Specialization L-preorder of stratified L-fuzzy convergence spaces

Let (L, *, 1) be a commutative, strictly two-sided quantale with the underling lattice L being meet-continuous. In this paper, we introduce a notion of stratified L-fuzzy convergence space based on the theory of fuzzy orders, which is a common generalization of both crisp convergence space and stratified L-topological space. Then we investigate a notion of specialization L-preorder of stratified L-fuzzy convergence spaces, and prove that it is also a common generalization of both the specialization order of crisp convergence space and the specialization L-preorder of stratified L-topological space.