Soft Computing

, Volume 15, Issue 6, pp 1161–1172 | Cite as

Granular computing based on fuzzy similarity relations

Focus

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.

Keywords

Fuzzy similarity relation Granular fuzzy sets Lower and upper approximation operators Attribute reduction 

Notes

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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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of Mathematics and PhysicsNorth China Electric Power UniversityBeijingPeople’s Republic of China
  2. 2.Beijing Key Laboratory of Safety and Clean Utilization of EnergyNorth China Electric Power UniversityBeijingChina
  3. 3.Faculty of Engineering, School of Computing and MathematicsUniversity of UlsterJordanstownNorthern Ireland, UK

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