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Multi-granulation rough sets based on tolerance relations

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Abstract

The original rough set model is primarily concerned with the approximations of sets described by a single equivalence relation on the universe. Some further investigations generalize the classical rough set model to rough set model based on a tolerance relation. From the granular computing point of view, the classical rough set theory is based on a single granulation. For some complicated issues, the classical rough set model was extended to multi-granulation rough set model (MGRS). This paper extends the single-granulation tolerance rough set model (SGTRS) to two types of multi-granulation tolerance rough set models (MGTRS). Some important properties of the two types of MGTRS are investigated. From the properties, it can be found that rough set model based on a single tolerance relation is a special instance of MGTRS. Moreover, the relationship and difference among SGTRS, the first type of MGTRS and the second type of MGTRS are discussed. Furthermore, several important measures are presented in two types of MGTRS, such as rough measure and quality of approximation. Several examples are considered to illustrate the two types of multi-granulation tolerance rough set models. The results from this research are both theoretically and practically meaningful for data reduction.

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Acknowledgments

This paper is supported by National Natural Science Foundation of China (No.61105041,71071124 and 11001227), Natural Science Foundation Project of CQ CSTC (No.cstc2011jjA40037), and Science and Technology Program of Board of Education of Chongqing (KJ120805).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Chongqing University of Technology, Chongqing, 400054, People’s Republic of China

    Weihua Xu, Qiaorong Wang & Xiantao Zhang

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  1. Weihua Xu
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  2. Qiaorong Wang
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  3. Xiantao Zhang
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Correspondence to Weihua Xu.

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Communicated by L. Spada.

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Xu, W., Wang, Q. & Zhang, X. Multi-granulation rough sets based on tolerance relations. Soft Comput 17, 1241–1252 (2013). https://doi.org/10.1007/s00500-012-0979-1

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