Some extensions of covering-based multigranulation fuzzy rough sets from new perspectives

Covering-based multigranulation fuzzy rough sets are a natural extension of the multigranulation rough sets by replacing crisp sets with fuzzy sets. Recently, the covering-based multigranulation fuzzy rough sets in terms of the family of a fuzzy β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document}-neighborhoods is due to Zhan et al. (Artif Intell Rev 53(2):1093–1126). As a generalization to Zhan’s method which pointed to increase the lower approximation and decrease the upper approximation, the proposed article aims to introduce the notion of a family of fuzzy complementary β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document}-neighborhood and thus four types of covering-based optimistic (pessimistic) multigranulation fuzzy rough sets models are presented. Also, four new kinds of covering-based M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {M}$$\end{document}-optimistic (pessimistic) multigranulation fuzzy rough sets models are constructed. Some characterizations of these models and its related with Zhan’s model are studied. A comparison between these new types of multigranulation fuzzy rough sets will be discussed. Finally, we apply our proposed models with an algorithm on certain forms of drugs which may help the expert in decision making, especially, in medicine.