  By using the space of fuzzy numbers, in e.g. [5] have been considered several
complete metric spaces (called here {\bf FN}-type spaces) endowed with addition
and scalar multiplication, such that the metrics have nice properties but the
spaces are not linear, i.e. are not groups with respect to addition and the
scalar multiplication is not, in general, distributive with respect to usual
scalar addition. This paper deals with the form of linear continuous
functionals defined on these spaces.
