A note on fuzzy Hilbert spaces

Article type: Research Article

Authors: Daraby, Bayaz^* | Solimani, Zahra | Rahimi, Asghar

Affiliations: Department of Mathematics, University of Maragheh, Maragheh, Iran

Correspondence: [*] Corresponding author. Bayaz Daraby, Department of Mathematics, University of Maragheh, Maragheh, Iran. Tel./Fax: +98 4137276068; E-mail: bdaraby@maragheh.ac.ir.

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.

Keywords: Felbin norm, fuzzy norm, fuzzy inner product spaces, fuzzy Hilbert space

DOI: 10.3233/IFS-162143

Journal: Journal of Intelligent & Fuzzy Systems, vol. 31, no. 1, pp. 313-319, 2016