On three types of $L$-fuzzy $\beta$-covering-based rough sets

• URL: http://arxiv.org/abs/2206.11025v1
• Date: Fri, 13 May 2022 05:30:51 GMT
• Title: On three types of $L$-fuzzy $\beta$-covering-based rough sets
• Authors: Wei Li, Bin Yang, Junsheng Qiao
• Abstract summary: We study the axiom sets, matrix representations and interdependency of three pairs of $L$-fuzzy $beta$-covering-based rough approximation operators. We present the necessary and sufficient conditions under which two $L$-fuzzy $beta$-coverings can generate the same lower and upper rough approximation operations.
• Score: 16.843434476423305
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we mainly construct three types of $L$-fuzzy $\beta$-covering-based rough set models and study the axiom sets, matrix representations and interdependency of these three pairs of $L$-fuzzy $\beta$-covering-based rough approximation operators. Firstly, we propose three pairs of $L$-fuzzy $\beta$-covering-based rough approximation operators by introducing the concepts such as $\beta$-degree of intersection and $\beta$-subsethood degree, which are generalizations of degree of intersection and subsethood degree, respectively. And then, the axiom set for each of these $L$-fuzzy $\beta$-covering-based rough approximation operator is investigated. Thirdly, we give the matrix representations of three types of $L$-fuzzy $\beta$-covering-based rough approximation operators, which make it valid to calculate the $L$-fuzzy $\beta$-covering-based lower and upper rough approximation operators through operations on matrices. Finally, the interdependency of the three pairs of rough approximation operators based on $L$-fuzzy $\beta$-covering is studied by using the notion of reducible elements and independent elements. In other words, we present the necessary and sufficient conditions under which two $L$-fuzzy $\beta$-coverings can generate the same lower and upper rough approximation operations.

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