On -fuzzy convergence spaces

This paper presents a definition of ( L , M ) -fuzzy convergence spaces. It is shown that the category ( L , M ) -FC of ( L , M ) -fuzzy convergence spaces, which embeds the category ( L , M ) -FTop of ( L , M ) -fuzzy topological spaces as a reflective subcategory, is a Cartesian closed topological category. Further, it is proved that the category of (topological) pretopological ( L , M ) -fuzzy convergence spaces is isomorphic to the category of (topological) ( L , M ) -fuzzy quasi-coincident neighborhood spaces. Moreover, the relations among ( L , M ) -fuzzy convergence spaces, pretopological ( L , M ) -fuzzy convergence spaces and topological ( L , M ) -fuzzy convergence spaces are investigated in the categorical sense.