期刊
APPLIED MATHEMATICAL MODELLING
卷 35, 期 4, 页码 1798-1809出版社
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2010.10.010
关键词
Fuzzy sets; Rough sets; Fuzzy relation; Fuzzy compatible relation; Fuzzy rough sets
资金
- National Natural Science Foundation of China [70671004, 71071113]
- A Foundation for the Author of National Excellent Doctoral Dissertation of PR China [200782]
- Shanghai Education Development Foundation
- Shanghai Education Committee [08SG21]
- Shanghai Pujiang Program
- Shanghai philosophical and social foundation
The concept of the rough set was originally proposed by Pawlak as a formal tool for modeling and processing incomplete information in information systems. Then in 1990. Dubois and Prade first introduced the rough fuzzy sets and fuzzy rough sets as a fuzzy extension of the rough sets. The aim of this paper is to present a new extension of the rough set model on the different universe. i.e., the fuzzy rough sets model between two different universes is presented based on the fuzzy compatible relation (R) over tilde alpha, which is defined by a fuzzy relation (R) over tilde between two different non-empty universes U and V and the threshold alpha(alpha is an element of (0,1]). Several properties of this rough sets model are given, and the relationships of this model with others rough set model are examined, too. Furthermore, we also discuss two extended models of the fuzzy rough sets model based on the fuzzy rough set model on different universes. i.e., the degree fuzzy rough set and the variable precision fuzzy rough set. Meanwhile, some principal conclusions of this two rough sets model are also established. Finally, a test example is applied to interpret the background of the application and the ideals for the fuzzy rough sets model that is presented in this paper. (C) 2010 Elsevier Inc. All rights reserved.
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