Abstract The tolerance rough set is developed as one of the outstanding extensions of the Pawlak's rough set model under incomplete information, and the limited tolerance relation is developed to overcome the problem that objects leniently satisfy the tolerance relation. However, the classification based on the limited tolerance relationship cannot reflect the matching degree of uncertain information of objects. In this article, we explore the influence of null values in an incomplete system, and propose the constrained tolerance relation based on the matching degree of uncertain information of objects. The proposed rough set based on the constrained tolerance relation can provide a more detailed structure of an object class through threshold. Proofs and example analyses further show the rationality and superiority of the proposed model.
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