On some types of fuzzy covering-based rough sets

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• 作者：Bin Yang^a ; ^b ; ^{binyang0906@whu.edu.cn} ; Bao Qing Hu^a ; ^b ; ^{bqhu@whu.edu.cn}
• 关键词：Fuzzy sets ; Fuzzy β-covering ; Fuzzy covering-based rough sets ; Fuzzy β-neighborhood ; Fuzzy complementary β-neighborhood
• 刊名：Fuzzy Sets and Systems
• 出版年：2017
• 出版时间：1 April 2017
• 年：2017
• 卷：312
• 期：Complete
• 页码：36-65
• 全文大小：535 K
• 卷排序：312

文摘

Fuzzy coverings are a natural extension of the coverings by replacing crisp sets with fuzzy sets. Recently, an excellent introduction to the definition of a fuzzy β-covering is due to Ma and two fuzzy covering-based rough set models are presented. In this paper, by introducing some new definitions of fuzzy β-covering approximation spaces, the properties of fuzzy β-covering approximation spaces and Ma's fuzzy covering-based rough set models are studied. Furthermore, three new types of fuzzy covering-based rough set models as generalizations of Ma's models are first proposed in this paper. First, some properties of fuzzy β-covering and its fuzzy β-neighborhood family are proposed. We present a necessary and sufficient condition for fuzzy β-neighborhood family induced by a fuzzy β-covering to be equal to the fuzzy β-covering itself. Then we study the characterizations of Ma's fuzzy covering-based rough set models and give a necessary and sufficient condition for two fuzzy β-coverings to generate the same fuzzy covering lower approximation or the same fuzzy covering upper approximation. Finally, this paper proposes three new types of fuzzy covering-based rough set models by introducing a new notion of a fuzzy complementary β-neighborhood.