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3-Way Concept Analysis Based on 3-Valued Formal Contexts

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Abstract

As the basic form of data presentation, formal contexts play an elementary and important role in formal concept analysis and in 3-way concept analysis. In fact, many data tables are similar in form to formal contexts. Therefore, these data tables can be studied collectively in a similar framework, and such a study can be significant in knowledge discovery. We propose the notion of 3-valued formal contexts after analyzing the shared characteristics of different data forms such as incomplete formal contexts, conflict situations and other similar cases. After close studies of 3-valued formal contexts, this paper adopts 3-way concept analysis to define 3-valued operators and construct 3-valued concept lattices and finally interpret the meaning of 3-valued operators and discuss the relationship between 3-valued lattices and existing approximation concept lattices. The essence of this method is to present, via 3-way concept analysis, potential information and structure. And 3-way concept analysis shows the common properties of the objects, jointly possessed or jointly not possessed, positive or negative, even the uncertain information. So, this paper actually provides a new model for cognition. Apart from the universal applicability, 3-valued contexts can also be fixed into formal concept analysis. That is, many problems can be studied in the framework of formal concept analysis.

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Acknowledgements

This work is partially supported by the National Natural Science Foundation of China (Grant Nos. 61772021, 61976244 and 62006190) and the Natural Science Basic Research Program of Shaanxi (Program No. 2021JM-141). We appreciate Prof. Yiyu Yao for his constructive suggestion to this work.

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  1. School of Computer Science and Technology, Xidian University, Xi’an, 710071, PR China

    Jianjun Qi

  2. School of Mathematics, Northwest University, Xi’an, 710127, PR China

    Ling Wei & Ruisi Ren

  3. Institute of Concepts, Cognition and Intelligence, Northwest University, Xi’an, 710127, PR China

    Jianjun Qi, Ling Wei & Ruisi Ren

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Correspondence to Jianjun Qi.

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Qi, J., Wei, L. & Ren, R. 3-Way Concept Analysis Based on 3-Valued Formal Contexts. Cogn Comput 14, 1900–1912 (2022). https://doi.org/10.1007/s12559-021-09899-6

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