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Robust Variable Threshold Fuzzy Concept Lattice with Application to Medical Diagnosis

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Abstract

Formal concept analysis is an effective tool for data analysis and visualization by means of concept lattice. Many concept lattice models have been studied in various settings. Variable threshold concept lattice is a fuzzy concept lattice constructed from fuzzy data. However, variable threshold concept lattice is not robust to noise because it employs a single threshold, instead of an interval to derive formal concepts. Thus, the paper introduces the tolerance threshold to variable threshold concept lattice, and forms the ROBust variable threshold fuzzy Concept Lattice (RobCL). By analyzing the properties of RobCL, we show that RobCL has some incremental characteristics and is able to model the incremental cognitive process, which makes RobCL distinctive from other concept lattice models. A comparative study shows that variable threshold concept lattice is just a special case of RobCL; in other words, when two thresholds coincide with each other, RobCL degenerates to variable threshold concept lattice and the incremental characteristics vanish. In addition, the proposed model is also applied to medical diagnosis and shows its superiority over the previous model.

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Notes

  1. Otherwise, if \(X^{(\alpha \beta )^{n-1}\alpha }=X^{(\alpha \beta )^{n}\alpha }\), then \(X^{{(\alpha \beta )}^{n}}=X^{((\alpha \beta )^{n-1}\alpha )\beta }=X^ {((\alpha \beta )^{n}\alpha )\beta }=X^{(\alpha \beta )^{n+1}}\), a contradiction with \(X^{(\alpha \beta )^{n}}\subset X^{(\alpha \beta )^{n+1}}\). Similarly, we have \(X^{(\alpha \beta )^{n}}\ne X^{(\alpha \beta )^{n-1}}\).

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Funding

This work was supported by the National Natural Science Foundation of China (No. 61972238, 62072294).

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Author notes

  1. Wang Tao and Li Deyu have contributed equally to this work.

Authors and Affiliations

  1. School of Computer and Information Technology, Shanxi University, Taiyuan, 030006, Shanxi, People’s Republic of China

    Yanhui Zhai, Tao Wang & Deyu Li

  2. Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education, Shanxi University, Taiyuan, 030006, Shanxi, People’s Republic of China

    Yanhui Zhai & Deyu Li

Authors
  1. Yanhui Zhai
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  2. Tao Wang
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  3. Deyu Li
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Correspondence to Yanhui Zhai.

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Zhai, Y., Wang, T. & Li, D. Robust Variable Threshold Fuzzy Concept Lattice with Application to Medical Diagnosis. Int. J. Fuzzy Syst. 26, 344–356 (2024). https://doi.org/10.1007/s40815-023-01570-6

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  • DOI: https://doi.org/10.1007/s40815-023-01570-6

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