$L-$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.