Rough Set Approximations in Multi-scale Interval Information Systems
With the view point of granular computing, the notion of a granule may be interpreted as one of the numerous small particles forming a larger unit. There are different granules at different levels of scale in data sets having hierarchical structures. Human beings often observe objects or deal with data hierarchically structured at different levels of granulations. And in real-world applications, there may exist multiple types of data in interval information systems. Therefore, the concept of multi-scale interval information systems is first introduced in this paper. The lower and upper approximations in multi-scale interval information systems are then defined, and the accuracy and the roughness are also explored. Monotonic properties of these rough set approximations with different levels of granulations are analyzed with illustrative examples.
KeywordsGranular computing Granules Interval information systems Multi-scale information systems Rough sets
This work is supported by grants from the National Natural Science Foundation of China (Nos. 61272021, 61202206 and 61173181), and the Zhejiang Provincial Natural Science Foundation of China (Nos. LZ12F03002, LY14F030001), and the Open Foundation from Marine Sciences in the Most Important Subjects of Zhejiang (No. 20130109).
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