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Logistic-Based Design of Fuzzy Interpretable Classifiers

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Abstract

The paper develops an idea of fuzzy evidential classifiers based on modification of logistic regression model and Dempster–Shafer methodology. The proposed approach is integrating the additional linguistic variable into the classifier. This variable considers different shades of truth for class membership hypotheses and enriches available information for decision-making. It leads to identification of pre-failure states and detecting anomalies, inconsistency, and incorrectness in the initial data. As a result of the research, linguistic log-regression model is shown, and its components are justified. The inference procedure based on the model is illustrated. In the end, a simple example of implementation is also shown.

The work was supported by RFBR grants Nos. 19-07-00263, 19-07-00195, 19-08-00152, 20-07-00100, and 20-37-51002.

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References

  1. Levitin, A.V.: Restrictions on the Power of Algorithms: Decision Trees. Algorithms. Introduction to Development And Analysis, pp. 409–417. Williams (2006)

    Google Scholar 

  2. Wang, Z., Wang, R., Gao, J., Gao, Z., Liang, Y.: Fault recognition using an ensemble classifier based on Dempster–Shafer Theory. Pattern Recogn. 99, 107079 (2020)

    Google Scholar 

  3. Smets, P.: Belief functions: the disjunctive rule of combination and the generalized Bayesian theorem. Int. J. Approx. Reason. 9, 1–35 (1993)

    Article  MathSciNet  Google Scholar 

  4. Gong, C., Zhi-gang, S., Wang, P.-H., Wang, Q.: Cumulative belief peaks evidential K-nearest neighbor clustering. Knowl.-Based Syst. 200, 105982 (2020). https://doi.org/10.1016/j.knosys.2020.105982

    Article  Google Scholar 

  5. Denoeux, T., Destercke, S., Cuzzolin, F., Martin, A.: Logistic regression revisited: belief function analysis. Belief Func.: Theory Appl. 11069, 57–64 (2018)

    Google Scholar 

  6. Magdalena, L.: Fuzzy systems interpretability: What, Why and How. In: Lesot, M.-J., Marsala, C. (eds.) Fuzzy Approaches for Soft Computing and Approximate Reasoning: Theories and Applications: Dedicated to Bernadette Bouchon-Meunier, pp. 111–122. Springer International Publishing, Cham (2021). https://doi.org/10.1007/978-3-030-54341-9_10

    Chapter  Google Scholar 

  7. Kovalev, S.M., Dolgiy, A.I.: Interpretability of fuzzy temporal models. Adv. Intell. Syst. Comput. 874, 223–234 (2019)

    Google Scholar 

  8. Dempster, A.P.: Upper and lower probabilities induced by a multivalued mapping. Ann. Math. Stat. 38, 325–339 (1967)

    Article  MathSciNet  Google Scholar 

  9. Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton, N.J. (1976)

    Book  Google Scholar 

  10. Denoeux, T.: Analysis of evidence-theoretic decision rules for pattern classification. Pattern Recogn. 30, 1095–1107 (1997)

    Article  Google Scholar 

  11. Su, Z.-G., Wang, P.-H.: Improved adaptive evidential k-NN rule and its application for monitoring level of coal powder filling in ball mill. J. Process Control 19, 1751–1762 (2009)

    Article  Google Scholar 

  12. Guettari, N., Capelle-Laiz´e, A.S., Carr´e, P.: Blind image steganalysis based on evidential k-nearest neighbors. 2016 IEEE International Conference on Image Processing, pp. 2742–2746 (2016)

    Google Scholar 

  13. Chen, X.-L., Wang, P.-H., Hao, Y.-S., Zhao, M.: Evidential KNNbased condition monitoring and early warning method with applications in power plant. Neurocomput. 315, 18–32 (2018)

    Google Scholar 

  14. Denoeux, T., Smets, P.: Classification using belief functions: the relationship between the case-based and model-based approaches. IEEE Trans. Syst. Man Cybern B 36, 1395–1406 (2006)

    Article  Google Scholar 

  15. Appriou, A.: Probabilit´es et incertitude en fusion de donn´ees multisenseurs. Revue Scientifique et Technique de la D´efense 11, 27–40 (1991)

    Google Scholar 

  16. Denoeux, T.: A k-nearest neighbor classification rule based on Dempster-Shafer theory. IEEE Trans. Syst. Man Cybern. 25, 804–813 (1995)

    Google Scholar 

  17. Jiao, L., Pan, Q., Feng, X., Yang, F.: An evidential k-nearest neighbor classification method with weighted attributes. In: Proceedings of the 16th International Conference on Information Fusion, pp. 145–150 (2013)

    Google Scholar 

  18. Liu, Z.-G., Pan, Q., Dezert, J.: A new belief-based K-nearest neighbor classification method. Pattern Recogn. 46, 834–844 (2013)

    Article  Google Scholar 

  19. Lian, C., Ruan, S., Denoeux, T.: An evidential classifier based on feature selection and two-step classification strategy. Pattern Recogn. 48, 2318–2327 (2015)

    Article  Google Scholar 

  20. Lian, C., Ruan, S., Denoeux, T.: Dissimilarity metric learning in the belief function framework. IEEE Trans. Fuzzy Syst. 24, 1555–1564 (2016)

    Article  Google Scholar 

  21. Su, Z.-G., Denoeux, T., Hao, Y.-S., Zhao, M.: Evidential K-NN classification with enhanced performance via optimizing a class of parametric conjunctive t-rules. Knowl.-Based Syst. 142, 7–16 (2018)

    Article  Google Scholar 

  22. Denoeux, T.: A neural network classifier based on Dempster-Shafer theory. IEEE Trans. Syst. Man Cybern. A 30, 131–150 (2000)

    Google Scholar 

  23. Smets, P.: The canonical decomposition of a weighted belief. In: International Joint Conference on Artificial Intelligence, pp. 1896–1901 (1995)

    Google Scholar 

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Correspondence to Alexander Dolgiy .

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Dolgiy, A., Kovalev, S., Kolodenkova, A., Sukhanov, A. (2021). Logistic-Based Design of Fuzzy Interpretable Classifiers. In: Kovalev, S.M., Kuznetsov, S.O., Panov, A.I. (eds) Artificial Intelligence. RCAI 2021. Lecture Notes in Computer Science(), vol 12948. Springer, Cham. https://doi.org/10.1007/978-3-030-86855-0_19

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  • DOI: https://doi.org/10.1007/978-3-030-86855-0_19

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