Variable precision multigranulation decision-theoretic fuzzy rough sets

This paper studies variable precision multigranulation fuzzy decision-theoretic rough sets in an information system. We firstly review definitions and properties of multigranulation fuzzy rough sets. A novel membership degree based on single granulation rough sets is proposed. Then two operators based on this membership degree are defined. By employing these operators, two types of variable precision multigranulation fuzzy rough sets in an information system are proposed. Finally, inspired by three-way decisions, we propose Type-1 variable precision multigranulation decision-theoretic fuzzy rough sets.