β-Interval attribute reduction in variable precision rough set model

The differences of attribute reduction and attribute core between Pawlak's rough set model (RSM) and variable precision rough set model (VPRSM) are analyzed in detail. According to the interval properties of precision parameter beta with respect to the quality of classification, the definition of attribute reduction is extended from a specific beta value to a specific beta interval in order to overcome the limitations of traditional reduct definition in VPRSM. The concept of beta-interval core is put forward which will enrich the methodology of VPRSM. With proposed ordered discernibility matrix and relevant interval characteristic sets, a heuristic algorithm can be constructed to get beta-interval reducts. Furthermore, a novel method, with which the optimal interval of precision parameter can be determined objectively, is introduced based on shadowed sets and an evaluation function is also given for selecting final optimal beta-interval reduct. All the proposed notions in this paper will promote the development of VPRSM both in theory and practice.