Novel results on G-lower L-fuzzy rough approximation operator in (O, G)-fuzzy rough set model

Lately, Jiang and Hu (H.B. Jiang, B.Q. Hu, On (O, G)-fuzzy rough sets based on overlap and grouping functions over complete lattices, Int. J. Approx. Reason. 144 (2022) 18-50.) put forward (O, G)-fuzzy rough sets via overlap and grouping functions over complete lattices. Meanwhile, they showed the characterizations of O-upper and G-lower L-fuzzy rough approximation operators in (O, G)-fuzzy rough set model based on some of specific L-fuzzy relations and studied the topological properties of the proposed model. Nevertheless, we discover that the partial results given by Jiang and Hu could be further optimized. So, as a replenish of the above article, in this paper, based on G-lower L-fuzzy rough approximation operator in (O, G)-fuzzy rough set model, we further explore several new conclusions on the relationship between G-lower L-fuzzy rough approximation operator and different L-fuzzy relations. In particular, the equivalent descriptions of relationship between G-lower L-fuzzy rough approximation operator and O-transitive (O-Euclidean) L-fuzzy relations are investigated, which are not involved in above literature and can make the theoretical results of this newly fuzzy rough set model more perfect.