Three-way decisions approach to multiple attribute group decision making with linguistic information-based decision-theoretic rough fuzzy set

This paper investigates the decision-theoretic rough sets involved multiple decision-makers with linguistic evaluation information for the uncertainty and risk under the framework of three-way decisions theory. We first discuss the probabilistic rough fuzzy set model with linguistic information for the value of objects on the universe about the attribute set. Subsequently, we present the decision-theoretic rough fuzzy set with linguistic information for the loss functions. Then, we establish the three-way decisions based on linguistic information-based decision-theoretic rough fuzzy set as well as the corresponded decision rules that satisfy minimum risk are given. Furthermore, we consider a kind of multiple attribute group decision making problem with linguistic information and then present a new decision model using the decision-theoretic rough fuzzy set with linguistic information-based three-way decisions. Finally, the proposed decision model and method is applied to an emergency decision making problem of unconventional emergency events, the steps and the principle of the proposed method are illustrated by a numerical example with the background of emergency decision-making.