Three-way group decision making based on multigranulation fuzzy decision-theoretic rough set over two universes

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.