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中文摘要：
研究了多粒度模糊粗糙集的表示问题。利用模糊集的分解定理思想首次用截集构造了多粒度模糊粗糙集模型，建立了基于截集的悲观和乐观多粒度模糊粗糙集模型。在该模型中，从模糊集的截集角度定义了悲观及其乐观多粒度模糊粗糙集的上下近似集，解决了多粒度模糊粗糙集的数学结构问题，证明了多粒度模糊粗糙集可以用一簇经典的多粒度粗糙集来表示。最后利用该模型证明了多粒度模糊粗糙集的一些结论。
英文摘要：
In this paper, the representation problem of multi-granulation fuzzy rough set is researched. Inspired by decomposition theorem of fuzzy set, a new multi-granulation fuzzy rough set model based on cut set is constructed firstly and the optimistic and pessimistic multi-granulation fuzzy rough set model based on cut set of fuzzy set are proposed. In these models, the lower and upper approximations of optimistic and pessimistic multi-granulation fuzzy rough set are defined by cut set. The mathematical structure of multi-granulation fuzzy rough set is given and proved that the multi-granulation fuzzy rough set can be represented as a class of multi-granulation rough sets. A lot of conclusions of multi-granulation fuzzy rough set are then proved by new model we proposed.
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