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β-Interval attribute reduction in variable precision rough set model

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Abstract

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 β with respect to the quality of classification, the definition of attribute reduction is extended from a specific β value to a specific β interval in order to overcome the limitations of traditional reduct definition in VPRSM. The concept of β-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 β-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 β-interval reduct. All the proposed notions in this paper will promote the development of VPRSM both in theory and practice.

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Acknowledgments

The authors wish to grateful acknowledge anonymous reviews for their valuable comments and recommendations. This work was supported by National Natural Science Foundation of China (Serial No. 60475019, 60775036, 60970061) and the Ph.D. programs Foundation of Ministry of Education of China (Serial No. 20060247039).

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Authors and Affiliations

  1. Department of Computer Science and Technology, Tongji University, Shanghai, 201804, People’s Republic of China

    Jie Zhou & Duoqian Miao

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  1. Jie Zhou
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  2. Duoqian Miao
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Correspondence to Jie Zhou.

Appendix

Appendix

See Table 8.

Table 8 WINE data set
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Zhou, J., Miao, D. β-Interval attribute reduction in variable precision rough set model. Soft Comput 15, 1643–1656 (2011). https://doi.org/10.1007/s00500-011-0693-4

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