In this paper, by means of \(\varvec{G}\) -lower and \(\varvec{O}\) -upper \(\varvec{L}\) -fuzzy rough approximation operators proposed by Jiang and Hu, we first introduce two new pairs of \(\varvec{L}\) -fuzzy rough approximation operators induced by overlap and grouping functions on complete lattices. These operators are respectively referred to as \(\varvec{L}^{\varvec{(1)}}\) -fuzzy rough approximation operators and \(\varvec{L}^{\varvec{(2)}}\) -fuzzy rough approximation operators. And then, we study several basic properties of them. Furthermore, we focus on topological properties of \(\varvec{L}^{\varvec{(2)}}\) -lower (resp. \(\varvec{L}^{\varvec{(2)}}\) -upper) fuzzy rough approximation operators in \(\varvec{L}^{\varvec{(2)}}\) -fuzzy rough approximation operators. Particularly, the set of fixed points of \(\varvec{L}^{\varvec{(2)}}\) -lower (resp. \(\varvec{L}^{\varvec{(2)}}\) -upper) fuzzy rough approximation operators forms an Alexandroff \(\varvec{L}\) -topology. Finally, we present the application of \(\varvec{L}^{\varvec{(2)}}\) -fuzzy rough approximation operators to the three-way decisions and the experimental results demonstrate that compared with the existing corresponding fuzzy rough set models derived from t-norms and t-conorms, our model exhibits superior classification performance.
