In this paper, we characterize T−soft ideals,T−fuzzy soft normal ideals over a ring and give a portion of their properties. Likewise, we present homomorphism, hostile to homomorphism, isomorphism and anti- isomorphism of T−fuzzy soft normal-ideals ordinary standards over the ring. In addition, we show that the image and preimage of homomorphism, hostile to homomorphism, isomorphism and against isomorphism of T-fuzzysoft normal ideals over the ring under certain conditions.