Granular variable precision L-fuzzy rough sets based on residuated lattices

Firstly, as for the beginning of this paper, we introduce the granular variable precision L-fuzzy rough sets based on residuated lattices with arbitrary L-fuzzy relations. And then, the equivalent expressions for the lower and upper approximation operators are given with L-fuzzy implications and L-fuzzy coimplications on arbitrary L-fuzzy relations, which can calculate the lower and upper approximation operators efficiently. Finally, some basic properties of the granular variable precision L-fuzzy rough sets on residuated lattices are investigated and the conclusions on the granular variable precision fuzzy rough sets are generalized into the situations of the truth values set becoming residuated lattices.