https://orcid.org/0000-0002-6500-7807
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Abstract
The purpose of this paper is to endow the fuzzy pseudo-norm in the sense of Morsi with many-valued topological structures. It is shown that there exists a one-to-one correspondence between any fuzzy pseudo-norm given by Morsi and a family of left continuous and non-ascending pseudo-norms. Then a fuzzifying topology induced by Morsi fuzzy pseudo-norms is introduced, it is proved that this fuzzifying topology is compatible with the vector structure. Based on this many-valued topological structure, the degree to fuzzy normed space which is Hausdorff, the degree to a sequence which is convergent, and the degree to a set which is bounded are studied. The layered characterizations of them are presented. Finally, the conclusion which a linear operator is fuzzy continuous if and only if it is fuzzy bounded is proved.
Acknowledgments
The author is grateful to the anonymous referees for carefully reading the manuscript and suggestions made to improve the presentation of the paper.
Disclosure statement
No potential conflict of interest was reported by the author(s).
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C. H. Yan
Dr Conghua Yan ( 1966–) is a Professor in the School of Math. Sciences, Nanjing Normal University. He received a B.A. from Nanjing Normal University of Jiangsu Province and Ph.D. also from Nanjing Normal University. He is a member of the Fuzzy Mathematics and Systems Association of the Systems Engineering Society of China. His interest includes fuzzy analysis, fuzzy topologies. Dr C.H. Yan published numerous articles and papers concerning fuzzy analysis, fuzzy topologies in the Journal of Fuzzy Sets and Systems, Information Sciences, Mathematicae Japonicae, International Journal of General Systems and more.