【摘要】 Vague集和粗糙集都是处理不确定性的数学工具，它们的结合具有研究意义.基于阶梯均值vague集构造一种新型粗糙集模型，并研究相关的模糊度、粗糙度等不确定性度量.定义阶梯均值vague粗糙集，确定上下近似与三支区域，研究该模型近似算子的并、交、补等运算性质.提出相应的模糊度、精确度、粗糙度、近似精度、近似质量，并得到关于论域剖分与层次集成的性质.提供数据实例，计算上下近似、三支区域、模糊度、粗糙度等概念，并验证相关性质.所得vague粗糙集及其不确定度量有利于深入不确定性处理.更多还原

【Abstract】 Both vague sets and rough sets are mathematical tools for dealing with uncertainty, and their combination has research significance.A new rough set model is constructed based on the averagestep-vague set, and its uncertainty measures such as ambiguity and roughness are studied.At first, the average-step-vague rough set is defined to determine its dual approximations and three-way regions, and u-nion, intersection and complement properties of approximation operators are studied.Then, corresponding ambiguity, accuracy, roughness, approximate precision and quality are proposed, and their properties on universe division and hierarchy integration are obtained.Finally, data examples are provided to calculate related notions of dual approximation, three-way regions, ambiguity, roughness, and thus corresponding properties are verified.The obtained vague rough set and its uncertainty measures profit in-depth uncertainty processing.更多还原