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

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.

Automated summary

This paper proposes a novel grey multi-criteria three-way decisions model based on grey incidence analysis and TOPSIS, which integrates three-way decision with grey system theory and expands totally ordered set evaluation-based three-way decisions. By considering multi-criteria information system and multi-criteria loss function matrix, the model calculates criteria weights and designs weighted aggregation operators for loss function with interval grey numbers, leading to grey multi-criteria three-way decision rules. The applicability and interpretability of the proposed model are validated through illustrative examples of complex equipment supplier selection and movie recommendation.