Granular computing based on fuzzy similarity relations Focus

First Online: 09 March 2010 DOI :
10.1007/s00500-010-0583-1

Cite this article as: Degang, C., Yongping, Y. & Hui, W. Soft Comput (2011) 15: 1161. doi:10.1007/s00500-010-0583-1 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

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CrossRef Authors and Affiliations 1. Department of Mathematics and Physics North China Electric Power University Beijing People’s Republic of China 2. Beijing Key Laboratory of Safety and Clean Utilization of Energy North China Electric Power University Beijing China 3. Faculty of Engineering, School of Computing and Mathematics University of Ulster Jordanstown Northern Ireland, UK