Affiliations:
College of Mathematics and Statistics, Northwest Normal University, Lanzhou, PR China
Correspondence:
[*]
Corresponding author. Junsheng Qiao, College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, PR China. E-mails: jsqiao@nwnu.edu.cn, jsqiao@whu.edu.cn.
Note: [1] This work was supported by the National Natural Science Foundation of China (62166037, 11901465), the Science and Technology Program of Gansu Province (20JR10RA101), the Outstanding Graduate Innovation Star Project of Gansu Province (2022CXZX-325).
Abstract: 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.
