In this paper we introduce the definition of standard fuzzy normed space, then we discuss several properties after we give an example to illustrate this notion. Then we define F-bounded operator as an introduction to define a standard fuzzy norm of an operator and if T is a linear operator from standard fuzzy normed space X into a standard fuzzy normed space Y we prove that T is continuous if and only if T is Fbounded.
Keywords: standard fuzzy normed space, F-bounded linear operator, a fuzzy norm of an operator