Stratified L-ordered convergence structures

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In this paper, a new kind of lattice-valued convergence structures on a universal set, called stratified L-ordered convergence structures, are presented by modifying the axiom for stratified L-generalized convergence structures in the fuzzy setting so as to make use of the intrinsic fuzzy inclusion order on the fuzzy power set. The category of stratified L-ordered convergence spaces described here is shown to be a reflective full subcategory in the category of stratified L-generalized convergence spaces, and hence it is topological and Cartesian-closed. As preparation, a further investigation of stratified L-filters is presented from the viewpoint that latticed-valued filters should be compatible with the intrinsic fuzzy inclusion order on the fuzzy power set.