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Optimal Granule Combination Selection Based on Multi-Granularity Triadic Concept Analysis

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Abstract

The thinking mode based on granule structure in granular computing essentially simulates the pattern of human thinking to solve problem. Such thinking for the study of knowledge discovery is also of significant importance in cognitive computing. Under such circumstances, the theory of multi-granularity formal concept analysis (MG-FCA) was proposed. But MG-FCA has not been applied to the analysis of three-dimensional data. Because three-dimensional data is very common and an important type of data in the real world, multi-granularity and knowledge discovery of three-dimensional data are two meaningful topics. In this paper, in order to solve the problem of three-dimensional data granularity, the idea of granularity of attributes is first introduced into triadic contexts on the basis of the relationship between triadic concept analysis and formal concept analysis. Moreover, the definition of multi-granularity triadic context is proposed, and some useful properties are studied. Then, for the purpose of realizing cross-granularity knowledge discovery in multi-granularity triadic contexts, two kinds of triadic contexts are given. As a matter of fact, for a specific problem, people often only need a solution to meet their needs. Thus, the problem of optimal granule combination selection is investigated, and the corresponding algorithms are explored. At last, for better understanding, an example with certain semantics is used to explain the proposed methods for multi-granularity triadic contexts. The main contribution as well as the significant feature of this study is to construct multi-level three-dimensional data structure and realize cross-granularity knowledge discovery. Our work will provide multi-granularity cognitive research method based on three-dimensional data.

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Acknowledgements

The authors would like to thank the reviewers for their valuable comments and helpful suggestions which lead to a significant improvement on the manuscript. This work was supported by the National Natural Science Foundation of China (Nos. 12101478, 12171392, 11971211, 61976130 and 61772021) and the Scientific Research Program Funded by Shaanxi Provincial Education Department (No. 19JK0380).

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Authors and Affiliations

  1. School of Science, Xi’an Polytechnic University, Xi’an, 710048, Shaanxi, PR China

    Qing Wan

  2. Faculty of Science, Kunming University of Science and Technology, Kunming, 650500, Yunnan, PR China

    Jinhai Li

  3. School of Mathematics, Northwest University, Xi’an, 710069, Shaanxi, PR China

    Ling Wei

  4. Institute of Concepts, Cognition and Intelligence, Northwest University, Xi’an, 710069, Shaanxi, PR China

    Qing Wan & Ling Wei

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  1. Qing Wan
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  2. Jinhai Li
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  3. Ling Wei
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Correspondence to Jinhai Li.

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Wan, Q., Li, J. & Wei, L. Optimal Granule Combination Selection Based on Multi-Granularity Triadic Concept Analysis. Cogn Comput 14, 1844–1858 (2022). https://doi.org/10.1007/s12559-021-09934-6

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