Fuzzy b-normed spaces are fuzzy normable

[EN] We introduce the notion of fuzzy b-normed space as a generalization of the concept of fuzzy normed space and also as a fuzzy counterpart of the classical concept of quasi-normed space in the sense of Hyers and Bourgin. We show that every fuzzy b-normed space is fuzzy normable and deduce that every fuzzy b-Banach space admits the structure of a fuzzy Banach space. These facts reveal striking di§erences with what happens in classical analysis, where there are emblematic examples of quasi-Banach spaces that are not normable.