Fuzzy bounded linear operators in Felbin's type fuzzy normed linear spaces (Q834507)

The authors introduce suitable definitions of strongly fuzzy boundedness and weakly fuzzy boundedness for a linear operator over fuzzy normed linear spaces, by means of which a slightly modified definition of fuzzy normed linear space in Felbin's sense is given. Then, the authors obtain the following results: (1) the equivalence of strongly (resp., weakly) fuzzy boundedness and strongly (resp., weakly) fuzzy continuity; (2) the expression of fuzzy norm of strongly (resp., weakly) fuzzy bounded linear operators; (3) the completeness of strongly (resp., weakly) fuzzy dual space for a fuzzy normed linear space; (4) the strong (resp., weak) form of the Hahn-Banach theorem for a fuzzy normed linear space.