Abstract In this project, we apply the max-min composition of fuzzy relation to show a given fuzzy relation is a fuzzy transitive, we redefine the equality of two fuzzy relations from [8], and by using the definitions of ideals and filters of a fuzzy lattice, and some basic results from [8], we introduce our result as, let (X, A) be a fuzzy lattice and Y X such that (Y; B) is a fuzzy sup-lattice where B = Aj Y Y . Then, Y\ " Y = f W Yg, where Y = supY and " Y = fx 2 X : A(y; x) > 0 for any y 2 Yg. By using this result we disprove that some Mezzom’s results about the properties of ideals and filters of a fuzzy lattice. Finally, we show that the intersections of all families of ideals and filters of a fuzzy lattice are ideals and filters of a fuzzy lattice . W