中文摘要：

基于rough集的偶序对（下近似,上近似）表示,通过改进基于rough集的逻辑系统L的方法引入新的rough蕴涵算子,研究了它的基本性质,并将其进一步拓广到一般正则双Stone代数中,证明了添加新蕴涵算子后的正则双Stone代数构成MV-代数。其次,以上述结果为背景,建立了一个基于rough蕴涵的逻辑形式系统RSL,其语义是扩展的rough双Stone代数;同时,引入RSL-代数的概念,并证明了逻辑系统RSL的标准完备性定理（基于由近似空间确定的标准RSL-代数）。最后,说明了逻辑系统RSL是著名模糊逻辑系统Luk（即Lukasiewicz连续值逻辑系统）的语义扩张,从而从一个特殊的视角揭示了rough集与模糊逻辑的联系。

英文摘要：

From the description of the pairs （low approximation, upper approximation） of rough sets, a new rough implication operator is introduced by modifying the method by Ref. [1], some algebraic properties of this rough implication operator are investigated, and these results are generalized to regular double Stone algebras and the following important result is proved： the regular double Stone algebra with the new rough implication operator is an MV-algebra. Further more a rough logic system RSL is constructed, its schematic is rough sets and extensional regular double Stone algebras. The completeness theorem of RSL is proved by introducing the notion of RSL-algebra. Finally, the relationship between rough logic RSL and fuzzy logic Luk （continuous-valued tukasiewicz logic system） is discussed.