Twofold rough approximations under incomplete information
Michinori Nakata, Hiroshi Sakai · International Journal of General Systems · 2013
A method using possible equivalence classes has been developed on information tables with missing values. The method essentially differs from the other methods in having the two features. One is to directly deal with missing values by using not actual but possible equivalence classes. The other is to consider both aspects of discernibility and indiscernibility of a missing value from another value. When information tables contain incomplete information, rough approximations are not unique. We have lower and upper bounds of the actual rough approximations. The lower and upper bounds correspond to certain and possible rough approximations, respectively. Therefore, rough approximations are twofold under incomplete information. The certain and possible rough approximations are linked with each other. The method creates the same rough approximations as the method of possible worlds. This justifies the method of possible equivalence classes. The method is free from the difficulty of computational complexity for the growth of the number of missing values. Furthermore, the method is free from the restriction that missing values may occur for only some specified attributes. Therefore, we can efficiently obtain certain and possible rough approximations between arbitrary sets of attributes having missing values.