不完备信息系统中属性增减下粗集近似概念的更新

考虑不完备信息系统中可能具有空值及多值的情况，对属性的增减导致给定集合的上、下近似集的更新的方法进行了探讨，推导和证明一组相关的计算公式，并通过例子加以验证，避免了信息系统中知识变化时需重新分类以计算近似集而带来的庞大的时空开销。建立了不完备信息系统中的知识依赖的概念，对于属性增减时知识依赖的度量变化进行了讨论，进行了相关定理的证明，为不完备信息系统中的动态信息处理提供了有效的数学理论方法。

Updating Approximate Concept of Rough Set Resulting from Inserting or Deleting Attributes in Incomplete Information System

The incomplete information systems in which the attribute may be of null value or multi-values are considered. The updating method of upper and lower approximate sets for a given set resulting from inserting or deleting attributes is explored. A group of relative formulas are deduced and proved through examples. The enormous spacial-temporal cost of reclassifying for computing approximate sets is then avoided when knowledge in the information system is changed. The concept of knowledge dependency in the incomplete information system is presented, and the change of the measurement of knowledge dependency is discussed with the attribute inserted or deleted. Some relative theorems, which can provide effective mathematical theory for the dynamic information managing in the incomplete information system, are proved.