Some Results on Fuzzy Inner Product Spaces

In this paper, we investigate some algebraic properties of fuzzy inner product spaces. In this regard, first we present some examples of fuzzy inner product spaces. Then, we introduce a fuzzy inner product space in the Cartesian product of vector spaces. Also, we prove that for a linear transformation T : V -- W, there exists a fuzzy inner product space in V, if and only if there exists a fuzzy inner product space in W. Further, we investigate the relationship between sub-spaces of an arbitrary vector space V and fuzzy inner product space in V. Finally, we conclude that the sum of two fuzzy inner product spaces in V and scalar product of a fuzzy inner product spaces in V are fuzzy inner product spaces in V