Some Properties of Fuzzy Soft Metric Space
Keywords:
Fuzzy soft metric space, Fuzzy soft bounded set, Fuzzy soft convergence of sequences, Fuzzy soft continuous function.
Abstract
In this paper we introduce the notion fuzzy soft metric space after that we define open fuzzy soft ball, fuzzy soft bounded set, fuzzy soft convergence of sequences, fuzzy soft continuous function from a fuzzy soft metric space to another fuzzy metric space then we study this space and some basic results are investigated.
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References
[1] Molodtsov, D., Soft Set Theory- First Results, Computer Math. Appl. Vol.37(4/5), 1999, 19-31.
[2] Maji, P. K. ,Biswas, R. and Roy, A. R. , Fuzzy Soft Set, J. FuzzyMath. ,Vol. 9(3), 2001, 589-602.
[3] Ahmad, B. and Kharal, A. ,On Fuzzy Soft Set, Hindawi Publishing Corporation, Advance in Fuzzy Systems, Article ID 586507, 6 pages,2009.
[4] Varol, B. P. ,Shostak, A, P. and Aygun, H. ,Categories Related to Topology Viewed as Soft Set, Proceeding of the 17 Conference of the European Society for fuzzy logic and technology, 2011, 883-890.
[5] Varol, B. P. and Aygun, H. ,Fuzzy Soft Topology, Hacettepe J. of Math. And Statistics, Vol.41(3), 2012, 407-419.
[6] Sadeqi I, Kia F. Fuzzy normed linear space and its topological structure,
Chaos Solitions and Fractals, 2009,40 (5): 2576-2589.
[7] Kider J. On fuzzy normed spaces, Eng. & Tech. Journal, 2011, 29(9):1790-1795.
[8] Kider J. Completion of fuzzy normed spaces, Eng. & Tech. Journal, 2011, 29(10)
[9] Kider J. New fuzzy normed spaces, J. Baghdad Sci. 2012, 9: 559-564.
:2004-2012.
[1] Nadaban S. Fuzzy continuous mapping in fuzzy normed linear spaces, I. J.
Computer Communications and Control, 2015, 10 (6): 834-842.
[11] Kider J, Kadhum N. 2017 Properties of fuzzy norm of fuzzy bounded operators,
Iraqi Journal of Science, 2017, 58(3A):1237-1281.
[12] Kadhum N., On fuzzy norm of a fuzzy bounded operator on fuzzy normed
spaces, M.Sc. Thesis 2017, University of Technology, Iraq.
[13] Ali A., Properties of Complete Fuzzy Normed Algebra, M.Sc. Thesis 2018,
University of Technology, Iraq.
[14] Kider J, Ali A. , Properties of fuzzy absolute value on and properties finite
dimensional fuzzy normed space. Iraqi Journal of Science,2018, 59(2B): 909-916.
[15] Kider J, Gheeab M. Properties of a General Fuzzy Normed Space, Iraqi Journal
of Science2018 (To appear ).
[16] Kider J, Gheeab M. Properties of The Space GFB(V, U), Journal of AL-
Qadisiyah for computer science and mathematics 2019, 11(1):102-110
[17] Kider J, Kadhum N. , Properties of Fuzzy Compact Linear Operators on Fuzzy
Normed Spaces, Baghdad Science Journal, 201916(1):104-110.
[18] Hussin, E. A.,On some properties of finite dimensional fuzzy antinormed spaces
and Fuzzy antiinner product spaces, M. Sc. Theses, Department of Mathematics,
College of Sciences for Women, University of Baghdad, 2019.
[1] Molodtsov, D., Soft Set Theory- First Results, Computer Math. Appl. Vol.37(4/5), 1999, 19-31.
[2] Maji, P. K. ,Biswas, R. and Roy, A. R. , Fuzzy Soft Set, J. FuzzyMath. ,Vol. 9(3), 2001, 589-602.
[3] Ahmad, B. and Kharal, A. ,On Fuzzy Soft Set, Hindawi Publishing Corporation, Advance in Fuzzy Systems, Article ID 586507, 6 pages,2009.
[4] Varol, B. P. ,Shostak, A, P. and Aygun, H. ,Categories Related to Topology Viewed as Soft Set, Proceeding of the 17 Conference of the European Society for fuzzy logic and technology, 2011, 883-890.
[5] Varol, B. P. and Aygun, H. ,Fuzzy Soft Topology, Hacettepe J. of Math. And Statistics, Vol.41(3), 2012, 407-419.
[6] Sadeqi I, Kia F. Fuzzy normed linear space and its topological structure,
Chaos Solitions and Fractals, 2009,40 (5): 2576-2589.
[7] Kider J. On fuzzy normed spaces, Eng. & Tech. Journal, 2011, 29(9):1790-1795.
