Abstract: The double quantization method can describe the uncertainty nature of decision object in approximate space. In this paper, the basic model of dual quantization rough set is discussed under the framework of double domain. The background and significance of the double-domain quantization rough set are given by the practical decision-making problem. The basic definition of the double - domain quantization rough set is given by combining the classical variable precision rough set and the degree rough set. Furthermore, the basic properties of the upper and lower approximations and the relationship with the existing rough set model are systematically discussed, and the matrix calculation method is given. Finally, based on the established theoretical model and method, it gives the application of dual-domain quantization rough set in disease diagnosis decision-making. The application of theoretical model is illustrated by an example.

Key words: variable precision rough set, degree rough set, double quantification, two universes

摘要： 双量化方法能够比较全面地刻画近似空间中决策对象的不确定性本质。在双论域框架下讨论了双量化粗糙集的基本模型。通过现实中理疗诊断决策问题给出了双论域量化粗糙集研究的背景和意义，进而通过结合经典变精度粗糙集和程度粗糙集给出了双论域量化粗糙集的基本定义。系统地讨论了其上下近似的基本性质以及与已有粗糙集模型的关系，并给出了其上下近似的矩阵计算方法。基于所建立的理论模型与方法，给出了双论域量化粗糙集在疾病诊断决策中的应用，通过应用算例说明了理论模型的应用过程。

关键词: 变精度粗糙集, 程度粗糙集, 双量化, 双论域