Dynamic Maintenance of Approximations Under a Rough-set Based Variable Precision Limited Tolerance Relation
Hongmei Chen, Tianrui Li and Da Ruan
Approximations are basic operators in rough sets theory. Both certain and uncertain rules can be well induced from different regions partitioned by approximations. In the dynamic change of an information system, approximations of a concept vary with time. In this paper, we extend the variable precision rough sets to Variable Precision Limited Tolerance Relation based Rough Sets (VPLTRRS) in Incomplete Information Systems (IIS). The VPLTRRS has tolerance to errors and can deal with data with missing values. We propose new definitions of coarsening and refining attribute values in IIS and present properties of approximations in terms of coarsening and refining attribute values in IIS. We further develop algorithms to dynamic maintenance of approximations under VPLTRRS. With examples to explain the incremental updating method, we validate by extensive experimental evaluation results the effectiveness of the proposed approach for dynamic maintenance approximations under VPLTRRS.
Keywords: Granular computing, Rough sets, Incomplete information system, Limited tolerance relation, Dynamic maintenance, Approximations.