Optimal Scale Selection for Generalized Multi-Scale Set-Valued Decision Systems

In order to observe, represent, analyze and make decisions on the same object at different granularity, multi-scale information system is proposed. Considering that the value of an object in each scale of attribute is multiple, multi-scale information system is further extended to multi-scale set-valued information system. However, existing researches on multi-scale set-valued information systems assume that all attributes must have the same number of scales, and this assumption makes all attributes can only be combined at the same scale. Moreover, the optimal scale only considers the consistency or uncertainty of the decision system, and ignores the cost of practical application. To solve the above problems, a generalized multi-scale set-valued decision system with cost is defined, and the variation trend of uncertainty and the cost of decision system with different scale combinations is analyzed. Then, in order to improve the time efficiency, a scale space updating method based on three-way decisions is proposed. Finally, an optimal scale selection method is proposed to minimize the uncertainty and cost based on users’ requirement. The experimental results show that the proposed method can not only obtain the optimal scale by combining the uncertainty and cost, but also effectively improve the computational efficiency compared with the method of lattic mode (LM).