Faithful regularised classification over linguistic fuzzy rule activations

[1] R. Agarwal, L. Melnick, N. Frosst, X. Zhang, et al., Neural additive models: Interpretable machine learning with neural nets, In Advances in Neural Information Processing Systems, 34 (2021). https://doi.org/10.5555/ 3540261.3540620

[2] J. Alcalá-Fdez, R. Alcalá, F. Herrera, A fuzzy association rule-based classification model for high-dimensional problems with genetic rule selection and lateral tuning, IEEE Transactions on Fuzzy Systems, 19(5) (2011), 857 872. https://doi.org/10.1109/TFUZZ.2011.2147794

[3] E. Angelino, N. Larus-Stone, D. Alabi, M. Seltzer, et al., Learning certifiably optimal rule lists for categorical data, Journal of Machine Learning Research, 18(1) (2017), 1-78. https://doi.org/10.5555/3122009.3290419

[4] A. Barredo Arrieta, N. Díaz-Rodríguez, J. Del Ser, A. Bennetot, et al., Explainable artificial intelligence (XAI): Concepts, taxonomies, opportunities and challenges toward responsible AI, Information Fusion, 58 (2020), 82-115. https://doi.org/10.1016/j.inffus.2019.12.012

[5] R. Batuwita, V. Palade, FSVM-CIL: Fuzzy support vector machines for class imbalance learning, IEEE Transactions on Fuzzy Systems, 18(3) (2010), 558-571. https://doi.org/10.1109/TFUZZ.2010.2042721

[6] C. Bénard, G. Biau, S. Da Veiga, E. Scornet, SIRUS: Stable and interpretable RUle Set for classification, Electronic Journal of Statistics, 15(1) (2021), 427-505. https://doi.org/10.1214/20-EJS1792

[7] J. Cao, T. Zhou, S. Zhi, S. Lam, et al., Fuzzy inference system with interpretable fuzzy rules: Advancing explainable artificial intelligence for disease diagnosis-a comprehensive review, Information Sciences, 662 (2024). https:// doi.org/10.1016/j.ins.2024.120212

[8] R. Caruana, Y. Lou, J. Gehrke, P. Koch, et al., Intelligible models for HealthCare: Predicting pneumonia risk and hospital 30-day readmission, In Proceedings of the 21st ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, (2015), 1721-1730. https://doi.org/10.1145/2783258.2788613

[9] J. Cervantes, F. Garcìa-Lamont, L. Rodríguez-Mazahua, A. López, A comprehensive survey on support vector machine classification: Applications, challenges and trends, Neurocomputing, 408 (2020), 189-215. https://doi. org/10.1016/j.neucom.2019.10.118

[10] C. H. Chang, R. Caruana, A. Goldenberg, NODE-GAM: Neural generalized additive model for interpretable deep learning, In International Conference on Learning Representations, (2021). https://doi.org/10.48550/arXiv. 2106.01613

[11] Y. Chen, J. Z. Wang, Support vector learning for fuzzy rule-based classification systems, IEEE Transactions on Fuzzy Systems, 11(6) (2003), 716-728. https://doi.org/10.1109/TFUZZ.2003.819843

[12] J. Demšar, Statistical comparisons of classifiers over multiple data sets, Journal of Machine Learning Research, 7 (2006), 1-30.

[13] D. Dua, C. Graff, UCI machine learning repository, University of California, Irvine, School of Information and Computer Sciences, (2019). http://archive.ics.uci.edu/ml

[14] M. Elkano, M. Galar, J. A. Sanz, A. Fernandez, et al., Enhancing multiclass classification in FARC-HD fuzzy classifier: On the synergy between n-dimensional overlap functions and decomposition strategies, IEEE Transactions on Fuzzy Systems, 23(5) (2015), 1562-1580. https://doi.org/10.1109/TFUZZ.2014.2370677

[15] M. Friedman, A comparison of alternative tests of significance for the problem of m rankings, The Annals of Mathematical Statistics, 11(1) (1940), 86-92. https://doi.org/10.1214/aoms/1177731944

[16] J. H. Friedman, B. E. Popescu, Predictive learning via rule ensembles, The Annals of Applied Statistics, 2(3) (2008), 916-954. https://doi.org/10.1214/07-AOAS148

[17] X. Gu, J. Han, Q. Shen, P. P. Angelov, Autonomous learning for fuzzy systems: A review, Artificial Intelligence Review, 56(8) (2023), 7549-7595. https://doi.org/10.1007/s10462-022-10355-6

[18] S. Holm, A simple sequentially rejective multiple test procedure, Scandinavian Journal of Statistics, 6(2) (1979), 65-70. https://www.jstor.org/stable/4615733

