In this work, we study the relation between the concept lattice of Wille ([5], [6]) and the $L-Fuzzy$ concept lattice ([2]) developed by us. To do it, we have defined an application $g$ that associates to each concept of Wille an $L-Fuzzy$ concept. The main point of this work is to prove that if we are working with a crisp relation between an object set and an attribute set, the concept lattice of Wille is a sublattice of the $L-Fuzzy$ concept lattice. At the end, we show a typical example in the formal concept theory where we have constructed the $L-Fuzzy$ concept lattice.