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 uncertain-ty measures such as ambiguity and roughness are studied.At first,the average-step-vague rough set is defined to de-termine its dual approximations and three-way regions,and u-nion,intersection and complement properties of approxi-mation 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 cor-responding properties are verified.The obtained vague rough set and its uncertainty measures profit in-depth uncer-tainty processing.
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