$l-$ordered fuzzifying convergence spaces

based on a complete heyting algebra, we modify the definition oflattice-valued fuzzifying convergence space using fuzzy inclusionorder and construct in this way a cartesian-closed category, calledthe category of $l-$ordered fuzzifying convergence spaces, in whichthe category of $l-$fuzzifying topological spaces can be embedded.in addition, two new categories are introduced, which are called thecategory of principal $l-$ordered fuzzifying convergence spaces andthat of topological $l-$ordered fuzzifying convergence spaces, andit is shown that they are isomorphic to the category of$l-$fuzzifying neighborhood spaces and that of $l-$fuzzifyingtopological spaces respectively.