On three types of L-fuzzy β-covering-based rough sets

In this paper, we mainly establish three types of L-fuzzy /3-covering-based rough set models and study the axiomatic charac-terizations, matrix representations and interdependency of their rough approximation operators. Firstly, we propose three pairs of L-fuzzy /3-covering-based rough approximation operators by constructing the notions such as /3-subsethood degree and /3-degree of intersection. And then, three pairs of the axiomatic characterizations about L-fuzzy /3-covering-based rough approximation op-erators 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 /3-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 approxima-tion operators based on L-fuzzy /3-covering is explored in light of reducible elements and independent elements. Meanwhile, we present the necessary and sufficient conditions under which two L-fuzzy /3-coverings can generate the same lower and upper rough approximation operations.& COPY; 2023 Elsevier B.V. All rights reserved.