Granular computing based on fuzzy similarity relations
 Chen Degang,
 Yang Yongping,
 Wang Hui
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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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 Title
 Granular computing based on fuzzy similarity relations
 Journal

Soft Computing
Volume 15, Issue 6 , pp 11611172
 Cover Date
 20110601
 DOI
 10.1007/s0050001005831
 Print ISSN
 14327643
 Online ISSN
 14337479
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

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

 Chen Degang ^{(1)}
 Yang Yongping ^{(2)}
 Wang Hui ^{(3)}
 Author Affiliations

 1. Department of Mathematics and Physics, North China Electric Power University, Beijing, 102206, People’s Republic of China
 2. Beijing Key Laboratory of Safety and Clean Utilization of Energy, North China Electric Power University, Beijing, 102206, China
 3. Faculty of Engineering, School of Computing and Mathematics, University of Ulster, Jordanstown, Northern Ireland, UK