technology, 6, 105-112.
10. Paudel, G. P., Pahari, N. P., & Kumar, S. : Application of fuzzy logic through the Bellmen-Zadeh maximin method, Journal of Nepal Mathematical Society, 5(1) (2022), 41-47.
11. Paudel, G. P., Pahari, N. P., & Kumar, S. (2022). Double sequence space of Fuzzy real numbers defined by Orlicz function. The Nepali Mathematical Sciences Report, 39(2), 85-94.
12. Paudel, G. P., Pahari, N. P., & Kumar, S. (2022). Generalized form of p-bounded variation of sequences of fuzzy real numbers. Pure and Applied Mathematics journal, 11(3), 47-50.
13. Paudel, G. P., Sahani, S. K., & Pahari, N. P. (2022). On Generalized Form of Difference Sequence Space of Fuzzy Real Numbers Defined by Orlicz Function. Nepal Journal of Mathematical Sciences, 3(2), 31-38.
14. Paudel, G. P., Sahani, S. K., & Pahari, N. P. (2022). Generalized Form of Difference Sequence Space of Fuzzy Real Numbers Defined by Orlicz Function. Nepal Journal of Mathematical Sciences, 3(2).
15. Paudel, G. P., Pahari, N. P., & Kuimar, S. (2023). Topological Properties of Difference Sequence Space Through Orlicz-Paranorm function, Advances and Applications in Mathematical Sciences, 22(8), 1689-1703.
16. Paudel, G. P., Pahari, N. P., & Kumar, S. (2022): On sequence space of fuzzy real numbers defined by Orlicz functioin and paranorm, Jilin Daxue Xuebao (Gongxueban)/Journal of Jilin University (Engineering and Technology Edition), 42(2-2023)(2023), 494-509.
17. Paudel, G. P., Upadhyay, P. K., & Baral, A. : Fuzzy arithmetic–based algorithm for identifying medical conditions for better treatment, Mikailalsys Journal of Mathematics and Statistics, 1(1), 35-46, 2023.
18. Savas, E., & Patterson, R. F. (2007). Double sequence spaces are defined by Orlicz functions. Iranian Journal of Science and Technology (Sciences), 31(2), 183-188.
19. Tripathy, B.C. and Sharma B. (2008). Sequences of fuzzy numbers defined by orlicz function. MathematicSlovaca,58,621-628
20. Zadeh, L. A. (2008). Is there a need for fuzzy logic? .Information Sciences, 178(13), 2751-2779.
