Multi-scale decision systems with test cost and applications to three-way multi-attribute decision-making

In real life, humans often need to deal with data hierarchically structured at different levels. The more detailed data that is collected, the greater the cost will be. When humans make decisions, they often want to achieve the goal while paying a lower cost. Therefore, it is necessary to construct a multi-scale three-way multi-attribute decision-making model with cost consideration. First, this paper proposes a multi-scale decision system with test cost, considering the conditional attribute costs at different scales. Second, the optimal scale is selected based on information entropy and total test cost. Then, we construct a new neighborhood, probability function, and relative loss function. On this basis, we establish a three-way decision model for multi-scale decision systems to solve multi-attribute decision-making problems. Finally, the experiments show that the proposed method can effectively reduce the cost while achieving the decision-making goal, demonstrating the effectiveness and superiority of the method.