Abstract
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.
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