Some Results in Fuzzy 2- Metric Space
DOI:
https://doi.org/10.29304/jqcm.2022.14.1.890Keywords:
Fuzzy2- metric space, convergent sequence, Compact fuzzy 2-metric space, Fuzzy totally boundedAbstract
The notion of fuzzy 2-metric space and its essential features are initially examined in this study. Following that, the ideas of compact fuzzy2- metric space and fuzzy totally bounded space are discussed. Furthermore, the essential theorems relating to these concepts are established. In particular, we prove that a fuzzy 2- metric space which is compact must be complete.
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References
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[2] AHLER S. G. (1964). Lineare 2-normierte Raume, Math. Nachr. 28(1-2), 1–43.
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[10] Hussein M., Z. (2018). On the(G.n)_ Tupled fixed point theorems in fuzzy metric space. Journal of Al-Qadisiyah for Computer Science and Mathematics, 10(2), Math Page 15 - 25.
[11]Isabelle, .B.( 2015). Fuzzy sets for image processing and understanding. Fuzzy Sets and Systems, 281 (15), 280-291.
[12]Jialiang, X., Qingguo, L,Shuili Chen, & Huan H.(2016). The fuzzy metric space based on fuzzy measure. Open Math, 14,603–612.
[13]Ju, M. K.& Keun, Y.(2019). Approximation Properties in Felbin Fuzzy Normed Spaces. Math J., 22:1-14.
[14]Kaleva, O. & Seikkala, S.(1984). On fuzzy metric spaces. Fuzzy Sets and Systems, 12, 215-229.
[15]Kocinac, L.，Cetkin, V. & Dolicanin, D.(2020).Selective Properties of Fuzzy 2-Metric Spaces. SER. A: APPL. MATH. INFORM. AND MECH,12(2),67-73.
[16]Kramosil, I. & Michalek J.(1975). Fuzzy metric and statistical metric spaces, Kybernetika ll , 336-344.
[17]Mayada, N. M. & Raghad, I. S.( 2021). Bounded Linear Transformations in G-Fuzzy Normed Linear Space. Journal of Al-Qadisiyah for Computer Science and Mathematics.13(1), 110–119.
[18]Mehmet, .S.(2016) . An Application of Fuzzy Sets to Veterinary Medicine. Theory and Applications of Mathematics & Computer Science, 6 (1) 1–12.
[19] Noori, F.A., & A . Abd alsaheb, D. (2017). Separation theorem for fuzzy normed space. Journal of Al-Qadisiyah for Computer Science and Mathematics, 6(2), 53-64.
[20] Noori, F.A., & H . Hadi, S. (2017). Some New result of Compact sets in fuzzy metric space. Journal of Al-Qadisiyah for Computer Science and Mathematics, 6(2), 77-82.
[21] Noori, F.A., & William Twair, H. (2017). Some Results on Weak and Strong Fuzzy Convergence for Fuzzy Normed Spaces. Journal of Al-Qadisiyah for Computer Science and Mathematics, 7(2), 126-131.
[22]Raghad, I. S.(2012). Product of Two Fuzzy Normed Spaces and its Completion. Engineering and Technology Journal, 30 (11), 1925-1934.
[23]Raghad, I. S.(2021). Compactness Property of Fuzzy Soft Metric Space and Fuzzy Soft Continuous Function.Iraqi Journal of Science, 62(9),
3031-3038.
[24]Raghad, I. S. ( 2021). Fuzzy Convergence Sequence and Fuzzy Compact Operators on Standard Fuzzy Normed Spaces. Baghdad
Science Journal,18(4), 1204-1211.
[25] Sabri, R., RASHEED, M., Alabdali, O., SHIHAB, S., & RASHID, T. (2021). On Some Properties in Fuzzy Metric Space. Journal of Al-Qadisiyah for Computer Science and Mathematics, 13(1), Math Page 55.
[26]Schweizer, B.& Sklar, A. (1960). Statistical metric spaces. Pacific J. Math., 10: 314–334.
[27]Sharma, S. (2002). On Fuzzy Metric Space. Southeast Asian Bulletin of Mathematics, 26, 133-145.
.
[28]Swati, B. K.r.(2019).A Study Of Fuzzy Metric Space. IJEDR, 7(3),186-188.
[29]Valentı́n, G & Salvador, R.(2000). Some properties of fuzzy metric spaces. Fuzzy Sets and Systems, 115 ( 3), 485-489.
[30]Zimmerman, H. J.( 1985).Fuzzy Sets Theory and Its Application. Kluwer Academic Publisher, Dordrecht.
[2] AHLER S. G. (1964). Lineare 2-normierte Raume, Math. Nachr. 28(1-2), 1–43.
[3]Alias, B. (2021).On a Fuzzy Metric Space and Fuzzy Convergence. Proyecciones Journal of Mathematics, 40( 5), 1279-1299.
[4]Amit, K. A. &Alam, M. Z. (2018).Continuous Fuzzy Mappings In Fuzzy Metric Space. GSJ, 6 (7), 612-620.
