Rough set model of incomplete information systems based on the weighted threshold tolerance relation

In order to overcome the shortage that attribute weights are not taken into consideration in the existing extensions of rough sets under incomplete information systems, a new rough set model is proposed based on the weighted threshold tolerance relation. The new model calculates the weights according to the information quantity of the incomplete information system without outside knowledge, so the weights are objective. Moreover, the model introduces a threshold to adjust the strictness degree of the weighted threshold tolerance class, which not only combines subjective requirements into consideration, but also excludes objects in advance that do not reach the threshold and can not be in the same weighted threshold tolerance class with other objects. This exclusion will not influence the completeness of the classes. Contrastive analysis of an example shows that the proposed extension of a rough set based on the weighted threshold tolerance relation accords with the fact of an incomplete information system and is more applicable compared with other models.