Abstract: The three-way decision offers new perspectives for solving uncertain decision problems, especially categorical decision-making. However, in reality, the preference information of the decision object may be vague and uncertain. To address this issue, we construct a grey relation analysis based three-way decision model in a grey system environment. First, based on an improved grey correlation similarity measure, we investigate how the conditional probabilities of decision events are constructed. Subsequently, according to the information entropy, we established the objective optimization model and calculated the optimal weight of each index. Considering the delay cost and the uncertainty of the loss function, the grey relative loss function matrix is constructed based on the uncertain information of decision objects. Based on this, we establish the optimal thresholds method with the relative loss function and devise the decision rules. Using the established decision rules, we can obtain the classification results of all decision objects. Finally, the proposed model is used to deal with the users’ classification problems in the movie recommendation system, which demonstrates the validity and feasibility of the model.  

Key words: Grey Incidence Analysis, Three-way Decisions, Conditional Probability, Delay Cost