Fuzzifying topology induced by Morsi fuzzy pseudo-norms

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.