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Multi-scaled concept lattices based on neighborhood systems

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Abstract

Formal concept analysis (FCA) has been applied to many fields as an effective tool for data analysis and knowledge discovery. In fact, the problem of obtaining a concept lattice of appropriate complexity and size is one of the most important problems of FCA. In this paper, based on a kind of Galois connection via a concept of inclusion degree using a special neighborhood system, we propose a multi-scaled concept lattice. The presented method can effectively reduce the number of concepts, while conserving the main formal structure. A formal context can be converted into an induced context through a kind of inclusion degree which is used to cope with a special covering of the objects set. Moreover, we show that the concept lattice produced by the original context is equal to the concept lattice produced by the induced context. Finally, the multi-scaled concept lattice determined by an inclusion degree is constructed from the induced context.

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Acknowledgments

The authors would like to thank the anonymous reviewers for their helpful and constructive comments which helped to enhance the presentation of this paper. This work was supported by Grants from the National Nature Science Foundation of China (Nos. 61573127, 61300153 and 61502144) the Natural Science Foundation of Hebei Province of PR China (No. A2014205157, A2013208175), the Science Foundation of Hebei Education Department of PR China (No. Q2012093), and by Training Program for Leading Talents of Innovation Teams in the Universities of Hebei Province (LJRC022).

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Ma, L., Mi, JS. & Xie, B. Multi-scaled concept lattices based on neighborhood systems. Int. J. Mach. Learn. & Cyber. 8, 149–157 (2017). https://doi.org/10.1007/s13042-016-0521-3

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