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经典粗糙集理论关注的是论域上的单个二元等价关系导出的集合的近似。将等价关系弱化为相似关系、相容关系或邻域关系等可得到多种拓展粗糙集模型。但以粒计算的观点来看,这些模型都是单粒度的。本文把单粒度的粗糙集模型推广到不完备信息系统中的多粒度粗糙集模型,用论域上的多个相容关系定义了集合的近似。研究了含有缺失数据的多粒度粗糙集模型的一些数学性质,定义了不完备环境下的多粒度粗糙集模型的近似精度,实例表明多粒度粗糙集模型比单粒度粗糙集模型具有更高的精度。
Classical rough set theory focuses on the approximation of a set derived from a single binary equivalence relation on the universe of discourse. Extending equivalence relations to similar relations, compatible relations or neighborhood relations can obtain a variety of extended rough set models. However, from a granular point of view, these models are all single-grain. In this paper, the single-granular rough set model is generalized to the multi-granular rough set model in incomplete information system, and the approximation of the set is defined by multiple conformable relations in the universe of discourse. Some mathematical properties of the multi-granularity rough set model with missing data are studied, and the approximate accuracy of the multi-granular rough set model is defined in an incomplete environment. The example shows that the multi-granularity rough set model has higher accuracy than the single-particle rough set model .