[8] Kider J. Completion of fuzzy normed spaces, Eng. & Tech. Journal, 2011, 29(10)
[9] Kider J. New fuzzy normed spaces, J. Baghdad Sci. 2012, 9: 559-564.
:2004-2012.
[1] Nadaban S. Fuzzy continuous mapping in fuzzy normed linear spaces, I. J.
Computer Communications and Control, 2015, 10 (6): 834-842.
[11] Kider J, Kadhum N. 2017 Properties of fuzzy norm of fuzzy bounded operators,
Iraqi Journal of Science, 2017, 58(3A):1237-1281.
[12] Kadhum N., On fuzzy norm of a fuzzy bounded operator on fuzzy normed
spaces, M.Sc. Thesis 2017, University of Technology, Iraq.
[13] Ali A., Properties of Complete Fuzzy Normed Algebra, M.Sc. Thesis 2018,
University of Technology, Iraq.
[14] Kider J, Ali A. , Properties of fuzzy absolute value on and properties finite
dimensional fuzzy normed space. Iraqi Journal of Science,2018, 59(2B): 909-916.
[15] Kider J, Gheeab M. Properties of a General Fuzzy Normed Space, Iraqi Journal
of Science2018 (To appear ).
[16] Kider J, Gheeab M. Properties of The Space GFB(V, U), Journal of AL-
Qadisiyah for computer science and mathematics 2019, 11(1):102-110
[17] Kider J, Kadhum N. , Properties of Fuzzy Compact Linear Operators on Fuzzy
Normed Spaces, Baghdad Science Journal, 201916(1):104-110.
[18] Hussin, E. A.,On some properties of finite dimensional fuzzy antinormed spaces
and Fuzzy antiinner product spaces, M. Sc. Theses, Department of Mathematics,
College of Sciences for Women, University of Baghdad, 2019.
[1] Molodtsov, D., Soft Set Theory- First Results, Computer Math. Appl. Vol.37(4/5), 1999, 19-31.
[2] Maji, P. K. ,Biswas, R. and Roy, A. R. , Fuzzy Soft Set, J. FuzzyMath. ,Vol. 9(3), 2001, 589-602.
[3] Ahmad, B. and Kharal, A. ,On Fuzzy Soft Set, Hindawi Publishing Corporation, Advance in Fuzzy Systems, Article ID 586507, 6 pages,2009.
[4] Varol, B. P. ,Shostak, A, P. and Aygun, H. ,Categories Related to Topology Viewed as Soft Set, Proceeding of the 17 Conference of the European Society for fuzzy logic and technology, 2011, 883-890.
[5] Varol, B. P. and Aygun, H. ,Fuzzy Soft Topology, Hacettepe J. of Math. And Statistics, Vol.41(3), 2012, 407-419.
[6] Sadeqi I, Kia F. Fuzzy normed linear space and its topological structure,
Chaos Solitions and Fractals, 2009,40 (5): 2576-2589.
[7] Kider J. On fuzzy normed spaces, Eng. & Tech. Journal, 2011, 29(9):1790-1795.
[8] Kider J. Completion of fuzzy normed spaces, Eng. & Tech. Journal, 2011, 29(10)
[9] Kider J. New fuzzy normed spaces, J. Baghdad Sci. 2012, 9: 559-564.
:2004-2012.
[1] Nadaban S. Fuzzy continuous mapping in fuzzy normed linear spaces, I. J.
Computer Communications and Control, 2015, 10 (6): 834-842.
[11] Kider J, Kadhum N. 2017 Properties of fuzzy norm of fuzzy bounded operators,
Iraqi Journal of Science, 2017, 58(3A):1237-1281.
[12] Kadhum N., On fuzzy norm of a fuzzy bounded operator on fuzzy normed
spaces, M.Sc. Thesis 2017, University of Technology, Iraq.
[13] Ali A., Properties of Complete Fuzzy Normed Algebra, M.Sc. Thesis 2018,
University of Technology, Iraq.
[14] Kider J, Ali A. , Properties of fuzzy absolute value on and properties finite
dimensional fuzzy normed space. Iraqi Journal of Science,2018, 59(2B): 909-916.
[15] Kider J, Gheeab M. Properties of a General Fuzzy Normed Space, Iraqi Journal
of Science2018 (To appear ).
[16] Kider J, Gheeab M. Properties of The Space GFB(V, U), Journal of AL-
Qadisiyah for computer science and mathematics 2019, 11(1):102-110
[17] Kider J, Kadhum N. , Properties of Fuzzy Compact Linear Operators on Fuzzy
Normed Spaces, Baghdad Science Journal, 201916(1):104-110.
