Some properties of two-fuzzy pre-Hilbert space

الملخص EN

We introduce the definition of a two-fuzzy pre Hilbert space (two-fuzzy inner product space) and discuss some properties of this spaces ,and we use the definition of two-fuzzy pre Hilbert space to introduce the definitions of (level complete in two-fuzzy Hilbert , fuzzy orthogonality) .

Also, introduce some important theorems with their proofs.

Moreover, crisp inner product and orthogonality are established .