A Modified Rough Set Approach to Incomplete Information Systems

The key point of the tolerance relation or similarity relation presented in the literature is to assign a “null” value to all missing attribute values. In other words, a “null” value may be equal to any value in the domain of the attribute values. This may cause a serious effect in data analysis and decision analysis because the missing values are just “missed” but they do exist and have an influence on the decision. In this paper, we will introduce the modified similarity relation denoted by MSIM that is dependent on the number of missing values with respect to the number of the whole defined attributes for each object. According to the definition of MSIM, many problems concerning the generalized decisions are solved. This point may be used in scaling in statistics in a wide range. Also, a new definition of the discernibility matrix, deduction of the decision rules, and reducts in the present of the missing values are obtained.