Fuzzy inner product spaces

In this paper, we show that all results obtained recently on fuzzy inner product spaces are obvious. To achieve this goal, we modify the definition of the fuzzy inner product space and then we mention and prove some monotonicity and orthogonality properties of the new fuzzy inner product space. Finally, we describe fuzzy inner products in terms of families of crisp inner products. Namely, any fuzzy inner product corresponds to a family of crisp inner products and vice versa. (C) 2015 Elsevier B.V. All rights reserved.