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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