Some properties of L-fuzzy approximation spaces based on bounded integral residuated lattices

In this paper, we present a general framework for the study of L-fuzzy rough sets based on bounded integral residuated lattices. We introduce and discuss the notions of L-fuzzy topological spaces, left (right) lower and left (right) upper L-fuzzy approximation operators based on a complete bounded integral residuated lattice, investigate union, intersection, and composition operations of L-fuzzy approximation spaces, and study some properties of the L-fuzzy topologies generated by these L-fuzzy rough approximation operators and the L-relations induced by an L-fuzzy topology.