Three-way decisions based on decision-theoretic rough sets under linguistic assessment with the aid of group decision making

•We provide a method of the determination of the two types of parameters used in the DTRS.•The application of DTRS is extended to the scenarios of qualitative evaluation.•An algorithm is designed to improve the inconsistency of multi-attribute group decision making under linguistic assessment.

Based on decision-theoretic rough set model of three-way decisions, we augment the existing model by introducing linguistic terms. Considering the two types of parameters being used in the three-way decisions with linguistic assessment, a certain type of novel three-way decisions based on the Bayesian decision procedure is constructed. In this way, three-way decisions with decision-theoretic rough sets are extended to the qualitative environment. With the aid of multi-attribute group decision making, the values of these parameters are determined. An adaptive algorithm supporting consistency improvement of multi-attribute group decision making is designed. Then, we optimize the scales of the linguistic terms with the use of particle swarm optimization. The values of these parameters of three-way decisions are aggregated when proceeding with group decision making. Finally, the proposed model of three-way decisions with linguistic assessment is applied to the selection process of new product ideas.

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