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On \((G_O,O)-\)fuzzy rough sets based on overlap and grouping functions over complete lattices

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Abstract

Rough sets, as a tool for handling uncertain data, have been successfully applied to solve practical problems. Many scholars have conducted various studies on rough sets, especially on various rough set models and upper and lower approximation operators. Recently, these studies have gradually begun to expand on lattice values. The other side of the shield, overlap and grouping functions, come as two distinct from the ordinary binary aggregation functions, due to their not necessarily associative property, have become two new mathematical models for processing information and have been successfully applied in practice. As a result, in this study, \((G_O,O)-\)fuzzy rough sets based on the overlap and grouping functions on the complete lattices are introduced and their topological properties are evaluated, further promoting the concept of rough sets. First, the \(G_O-\)lower \(L-\)fuzzy rough approximation operator is defined the lower approximation operator in the \((G_O,O)-\)fuzzy rough set on complete lattices utilizing \(QL-\)implications, as well as, the upper approximation operator in \((G_O,O)-\)fuzzy rough set on complete lattices is filled by the \(O-\)upper \(L-\)fuzzy rough approximation operator which is formulated by Jiang and Hu in \((G,O)-\)fuzzy rough set. Second, we talk about some basic properties of the \((G_O,O)-\)fuzzy rough set on complete lattices; moreover, the discussion of these basic properties mainly focus on \(G_O-\)lower \(L-\)fuzzy approximation operator. Third, it is considered the characterization of the \((G_O,O)-\)fuzzy approximation operator by making use of various classes of \(L-\)fuzzy relations. Finally, we study the topological properties of \((G_O,O)-\)fuzzy rough set.

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Acknowledgements

The work described in this paper was supported by grants from the National Natural Science Foundation of China (Grant nos. 11971365 and 11571010) and the Key Project of Guangxi Natural Science Foundation (Grant No. 2023GXNSFDA026006).

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Authors and Affiliations

  1. School of Mathematics and Physics, Guangxi Minzu University, Nanning, 530006, People’s Republic of China

    Jingpu Chang & Bao Qing Hu

  2. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, People’s Republic of China

    Bao Qing Hu

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  1. Jingpu Chang
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Correspondence to Bao Qing Hu.

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Communicated by Junsheng Qiao.

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Chang, J., Hu, B.Q. On \((G_O,O)-\)fuzzy rough sets based on overlap and grouping functions over complete lattices. Comp. Appl. Math. 42, 352 (2023). https://doi.org/10.1007/s40314-023-02489-2

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