The determination of three-way decisions with decision-theoretic rough sets considering the loss function evaluated by multiple experts

One of the main aims of a theory of three-way decisions is to model a cohort of human ways of dealing with problems and how to go about information processing considering applications in designing and implementing intelligent systems. Three-way decision with decision-theoretic rough sets is a new model characterized by the conditional risk, the loss functions and the minimum-risk decision rules. We provide a three-way decisions approach using loss functions evaluated by multiple experts based on the Bayesian decision theory. In this paper, we propose the methodologies of the aggregation of loss functions of decision-theoretic rough sets under group decision-making environment. Then we further compare them with that of the existing papers, which focus on the aggregation of the thresholds. We also construct basic model of three-way group decisions. Finally, an empirical study of evaluating the loss functions validates the reasonability and effectiveness of the proposed models. The contributions of the study are as follows: group decision-making is regarded as a knowledge based, which makes the decision more convincing as compared to single-person methods. Considering the different situations, we mainly design the corresponding aggregation operators of loss functions. Our new approach provides the methodologies of the aggregation of loss functions which in turn are used to compute the thresholds for the determination or construction of the basic rules of three-way group decision-making.