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Neighborhood based concept lattice

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Abstract

With the expansion of database, the complexity of concept lattices grows rapidly. Therefore, the compression of formal concepts becomes particularly important. To solve this problem, we present neighborhood based concept lattice. Firstly, two pairs of approximation operators are presented to construct 1-neighborhood object-induced concept lattice and 1-neighborhood attribute-induced concept lattice. Then, the pseudo similarity between objects and the pseudo similarity between attributes are introduced. 1-neighborhood object-induced concept lattice based on coverings and 1-neighborhood attribute-induced concept lattice based on coverings are proposed based on pseudo similarities. The neighborhoods are adjusted by the pseudo similarity, and the number of the neighborhood based concepts can be compressed. Besides, the relationship between neighborhood based concept lattice and Wille’s concept lattice is discussed. We prove that the intents of 1-neighborhood object-induced concepts based on minimal (resp. maximal) intersection neighborhood are the intents of Wille’s formal concepts. Meanwhile, the extents of 1-neighborhood attribute-induced concepts based on minimal (resp. maximal) intersection neighborhood are the extents of Wille’s formal concepts. In addition, the multi-neighborhood concept lattice is presented, the relationship between 1-neighborhood concept lattice and multi-neighborhood concept lattice is discussed. Finally, the experimental results show that the compressing of neighborhood based concept lattice is more effective when parameter values are smaller.

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Acknowledgments

This work has been partially supported by the National Natural Science Foundation of China (Grant No. 61976130). This work has been partially supported by the China Scholarship Council (Grant No. 202107000028)

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Authors and Affiliations

  1. School of Mathematics, Southwest Jiaotong University, Chendu, 610031, Sichuan, People’s Republic of China

    Han Yang, Keyun Qin & Lei Yang

  2. Department of Computer Science, University of Regina, Regina, S4S 0A2, Saskatchewan, Canada

    Han Yang

  3. School of Computing and Artificial Intelligence, Southwest Jiaotong University, Chendu, 611756, Sichuan, People’s Republic of China

    Qian Hu

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  1. Han Yang
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  2. Keyun Qin
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  3. Qian Hu
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  4. Lei Yang
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Correspondence to Han Yang.

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Yang, H., Qin, K., Hu, Q. et al. Neighborhood based concept lattice. Appl Intell 53, 6025–6040 (2023). https://doi.org/10.1007/s10489-022-03828-2

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