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A Fuzzy Neural Network Classifier and Its Dual Network for Adaptive Learning of Structure and Parameters

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Abstract

A novel Fuzzy Neural Network Classifier (FNNC) with high classification accuracy is proposed in this paper. To alleviate rule explosion, the adaptive learning of the structure is performed in the proposed model. The dual structure of the model is designed, and the parameter conversion method of the two models during training is offered, so the gradient descent and back propagation methods can be used to train our model without intervention. The nodes in the model are composed of fuzzy membership functions, fuzzy logic connectives, and classification categories, which make it easy to transform the trained model into fuzzy rules and provide interpretations. Finally, the methods of rule extraction and reduction are further offered, and the causality contained in the model is analyzed. Compared with several existing neuro-fuzzy models on UCI and KEEL datasets, the results indicate that the proposed FNNC can achieve high classification accuracy and meanwhile provide interpretations in the form of fuzzy rules. The proposed method can achieve high accuracy without intervention while showing the decision process, reasons, and basis for classification. Moreover, by interpretations in the form of fuzzy rules that conform to human intuition, the proposed model can help people better understand, grasp, and analyze the classification process. Therefore, it has good application prospects in the classification problems that require the model to be transparent and interpretable, especially in the high-risk decision-making fields.

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References

  1. Das, R., Sen, S., Maulik, U.: A survey on fuzzy deep neural networks. ACM Comput. Surv. 53(3), 1–25 (2020)

    Article  Google Scholar 

  2. Takagi, T., Sugeno, M.: Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man Cybern. SMC 15(1), 116–132 (1985)

    Article  MATH  Google Scholar 

  3. Souza, P.: Fuzzy neural networks and neuro-fuzzy networks: A review the main techniques and applications used in the literature. Appl. Soft Comput. 92(106275), 258 (2020)

    Google Scholar 

  4. Zeng, K., Zhang, N.Y., Xu, W.L.: A comparative study on sufficient conditions for Takagi-Sugeno fuzzy systems as universal approximators. IEEE Trans. Fuzzy Syst. 8(6), 773–780 (2000)

    Article  Google Scholar 

  5. Jang, J.S.R.: ANFIS: adaptive-network-based fuzzy inference system. IEEE Trans. Syst. Man Cybern. 23(3), 665–685 (1993)

    Article  Google Scholar 

  6. Rajurkar, S., Verma, N. K.: Developing deep fuzzy network with Takagi Sugeno fuzzy inference system. In: FUZZ-IEEE, pp. 1–6 (2017).

  7. Wang, L.X.: Fast training algorithms for deep convolutional fuzzy systems with application to stock index prediction. IEEE Trans. Fuzzy Syst. 28(7), 1301–1314 (2020)

    Google Scholar 

  8. Gu, S., Chung, F., Wang, S.: A novel deep fuzzy classifier by stacking adversarial interpretable TSK fuzzy sub-classifiers with smooth gradient information. IEEE Trans. Fuzzy Syst. 28(7), 1369–1382 (2020)

    Google Scholar 

  9. Deng, Z., Choi, K., Chung, F., Wang, S.: Scalable TSK fuzzy modeling for very large datasets using minimal-enclosing-ball approximation. IEEE Trans. Fuzzy Syst. 19(2), 210–226 (2011)

    Article  Google Scholar 

  10. Zhang, Y., Ishibuchi, H., Wang, S.: Deep Takagi–Sugeno–Kang fuzzy classifier with shared linguistic fuzzy rules. IEEE Trans. Fuzzy Syst. 26(3), 1535–1549 (2018)

    Article  Google Scholar 

  11. Liu, Y., et al.: Brain dynamics in predicting driving fatigue using a recurrent self-evolving fuzzy neural network. IEEE Trans. Neural Netw. Learn. Syst. 27(2), 347–360 (2016)

    Article  Google Scholar 

  12. Fazzolari, M., et al.: A study on the application of instance selection techniques in genetic fuzzy rule-based classification systems: Accuracy-complexity trade-off. Knowl. Based Syst. 54, 32–41 (2013)

    Article  Google Scholar 

  13. Juang, C., Tsao, Y.: A type-2 self-organizing neural fuzzy system and its FPGA implementation. IEEE Trans. Syst. Man Cybern. 38(6), 1537–1548 (2008)

    Article  Google Scholar 

  14. Tang, J., et al.: An improved fuzzy neural network for traffic speed prediction considering periodic characteristic. IEEE Trans. Intell. Transp. Syst. 18(9), 2340–2350 (2017)

    Article  Google Scholar 

  15. Juang, C., Chen, C.: Data-driven interval type-2 neural fuzzy system with high learning accuracy and improved model interpretability. IEEE Trans. Cybern. 43(6), 1781–1795 (2013)

    Article  Google Scholar 

  16. Wang, Z., Zhang, W., Liu, N., Wang, J.: Scalable rule-based representation learning for interpretable classification. arXiv:2109.15103 [cs.LG], (2021).

