关键词: 覆盖Vague集，粗糙集，真隶属函数，假隶属函数，基数和

Abstract: Both covering-based rough sets and vague sets are the mathematical tools to deal with the uncertainty information. The former is the extension of the rough set theory and the latter of the fuzzy sets. Computing the lower and the upper approximations with the existing covering-based rough set models, some elements, which arc actually not sure whether they completely belong to the given set，may be put into the lower approximation. Similarly, some elements,which maybe belong to the given set,are excluded from the upper approximation. By analyzing carefully the relationship between the element of the universe and the covering-elements, a covering vague set was established. This covering vague set can reflect the degree of membership of every element of universe to the given set from a new viewpoint. Furthermore, some relationships between the covering vague set and some important concepts of covering-based rough sets were studied. Finally, the properties of a covering vague set that when a covering coincides with a partition were discussed.

Key words: Covering vague sets, Rough sets, Truth-membership function, False-membership function, Sum of base number