January 2021
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Journal of Nonlinear and Convex Analysis
Considering a completely distributive lattice L as the lattice background, the concepts of L-ordered N-convergence structures and L-fuzzy N-convergence structures are introduced. It is shown that the categories of these two kinds of fuzzy convergence spaces can contain that of L-fuzzy topological spaces as a reflective subcategory. Moreover, it is proved that the categories of topological L-ordered N-convergence spaces, topological L-fuzzy N-convergence spaces and L-fuzzy topological spaces are isomorphic.