Abstract
Jiang and Hu characterized (O,G)-fuzzy rough sets based on overlap and grouping functions over complete lattices with L-fuzzy negations, where L denotes a complete lattice. However, there are some faults in the study of (O,G)-fuzzy rough sets. As there exist complete lattices without strict L-fuzzy negations or L-fuzzy involutive negations, the properties of G-lower L-fuzzy rough approximation operators need be further discussed. Meanwhile, it is wrong that the G-lower L-fuzzy rough approximation operators preserve the arbitrary union of L-fuzzy sets and O-upper L-fuzzy rough approximation operators preserve the arbitrary intersection of L-fuzzy sets. Hence, the characterizations of (O,G)-fuzzy rough sets and multigranulation (O,G)-fuzzy rough sets need be rectifies. For the convenience of readers, a table is provided to show the correspondences among the conclusions.
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