Document Type : Research Paper
Author
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran
Abstract
In the current paper, consider the fuzzy normed linear space $(X,N)$ which is defined by Bag and Samanta. First, we construct a new fuzzy topology on this space and show that these spaces are Hausdorff locally convex fuzzy topological vector space. Some necessary and sufficient conditions are established to illustrate that the presented fuzzy topology is equivalent to two previously studied fuzzy topologies.
Keywords
[1] T. Bag and S. K. Samanta, Finite dimensional fuzzy normed linear spaces, J. Fuzzy Math.,
11(3) (2003), 687-705.
[2] T. Bag and S. K. Samanta, Fuzzy bounded linear operators, Fuzzy Sets and Systems, 151
(2005), 513-547.
[3] S. C. Cheng and J. N. Mordeson, Fuzzy linear operators and fuzzy normed linear spaces,
Bull. Cal. Math. Soc., 86 (1994), 429-436.
[4] N. F. Das and P. Das, Fuzzy topology generated by fuzzy norm, Fuzzy Sets and Systems, 107
(1999), 349-354.
[5] J. X. Fang, On I-topology generated by fuzzy norm, Fuzzy Sets and Systems, 157 (2006),
2739-2750.
[6] C. Felbin, Finite dimensional fuzzy normed linear space, Fuzzy Sets and Systems, 48 (1992),
239-248.
[7] O. Kaleva and S. Seikkala, On fuzzy metric spaces, Fuzzy Sets and Systems, 12 (1984),
215-229.
[8] I. Karmosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetica, 11
(1975), 326-334.
[9] A. K. Katsaras, Fuzzy topological vector spaces II, Fuzzy Sets and Systems, 12 (1984), 143-
154.
[10] M. Saheli, On fuzzy topology and fuzzy norm, Annals of Fuzzy Mathematics and Informatics,
10(4) (2015), 639647.
[11] J. Xiao and X. Zhu, Fuzzy normed space of operators and its completeness, Fuzzy Sets and
Systems, 133 (2003) 389-399.
[12] G. H. Xu and J. X. Fang, A new I-vector topology generated by a fuzzy norm, Fuzzy Sets and
Systems, 158 (2007), 2375-2385.
11(3) (2003), 687-705.
[2] T. Bag and S. K. Samanta, Fuzzy bounded linear operators, Fuzzy Sets and Systems, 151
(2005), 513-547.
[3] S. C. Cheng and J. N. Mordeson, Fuzzy linear operators and fuzzy normed linear spaces,
Bull. Cal. Math. Soc., 86 (1994), 429-436.
[4] N. F. Das and P. Das, Fuzzy topology generated by fuzzy norm, Fuzzy Sets and Systems, 107
(1999), 349-354.
[5] J. X. Fang, On I-topology generated by fuzzy norm, Fuzzy Sets and Systems, 157 (2006),
2739-2750.
[6] C. Felbin, Finite dimensional fuzzy normed linear space, Fuzzy Sets and Systems, 48 (1992),
239-248.
[7] O. Kaleva and S. Seikkala, On fuzzy metric spaces, Fuzzy Sets and Systems, 12 (1984),
215-229.
[8] I. Karmosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetica, 11
(1975), 326-334.
[9] A. K. Katsaras, Fuzzy topological vector spaces II, Fuzzy Sets and Systems, 12 (1984), 143-
154.
[10] M. Saheli, On fuzzy topology and fuzzy norm, Annals of Fuzzy Mathematics and Informatics,
10(4) (2015), 639647.
[11] J. Xiao and X. Zhu, Fuzzy normed space of operators and its completeness, Fuzzy Sets and
Systems, 133 (2003) 389-399.
[12] G. H. Xu and J. X. Fang, A new I-vector topology generated by a fuzzy norm, Fuzzy Sets and
Systems, 158 (2007), 2375-2385.
)