Al-Qadisiyah UniversityJournal of Al-Qadisiyah for Computer Science and Mathematics2074-02045220131228some properties of two -fuzzy pre-hilbert space1791174ENnoori F.Al-MayahiLayth S.IbrahaimJournal Article20131201We 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 .https://csm.iraqjournals.com/article_91174_ae13becddd64e5bbb3cdd30e27e358fa.pdf