[5]Bigand, .A & . Colot,. O. (2010) .Fuzzy filter based on interval-valued fuzzy sets for image filtering. Fuzzy Sets Syst,161 (1), 96–117.
[6]Ereeg, M. A.(1979). Metric spaces and fuzzy set theory. J. Math. Anal. Appl. 69, 205-230.
[7]Eyke, H.(2011).Fuzzy sets in machine learning and data mining. Applied Soft Computing, 11, 1493–1505.
[8]George, A. & Veeramani, P.V.(1994). On some results in fuzzy metric spaces. Fuzzy Sets and Systems. 64, 395-399.
[ 9]Govindan,, V& Murthyb, S.(2019).Solution and Hyers-Ulam Stability Of n-Dimensional Non-Quadratic Functional Equation In Fuzzy Normed
Space Using Direct Method. Fuzzy Sets Syst. , 16, 384–391.
[10] Hussein M., Z. (2018). On the(G.n)_ Tupled fixed point theorems in fuzzy metric space. Journal of Al-Qadisiyah for Computer Science and Mathematics, 10(2), Math Page 15 - 25.
[11]Isabelle, .B.( 2015). Fuzzy sets for image processing and understanding. Fuzzy Sets and Systems, 281 (15), 280-291.
[12]Jialiang, X., Qingguo, L,Shuili Chen, & Huan H.(2016). The fuzzy metric space based on fuzzy measure. Open Math, 14,603–612.
[13]Ju, M. K.& Keun, Y.(2019). Approximation Properties in Felbin Fuzzy Normed Spaces. Math J., 22:1-14.
[14]Kaleva, O. & Seikkala, S.(1984). On fuzzy metric spaces. Fuzzy Sets and Systems, 12, 215-229.
[15]Kocinac, L.，Cetkin, V. & Dolicanin, D.(2020).Selective Properties of Fuzzy 2-Metric Spaces. SER. A: APPL. MATH. INFORM. AND MECH,12(2),67-73.
[16]Kramosil, I. & Michalek J.(1975). Fuzzy metric and statistical metric spaces, Kybernetika ll , 336-344.
[17]Mayada, N. M. & Raghad, I. S.( 2021). Bounded Linear Transformations in G-Fuzzy Normed Linear Space. Journal of Al-Qadisiyah for Computer Science and Mathematics.13(1), 110–119.
[18]Mehmet, .S.(2016) . An Application of Fuzzy Sets to Veterinary Medicine. Theory and Applications of Mathematics & Computer Science, 6 (1) 1–12.
[19] Noori, F.A., & A . Abd alsaheb, D. (2017). Separation theorem for fuzzy normed space. Journal of Al-Qadisiyah for Computer Science and Mathematics, 6(2), 53-64.
[20] Noori, F.A., & H . Hadi, S. (2017). Some New result of Compact sets in fuzzy metric space. Journal of Al-Qadisiyah for Computer Science and Mathematics, 6(2), 77-82.
[21] Noori, F.A., & William Twair, H. (2017). Some Results on Weak and Strong Fuzzy Convergence for Fuzzy Normed Spaces. Journal of Al-Qadisiyah for Computer Science and Mathematics, 7(2), 126-131.
[22]Raghad, I. S.(2012). Product of Two Fuzzy Normed Spaces and its Completion. Engineering and Technology Journal, 30 (11), 1925-1934.
[23]Raghad, I. S.(2021). Compactness Property of Fuzzy Soft Metric Space and Fuzzy Soft Continuous Function.Iraqi Journal of Science, 62(9),
3031-3038.
[24]Raghad, I. S. ( 2021). Fuzzy Convergence Sequence and Fuzzy Compact Operators on Standard Fuzzy Normed Spaces. Baghdad
Science Journal,18(4), 1204-1211.
[25] Sabri, R., RASHEED, M., Alabdali, O., SHIHAB, S., & RASHID, T. (2021). On Some Properties in Fuzzy Metric Space. Journal of Al-Qadisiyah for Computer Science and Mathematics, 13(1), Math Page 55.
[26]Schweizer, B.& Sklar, A. (1960). Statistical metric spaces. Pacific J. Math., 10: 314–334.
[27]Sharma, S. (2002). On Fuzzy Metric Space. Southeast Asian Bulletin of Mathematics, 26, 133-145.
.
[28]Swati, B. K.r.(2019).A Study Of Fuzzy Metric Space. IJEDR, 7(3),186-188.
[29]Valentı́n, G & Salvador, R.(2000). Some properties of fuzzy metric spaces. Fuzzy Sets and Systems, 115 ( 3), 485-489.
[30]Zimmerman, H. J.( 1985).Fuzzy Sets Theory and Its Application. Kluwer Academic Publisher, Dordrecht.
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Published
2022-04-04
How to Cite
Sabri, R. I., Mohammedali, M. N., & Sadiq, F. A. (2022). Some Results in Fuzzy 2- Metric Space. Journal of Al-Qadisiyah for Computer Science and Mathematics, 14(1), Math Page 18– 23. https://doi.org/10.29304/jqcm.2022.14.1.890
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