Abbas Hasankhani - Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran
Akbar Nazari - Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran
Morteza Saheli - Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran

In the present paper we define the notion of fuzzy inner productand study the properties of the corresponding fuzzy norm. In particular, it isshown that the Cauchy-Schwarz inequality holds. Moreover, it is proved thatevery such fuzzy inner product space can be imbedded in a complete one andthat every subspace of a fuzzy Hilbert space has a complementary subspace.Finally, the notions of fuzzy boundedness and operator norm are introducedand the relationship between continuity and boundedness are investigated. Itis shown also that the space of all fuzzy bounded operators is complete.

Fuzzy norm, Fuzzy inner product, Fuzzy normed linear space, Fuzzy boundedness, Strong continuity