Multifuzzy $\beta$-Covering Approximation Spaces and Their Information Measures
Jianhua Dai, Xiongtao Zou, Yuhua Qian, Xizhao Wang · IEEE Transactions on Fuzzy Systems · 2022
Fuzzy$\beta$-covering rough sets, as an effective extension of covering-based rough sets, have been concerned by many researchers. All fuzzy$\beta$-covering rough set models are constructed under a corresponding fuzzy$\beta$-covering approximation space. However, fuzzy$\beta$-covering is difficult to find directly from the real data. Fortunately, fuzzy information granulation provides a reasonable and effective way to obtain fuzzy$\beta$-coverings from the real data. Since fuzzy information granulation is capable of generating multiple fuzzy$\beta$-coverings, we introduce the notion of multifuzzy$\beta$-covering approximation spaces. Fuzzy$\beta$-covering approximation spaces are a special case of multifuzzy$\beta$-covering approximation spaces. Besides, we employ fuzzy$\beta$-neighborhood operators with reflexivity and symmetry to characterize the similarity between samples. In this article, we first present the definition of multifuzzy$\beta$-covering approximation spaces and investigate some useful properties about fuzzy$\beta$-covering. Second, several information measures are explored in the context of multifuzzy$\beta$-covering approximation spaces. On this basis, a novel heuristic fuzzy$\beta$-covering reduction method with the measure of monotone conditional entropy is proposed. Moreover, a general framework of attribute reduction based on fuzzy$\beta$-covering reduction is also designed. Finally, through the comparative and experimental analyses with other four state-of-the-art attribute reduction methods, the effectiveness and superiority of the proposed method are verified.