MGRS: A multi-granulation rough set

  • Authors:

  • Yuhua Qian;Jiye Liang;Yiyu Yao;Chuangyin Dang

  • Affiliations:

  • Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education, Taiyuan, 030006 Shanxi, China and Department of Manufacturing Engineering and Engineering ...;Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education, Taiyuan, 030006 Shanxi, China;Department of Computer Science, University of Regina, Regina, Saskatchewan, Canada S4S 0A2;Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Hong Kong

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2010

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Abstract

The original rough set model was developed by Pawlak, which is mainly concerned with the approximation of sets described by a single binary relation on the universe. In the view of granular computing, the classical rough set theory is established through a single granulation. This paper extends Pawlak's rough set model to a multi-granulation rough set model (MGRS), where the set approximations are defined by using multi equivalence relations on the universe. A number of important properties of MGRS are obtained. It is shown that some of the properties of Pawlak's rough set theory are special instances of those of MGRS. Moreover, several important measures, such as accuracy measure@a, quality of approximation@c and precision of approximation@p, are presented, which are re-interpreted in terms of a classic measure based on sets, the Marczewski-Steinhaus metric and the inclusion degree measure. A concept of approximation reduct is introduced to describe the smallest attribute subset that preserves the lower approximation and upper approximation of all decision classes in MGRS as well. Finally, we discuss how to extract decision rules using MGRS. Unlike the decision rules (''AND'' rules) from Pawlak's rough set model, the form of decision rules in MGRS is ''OR''. Several pivotal algorithms are also designed, which are helpful for applying this theory to practical issues. The multi-granulation rough set model provides an effective approach for problem solving in the context of multi granulations.