  17. Nozaki, K., Ishibuchi, H., Tanaka, H.: Adaptive fuzzy rule-based classification systems. IEEE Trans. Fuzzy Syst. 4(3), 238–250 (1996)

    Article  Google Scholar 

  18. Ishibuchi, H., Yamamoto, T.: Rule weight specification in fuzzy rule-based classification systems. IEEE Trans. Fuzzy Syst. 13(4), 428–435 (2005)

    Article  Google Scholar 

  19. Cordon, O., del Jesus, M.J., Herrera, F.: A proposal on reasoning methods in fuzzy rule-based classification systems. Int. J. Approx. Reason. 20(1), 21–45 (1999)

    Article  Google Scholar 

  20. Payani, A., Fekri, F.: Learning algorithms via neural logic networks. arXiv:1904.01554 [cs.LG], (2019).

  21. Xing, Z.Y., Zhang, Y., Hou, Y.L., Jia, L.M.: On generating fuzzy systems based on pareto multi-objective cooperative coevolutionary algorithm. Int. J. Control Autom. Syst. 5(4), 444–455 (2007)

    Google Scholar 

  22. Ishibuchi, H., Nojima, Y., Nojima, Y.: Multiobjective genetic fuzzy systems. In: IEEE 5th International Workshop on Genetic and Evolutionary Fuzzy Systems, pp. 31–38 (2011).

  23. Chao, C.T., Chen, Y.J., Teng, C.C.: Simplification of fuzzy neural systems using similarity analysis. IEEE Trans. Syst. Man and Cyber. 26(2), 344–354 (1996)

    Article  Google Scholar 

  24. Setnes, M., Babuska, R., Kaymak, U., Lemke, H.R.N.: Similarity measures in fuzzy rule base simplification. IEEE Trans. Syst. Man and Cyber. 28(3), 376–386 (1998)

    Article  Google Scholar 

  25. Yen, J., Wang, L.: Simplifying fuzzy rule-based models using orthogonal transformation methods. IEEE Trans. Syst. Man and Cyber. 29(1), 13–24 (1999)

    Article  MathSciNet  Google Scholar 

  26. https://archive.ics.uci.edu/ml/datasets.html

  27. Alcal-fdez, J., et al.: Keel data-mining software tool: data set repository, integration of algorithms and experimental analysis framework. J. Multiple-Valued Logic Soft Comput. 17(2), 255–287 (2011)

    Google Scholar 

  28. Feng, S., Chen, C.L.P., Xu, L., Liu, Z.: On the accuracy-complexity trade-off of fuzzy broad learning system. IEEE Trans. Fuzzy Syst. 29(10), 2963–2974 (2021)

    Article  Google Scholar 

  29. Hinton, G.E., Osindero, S., Teh, Y.W.: A fast learning algorithm for deep belief nets. Neural Comput. 18(7), 1527–1554 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  30. Del Jesus, M.J., Hoffmann, F., Navascues, L.J., Sanchez, L.: Induction of fuzzy-rule-based classifiers with evolutionary boosting algorithms. IEEE Trans. Fuzzy Syst. 12(3), 296–308 (2004)

    Article  Google Scholar 

  31. Fazzolari, M., Alcal, R., Herrera, F.: A multi-objective evolutionary method for learning granularities based on fuzzy discretization to improve the accuracy-complexity trade-off of fuzzy rule-based classification systems: D-MOFARC algorithm. Appl. Soft Comput. 24, 470–481 (2014)

    Article  Google Scholar 

  32. Ishibuchi, H., Yamamoto, T., Nakashima, T.: Hybridization of fuzzy gbml approaches for pattern classification problems. IEEE Trans. Syst. Man Cybern. 35(2), 359–365 (2005)

    Article  Google Scholar 

  33. Juang, C., Chiu, S., Shiu, S.: Fuzzy system learned through fuzzy clustering and support vector machine for human skin color segmentation. IEEE Trans. Syst. Man Cybern. 37(6), 1077–1087 (2007)

    Article  Google Scholar 

  34. Demsar, J.: Statistical comparisons of classifiers over multiple data sets. J. Mach. Learn. Res. 7, 1–30 (2006)

    MathSciNet  MATH  Google Scholar 

  35. Turksen, I. B., et al.: Selecting a fuzzy logic operation from the DNF-CNF interval: how practical are the resulting operations. In: Proc. NAFIPS-FLINT, pp. 28–33 (2002).

  36. Gacto, M.J., Alcalá, R., Herrera, F.: Interpretability of linguistic fuzzy rule-based systems: an overview of interpretability measures. Inf. Sci. 181(20), 4340–4360 (2011)

    Article  Google Scholar 

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Acknowledgements

This work was supported by Defense Industrial Technology Development Program (JCKY2020601B018).

Funding

The work was supported in part by the Defense Industrial Technology Development Program, JCKY2020601B018.

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Authors and Affiliations

  1. Command & Control Engineering College, Army Engineering University of PLA, Nanjing, 210007, China

    Ke Zhang, Wen-Ning Hao, Xiao-Han Yu, Da-Wei Jin & Kun Yu

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  1. Ke Zhang
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Zhang, K., Hao, WN., Yu, XH. et al. A Fuzzy Neural Network Classifier and Its Dual Network for Adaptive Learning of Structure and Parameters. Int. J. Fuzzy Syst. 25, 1034–1054 (2023). https://doi.org/10.1007/s40815-022-01421-w

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  • DOI: https://doi.org/10.1007/s40815-022-01421-w

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