Abstract
In this paper, we mainly establish three types of L-fuzzy β-covering-based rough set models and study the axiomatic characterizations, matrix representations and interdependency of their rough approximation operators. Firstly, we propose three pairs of L-fuzzy β-covering-based rough approximation operators by constructing the notions such as β-subsethood degree and β-degree of intersection. And then, three pairs of the axiomatic characterizations about L-fuzzy β-covering-based rough approximation operators are investigated, respectively. In the meantime, we verify the independence of each axiom set. Thirdly, we give the matrix representations of three pairs of L-fuzzy β-covering-based rough approximation operators for efficient calculation of the lower and upper approximation operators through operations on matrices. Finally, the interdependency of three pairs of rough approximation operators based on L-fuzzy β-covering is explored in light of reducible elements and independent elements. Meanwhile, we present the necessary and sufficient conditions under which two L-fuzzy β-coverings can generate the same lower and upper rough approximation operations.
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