In the rough set theory and rough-fuzzy set theory, computation of approximations and edge and attributes reduction of decision table is import part of them.

在粗糙集理论及粗糙模糊集理论中，上下近似及边界的求解与决策表属性约简是它们的核心内容。

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We prove that the (upper) rough-fuzzy semigroup and the left(right, two-side) ideal are the generalization of corresponding notions defined on the fuzzy semigroup.

随后，证明了上粗模糊子半群与上粗模糊理想是通常的模糊子半群与模糊理想概念的扩张。

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Rough set theory and fuzzy set theory are two complementary mathematical tools for dealing with imprecision and uncertainty. Rough-fuzzy sets model is established by them.

粗糙集理论和模糊集理论是处理不确定和不精确问题的两种数学工具，它们有很强的互补性，将这两种理论相互融合可以建立粗糙模糊集模型。

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