Quantitative analysis for covering-based rough sets through the upper approximation number

  • Authors:

  • Shiping Wang;Qingxin Zhu;William Zhu;Fan Min

  • Affiliations:

  • School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China;School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China;Lab of Granular Computing, Zhangzhou Normal University, Zhangzhou 363000, China;Lab of Granular Computing, Zhangzhou Normal University, Zhangzhou 363000, China

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2013

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Abstract

Coverings are a useful form of data, while covering-based rough sets provide an effective tool for dealing with this data. Covering-based rough sets have been widely used in attribute reduction and rule extraction. However, few quantitative analyses for covering-based rough sets have been conducted, while many advances for classical rough sets have been obtained through quantitative tools. In this paper, the upper approximation number is defined as a measurement to quantify covering-based rough sets, and a pair of upper and lower approximation operators are constructed using the approximation number. The operators not only inherit some important properties of existing approximation operators, but also exhibit some new quantitative characteristics. It is interesting to note that the upper approximation number of a covering approximation space is similar to the dimension of a vector space or the rank of a matrix.