[18] Hussin, E. A.,On some properties of finite dimensional fuzzy antinormed spaces
and Fuzzy antiinner product spaces, M. Sc. Theses, Department of Mathematics,
College of Sciences for Women, University of Baghdad, 2019.
[2] Maji, P. K. ,Biswas, R. and Roy, A. R. , Fuzzy Soft Set, J. FuzzyMath. ,Vol. 9(3), 2001, 589-602.
[3] Ahmad, B. and Kharal, A. ,On Fuzzy Soft Set, Hindawi Publishing Corporation, Advance in Fuzzy Systems, Article ID 586507, 6 pages,2009.
[4] Varol, B. P. ,Shostak, A, P. and Aygun, H. ,Categories Related to Topology Viewed as Soft Set, Proceeding of the 17 Conference of the European Society for fuzzy logic and technology, 2011, 883-890.
[5] Varol, B. P. and Aygun, H. ,Fuzzy Soft Topology, Hacettepe J. of Math. And Statistics, Vol.41(3), 2012, 407-419.
[6] Sadeqi I, Kia F. Fuzzy normed linear space and its topological structure,
Chaos Solitions and Fractals, 2009,40 (5): 2576-2589.
[7] Kider J. On fuzzy normed spaces, Eng. & Tech. Journal, 2011, 29(9):1790-1795.
[8] Kider J. Completion of fuzzy normed spaces, Eng. & Tech. Journal, 2011, 29(10)
[9] Kider J. New fuzzy normed spaces, J. Baghdad Sci. 2012, 9: 559-564.
:2004-2012.
[1] Nadaban S. Fuzzy continuous mapping in fuzzy normed linear spaces, I. J.
Computer Communications and Control, 2015, 10 (6): 834-842.
[11] Kider J, Kadhum N. 2017 Properties of fuzzy norm of fuzzy bounded operators,
Iraqi Journal of Science, 2017, 58(3A):1237-1281.
[12] Kadhum N., On fuzzy norm of a fuzzy bounded operator on fuzzy normed
spaces, M.Sc. Thesis 2017, University of Technology, Iraq.
[13] Ali A., Properties of Complete Fuzzy Normed Algebra, M.Sc. Thesis 2018,
University of Technology, Iraq.
[14] Kider J, Ali A. , Properties of fuzzy absolute value on and properties finite
dimensional fuzzy normed space. Iraqi Journal of Science,2018, 59(2B): 909-916.
[15] Kider J, Gheeab M. Properties of a General Fuzzy Normed Space, Iraqi Journal
of Science2018 (To appear ).
[16] Kider J, Gheeab M. Properties of The Space GFB(V, U), Journal of AL-
Qadisiyah for computer science and mathematics 2019, 11(1):102-110
[17] Kider J, Kadhum N. , Properties of Fuzzy Compact Linear Operators on Fuzzy
Normed Spaces, Baghdad Science Journal, 201916(1):104-110.
[18] Hussin, E. A.,On some properties of finite dimensional fuzzy antinormed spaces
and Fuzzy antiinner product spaces, M. Sc. Theses, Department of Mathematics,
College of Sciences for Women, University of Baghdad, 2019.
[1] Molodtsov, D., Soft Set Theory- First Results, Computer Math. Appl. Vol.37(4/5), 1999, 19-31.
[2] Maji, P. K. ,Biswas, R. and Roy, A. R. , Fuzzy Soft Set, J. FuzzyMath. ,Vol. 9(3), 2001, 589-602.
[3] Ahmad, B. and Kharal, A. ,On Fuzzy Soft Set, Hindawi Publishing Corporation, Advance in Fuzzy Systems, Article ID 586507, 6 pages,2009.
[4] Varol, B. P. ,Shostak, A, P. and Aygun, H. ,Categories Related to Topology Viewed as Soft Set, Proceeding of the 17 Conference of the European Society for fuzzy logic and technology, 2011, 883-890.
[5] Varol, B. P. and Aygun, H. ,Fuzzy Soft Topology, Hacettepe J. of Math. And Statistics, Vol.41(3), 2012, 407-419.
[6] Sadeqi I, Kia F. Fuzzy normed linear space and its topological structure,
Chaos Solitions and Fractals, 2009,40 (5): 2576-2589.
[7] Kider J. On fuzzy normed spaces, Eng. & Tech. Journal, 2011, 29(9):1790-1795.
[8] Kider J. Completion of fuzzy normed spaces, Eng. & Tech. Journal, 2011, 29(10)
[9] Kider J. New fuzzy normed spaces, J. Baghdad Sci. 2012, 9: 559-564.
:2004-2012.
[1] Nadaban S. Fuzzy continuous mapping in fuzzy normed linear spaces, I. J.
Computer Communications and Control, 2015, 10 (6): 834-842.
