In this paper we introduce the concept of strong L-convexity by making use of the fuzzy inclusion order on the fuzzy power set. And the category of strong L-convex spaces is topological and is a co-reflective subcategory of the category of bi-stratified L-convex spaces. It is apparently different from the strong L-topology in the sense of Zhang that is exactly bi-stratified L-topology. Finally, we present that strong L-convexities can be characterized by algebraic L-ordered closure operators.
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