This nal project discusses two concepts of space, that is a fuzzy n-norm space and fuzzy n-inner product space for every natural number n ≥ 1. Then it is shown that for every k from 1 to n−1, it can be constructed a fuzzy (n−k)-norm space from fuzzy n-norm space. Next, for every k from 1 to n − 1 it can also be constructed a fuzzy (n − k)-inner product space from fuzzy n-inner pr…