Three-way group decision making based on multigranulation fuzzy decision-theoretic rough set over two universes - Sun, Bingzhen; Ma, Weimin; Xiao, Xia (International journal of approximate reasoning, 2017)
Decision-theoretic rough set provides a new perspective to handle decision-making problems under uncertainty and risk. The three-way decision theory proposed by Yao is based on rough set theory and is a natural extension of the classical two-way decision approach. In this paper, we introduce the idea of decision-theoretic rough set into multigranulation approximation space and explore the rough approximation of a fuzzy decision object under the framework of two universes. We construct a variable precision multigranulation fuzzy decision-theoretic rough set over two universes by using the concept of an arbitrary binary fuzzy relation class between two different universes and the probability measurement of a fuzzy event. Several interesting properties of the proposed model are addressed and the decision rules are also deduced using the concept of three-way decision-making over two universes. Moreover, two special types of optimistic and pessimistic models are given by using different precision parameters. We then present a new approach to multiple criteria group decision making problems, based on variable precision multigranulation fuzzy decision-theoretic rough set over two universes. Meanwhile, we establish a cost-based method for sorting among all alternatives of group decision-making problems. Finally, an example of handling a medical diagnosis problem illustrates this approach. •A new multigranulation fuzzy decision-theoretic rough set over two universes was defined.•The relationship between the proposed model with the existing decision-theoretic rough set models was established.•The three-way decision was deduced based on the multigranulation fuzzy decision-theoretic rough set over two universes.•Multigranulation fuzzy decision-theoretic rough set-based three-way group decision making method was established over two universes.