The research of rough sets in normed linear space

Authors:
Hui Sun;Qing Liu
Affiliations:
Department of Computer Science & Technology, Nanchang Institute of Technology, Nanchang, China;Department of Computer Science & Technology, Nanchang Institute of Technology, Nanchang, China
Venue:
RSCTC'06 Proceedings of the 5th international conference on Rough Sets and Current Trends in Computing
Year:
2006

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Abstract

As a new mathematical theory, rough sets have been applied to process imprecise, uncertain and incomplete data. The research of rough sets has been fruitful in finite and non-empty sets. Rough sets, however, only serve as a theoretic tool to discretize the real function. As far as the real function research is concerned, the research work to define rough sets in the real function is infrequent. In this paper, we exploit a new method to define rough sets in normed linear space. We put forward an upper and lower approximation definition, and make preliminary research in the properties of rough sets. A new theoretical tool is provided to study the approximation solutions to differential equation and functional variation in normed linear space.This research is significant in that it extends the application of rough sets to a new field.