[11] Kider J, Kadhum N. 2017 Properties of fuzzy norm of fuzzy bounded operators,
Iraqi Journal of Science, 2017, 58(3A):1237-1281.
[12] Kadhum N., On fuzzy norm of a fuzzy bounded operator on fuzzy normed
spaces, M.Sc. Thesis 2017, University of Technology, Iraq.
[13] Ali A., Properties of Complete Fuzzy Normed Algebra, M.Sc. Thesis 2018,
University of Technology, Iraq.
[14] Kider J, Ali A. , Properties of fuzzy absolute value on and properties finite
dimensional fuzzy normed space. Iraqi Journal of Science,2018, 59(2B): 909-916.
[15] Kider J, Gheeab M. Properties of a General Fuzzy Normed Space, Iraqi Journal
of Science2018 (To appear ).
[16] Kider J, Gheeab M. Properties of The Space GFB(V, U), Journal of AL-
Qadisiyah for computer science and mathematics 2019, 11(1):102-110
[17] Kider J, Kadhum N. , Properties of Fuzzy Compact Linear Operators on Fuzzy
Normed Spaces, Baghdad Science Journal, 201916(1):104-110.
[18] Hussin, E. A.,On some properties of finite dimensional fuzzy antinormed spaces
and Fuzzy antiinner product spaces, M. Sc. Theses, Department of Mathematics,
College of Sciences for Women, University of Baghdad, 2019.
[1] Molodtsov, D., Soft Set Theory- First Results, Computer Math. Appl. Vol.37(4/5), 1999, 19-31.
[2] Maji, P. K. ,Biswas, R. and Roy, A. R. , Fuzzy Soft Set, J. FuzzyMath. ,Vol. 9(3), 2001, 589-602.
[3] Ahmad, B. and Kharal, A. ,On Fuzzy Soft Set, Hindawi Publishing Corporation, Advance in Fuzzy Systems, Article ID 586507, 6 pages,2009.
[4] Varol, B. P. ,Shostak, A, P. and Aygun, H. ,Categories Related to Topology Viewed as Soft Set, Proceeding of the 17 Conference of the European Society for fuzzy logic and technology, 2011, 883-890.
[5] Varol, B. P. and Aygun, H. ,Fuzzy Soft Topology, Hacettepe J. of Math. And Statistics, Vol.41(3), 2012, 407-419.
[6] Sadeqi I, Kia F. Fuzzy normed linear space and its topological structure,
Chaos Solitions and Fractals, 2009,40 (5): 2576-2589.
[7] Kider J. On fuzzy normed spaces, Eng. & Tech. Journal, 2011, 29(9):1790-1795.
[8] Kider J. Completion of fuzzy normed spaces, Eng. & Tech. Journal, 2011, 29(10)
[9] Kider J. New fuzzy normed spaces, J. Baghdad Sci. 2012, 9: 559-564.
:2004-2012.
[1] Nadaban S. Fuzzy continuous mapping in fuzzy normed linear spaces, I. J.
Computer Communications and Control, 2015, 10 (6): 834-842.
[11] Kider J, Kadhum N. 2017 Properties of fuzzy norm of fuzzy bounded operators,
Iraqi Journal of Science, 2017, 58(3A):1237-1281.
[12] Kadhum N., On fuzzy norm of a fuzzy bounded operator on fuzzy normed
spaces, M.Sc. Thesis 2017, University of Technology, Iraq.
[13] Ali A., Properties of Complete Fuzzy Normed Algebra, M.Sc. Thesis 2018,
University of Technology, Iraq.
[14] Kider J, Ali A. , Properties of fuzzy absolute value on and properties finite
dimensional fuzzy normed space. Iraqi Journal of Science,2018, 59(2B): 909-916.
[15] Kider J, Gheeab M. Properties of a General Fuzzy Normed Space, Iraqi Journal
of Science2018 (To appear ).
[16] Kider J, Gheeab M. Properties of The Space GFB(V, U), Journal of AL-
Qadisiyah for computer science and mathematics 2019, 11(1):102-110
[17] Kider J, Kadhum N. , Properties of Fuzzy Compact Linear Operators on Fuzzy
Normed Spaces, Baghdad Science Journal, 201916(1):104-110.
[18] Hussin, E. A.,On some properties of finite dimensional fuzzy antinormed spaces
and Fuzzy antiinner product spaces, M. Sc. Theses, Department of Mathematics,
College of Sciences for Women, University of Baghdad, 2019.
Published
2020-06-16
How to Cite
Kider, J. (2020). Some Properties of Fuzzy Soft Metric Space. Al-Qadisiyah Journal of Pure Science, 25(3), Math.46-61. https://doi.org/10.29350/qjps.2020.25.3.1149
Issue
Section
Mathematics
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