A novel grey multi-criteria three-way decisions model and its application

Abstract Three-way decision provides a new research perspective for solving multi-criteria decision-making problems. Under grey environment and grey decision idea, this paper proposes a novel grey multi-criteria three-way decisions model based on grey incidence analysis and TOPSIS. The model realizes the effective fusion of three-way decision and grey system theory, and further extends the totally ordered set evaluation-based three-way decisions. Firstly, we use grey incidence analysis and TOPSIS to construct a new conditional probability for three-way decisions, which not only considers the difference in distance, but also the difference in the shape of the evaluation sequence curve. Considering the multi-criteria information system and multi-criteria loss function matrix, we construct a calculation method of criteria weights and design three weighted aggregation operators for loss function with interval grey numbers. According to key steps and algorithm, the grey multi-criteria three-way decision rules can be obtained. Finally, two illustrative example of complex equipment supplier selection and movie recommendation are utilized to validate the applicability and interpretability of our proposed model.