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چکیده
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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.
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