Abstract. Recently, Hasankhani et al. proved that any Felbin-fuzzy inner product space can be imbedded in a complete
Felbin-fuzzy inner product space or Felbin-fuzzy Hilbert space. In this paper, it is showed a general result that any classical
Hilbert space is a Felbin-fuzzy Hilbert space, so it shows that all results in classical Hilbert spaces are immediate consequences
of the corresponding results for Felbin-fuzzy Hilbert spaces. Moreover by an example, it is showed that the spectrum of the
category of Felbin-fuzzy Hilbert spaces is broader than the category of classical Hilbert spaces. Finally the authors are able
to state a transformation theorem from an ascending family of crisp inner product into Felbin-fuzzy inner product that shows
how to formulate the recent results.