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Granular computing based on fuzzy similarity relations

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Abstract

Rough sets and fuzzy rough sets serve as important approaches to granular computing, but the granular structure of fuzzy rough sets is not as clear as that of classical rough sets since lower and upper approximations in fuzzy rough sets are defined in terms of membership functions, while lower and upper approximations in classical rough sets are defined in terms of union of some basic granules. This limits further investigation of the existing fuzzy rough sets. To bring to light the innate granular structure of fuzzy rough sets, we develop a theory of granular computing based on fuzzy relations in this paper. We propose the concept of granular fuzzy sets based on fuzzy similarity relations, investigate the properties of the proposed granular fuzzy sets using constructive and axiomatic approaches, and study the relationship between granular fuzzy sets and fuzzy relations. We then use the granular fuzzy sets to describe the granular structures of lower and upper approximations of a fuzzy set within the framework of granular computing. Finally, we characterize the structure of attribute reduction in terms of granular fuzzy sets, and two examples are also employed to illustrate our idea in this paper.

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Acknowledgments

This paper is supported by a grant of NSFC (70871036) and a grant of National Basic Research Program of China (2009CB219801-3).

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Authors and Affiliations

  1. Department of Mathematics and Physics, North China Electric Power University, Beijing, 102206, People’s Republic of China

    Chen Degang

  2. Beijing Key Laboratory of Safety and Clean Utilization of Energy, North China Electric Power University, Beijing, 102206, China

    Yang Yongping

  3. Faculty of Engineering, School of Computing and Mathematics, University of Ulster, Jordanstown, Northern Ireland, UK

    Wang Hui

Authors
  1. Chen Degang
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  2. Yang Yongping
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  3. Wang Hui
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Correspondence to Chen Degang.

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Degang, C., Yongping, Y. & Hui, W. Granular computing based on fuzzy similarity relations. Soft Comput 15, 1161–1172 (2011). https://doi.org/10.1007/s00500-010-0583-1

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