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Granularity-driven trisecting-and-learning models for interval-valued rule induction

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Abstract

Three-way decision (3WD) theory and granular computing have recently received much attention as methods for thinking and problem solving. Based on the trisecting-and-acting model in the 3WD, this paper proposes two trisecting-and-learning models for rule induction, which begin with a constructed concept space and a search for the most suitable level of granularity in high-to-low and low-to-high manners, respectively. The learning results are sets of granules that can induce raw rules. By combining the advantages of granular computing and the trisecting-and-acting method, the models only need to process one or two parts of the trisecting result, simplifying the calculation. An interval-valued rule-inducing algorithm is proposed to obtain more general rules from raw rules. It coarsens the granularity further by merging the granules through the maximal adjacent relation of the learned granules. The interval-valued rules are obtained at the same time. The models in the paper are compatible with incomplete mixed data containing numeric, symbolic, do not care, and lost types. Symbolic data are converted into numeric types by considering their semantic order. This type of conversion enables intervals to be generated from symbolic data, producing more general rules. The rationality for allowing rules with missing data is also considered in this paper. Comparative analysis with existing works and experiments reveals the improvements of our models. Although there are a small fraction of incomplete rules and fewer intervalized rules on numeric data, the rules we induce have a higher coverage ratio and a much larger intervalized ratio for symbolic data. Moreover, our model induces simpler rules for all types of datasets.

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Data Availability

The datasets generated during and/or analysed during the current study are available in the UCI Machine Learning repository, https://archive.ics.uci.edu/ml/datasets.php.

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Funding

This work was supported by the National Natural Science Foundation of China (NO. 62172048) and China Scholarship Council (NO. 202006470014).

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Authors and Affiliations

  1. School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Yingxiao Chen & Ping Zhu

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

    Yingxiao Chen, Qiaoyi Li & Yiyu Yao

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  1. Yingxiao Chen
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  2. Ping Zhu
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Correspondence to Ping Zhu.

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Appendix A: Tables of experimental data

Appendix A: Tables of experimental data

Table 9 Rules of Shuttle-Landing data set
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Table 10 Rules of Iris data set
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Table 11 Rules of Car data set
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Table 12 Rules of Breast cancer data set
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Table 13 Rules of Balance scale data set
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Chen, Y., Zhu, P., Li, Q. et al. Granularity-driven trisecting-and-learning models for interval-valued rule induction. Appl Intell 53, 19685–19707 (2023). https://doi.org/10.1007/s10489-023-04468-w

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