[19] X. Hu, C. Rudin, M. Seltzer, Optimal sparse decision trees, In Advances in Neural Information Processing Systems, (2019), 7267-7275. https://doi.org/10.48550/arXiv.1904.12847 [20] J. C. Hühn, E. Hüllermeier, FURIA: An algorithm for unordered fuzzy rule induction, Data Mining and Knowledge Discovery, 19(3) (2009), 293-319. https://doi.org/10.1007/s10618-009-0131-8

[21] J. S. R. Jang, ANFIS: Adaptive-network-based fuzzy inference system, IEEE Transactions on Systems, Man, and Cybernetics, 23(3) (1993), 665-685. https://doi.org/10.1109/21.256541

[22] B. Letham, C. Rudin, T. H. McCormick, D. Madigan, Interpretable classifiers using rules and Bayesian analysis: Building a better stroke prediction model, The Annals of Applied Statistics, 9(3) (2015), 1350-1371. https://doi. org/10.1214/15-AOAS848

[23] C. F. Lin, S. D. Wang, Fuzzy support vector machines, IEEE Transactions on Neural Networks, 13(2) (2002), 464-471. https://doi.org/10.1109/72.991432

[24] C. T. Lin, C. M. Yeh, S. F. Liang, J. F. Chung, et al., Support-vector-based fuzzy neural network for pattern classification, IEEE Transactions on Fuzzy Systems, 14(1) (2006), 31-41. https://doi.org/10.1109/TFUZZ.2005. 861604

[25] Y. Lou, R. Caruana, J. Gehrke, Intelligible models for classification and regression, In Proceedings of the 18th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, (2012), 150-158. https: //doi.org/10.1145/2339530.2339556

[26] H. Nori, S. Jenkins, P. Koch, R. Caruana, InterpretML: A unified framework for machine learning interpretability, Arxive, (2019). https://doi.org/10.48550/arXiv.1909.09223

[27] F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, et al., Scikit-learn: Machine learning in Python, Journal of Machine Learning Research, 12 (2011), 2825-2830. https://doi.org/10.5555/1953048.2078195

[28] O. Rainio, J. Teuho, R. Klèn, Evaluation metrics and statistical tests for machine learning, Scientific Reports, 14(1) (2024), 6086. https://doi.org/10.1038/s41598-024-56706-x

[29] C. O. Retzlaff, A. Angerschmid, A. Saranti, D. Schneeberger, et al., Post-hoc vs ante-hoc explanations: xAI design guidelines for data scientists, Cognitive Systems Research, 86 (2024), 101243. https://doi.org/10.1016/ j.cogsys.2024.101243

[30] C. Rudin, Stop explaining black box machine learning models for high stakes decisions and use interpretable models instead, Nature Machine Intelligence, 1(5) (2019), 206-215. https://doi.org/10.1038/s42256-019-0048-x

[31] C. Rudin, C. Chen, Z. Chen, H. Huang, et al., Interpretable machine learning: Fundamental principles and 10 grand challenges, Statistics Surveys, 16 (2022), 1-85. https://doi.org/10.1214/21-SS133

[32] J. A. Sanz, A. Fernández, H. Bustince, F. Herrera, IVTURS: A linguistic fuzzy rule-based classification system based on a new interval-valued fuzzy reasoning method with tuning and rule selection, IEEE Transactions on Fuzzy Systems, 21(3) (2013), 399-411. https://doi.org/10.1109/TFUZZ.2013.2243153

[33] D. Slack, S. Hilgard, E. Jia, S. Singh, et al., Fooling LIME and SHAP: Adversarial attacks on post hoc explanation methods, In Proceedings of the AAAI/ACM Conference on AI, Ethics, and Society (AIES), (2020), 180-186. https://doi.org/10.1145/3375627.3375830

[34] K. Sokol, P. Flach, Interpretable representations in explainable AI: From theory to practice, Data Mining and Knowledge Discovery, 38(5) (2024), 3102-3140. https://doi.org/10.1007/s10618-024-01010-5

[35] F. Wilcoxon, Individual comparisons by ranking methods, Biometrics Bulletin, 1(6) (1945), 80-83. https://doi. org/10.2307/3001968

[36] X. Yang, G. Zhang, J. Lu, J. Ma, A kernel fuzzy c-means clustering-based fuzzy support vector machine algorithm for classification problems with outliers or noises, IEEE Transactions on Fuzzy Systems, 19(1) (2011), 105-115. https://doi.org/10.1109/TFUZZ.2010.2087382

[37] S. M. Zhou, J. Q. Gan, Constructing L2-SVM-based fuzzy classifiers in high-dimensional space with automatic model selection and fuzzy rule ranking, IEEE Transactions on Fuzzy Systems, 15(3) (2007), 398-409. https: //doi.org/10.1109/TFUZZ.2006.882464