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Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 394))

Abstract

Interpretability has been always present in Machine Learning and Artificial Intelligence. However, it is difficult to measure it (even to define it), and quite commonly it collides with other properties as accuracy, with a clear meaning and well defined metrics. This situation has reduced its influence in the area. But due to different external reasons, interpretability is now gaining importance in Artificial Intelligence, and particularly in Machine Learning. This new situation has two effects on the field of fuzzy systems. First, considering the capability of the fuzzy formalism to describe complex phenomena in terms that are quite close to human language, fuzzy systems have gained significant presence as an interpretable modeling tool. Second, the attention paid to interpretability of fuzzy systems, that grew during the first decade of this century and then experienced a certain decay, is growing again. The present paper will consider four questions regarding interpretability: what is, why is it important, how to measure it, and how to achieve it. These questions will be first introduced in the general framework of Artificial Intelligence, to be then focused from the point of view of fuzzy systems.

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References

  1. EU General Data Protection Regulation. https://eugdpr.org/. Accessed 30 Sept 2018

  2. Explainable Artificial Intelligence (XAI). https://www.darpa.mil/program/explainable-artificial-intelligence. Accessed 30 Sept 2018

  3. Alonso, J., Castiello, C., Mencar, C.: Interpretability of fuzzy systems: current research trends and prospects. In: Kacprzyk, J., Pedrycz, W. (eds.) Springer Handbook of Computational Intelligence, pp. 219–237. Springer (2015)

    Google Scholar 

  4. Alonso, J.M., Magdalena, L., González-Rodríguez, G.: Looking for a good fuzzy system interpretability index: an experimental approach. Int. J. Approx. Reason. 51(1), 115–134 (2009)

    Article  MathSciNet  Google Scholar 

  5. Alonso, J.M., Magdalena, L., Guillaume, S.: HILK: a new methodology for designing highly interpretable linguistic knowledge bases using the fuzzy logic formalism. Int. J. Intell. Syst. 23(7), 761–794 (2008)

    Article  Google Scholar 

  6. Babuska, R.: Fuzzy Modeling and Control. Kluwer, Norwell, MA (1998)

    Google Scholar 

  7. Babuska, R.: Data-driven fuzzy modeling: transparency and complexity issues. In: Proceedings of the European Symposium on Intelligent Techniques ESIT’99. ERUDIT, Crete, Greece (1999)

    Google Scholar 

  8. Bardossy, A., Duckstein, L.: Fuzzy Rule-Based Modeling with Application to Geophysical, Biological and Engineering Systems. CRC Press (1995)

    Google Scholar 

  9. Bodenhofer, U., Bauer, P.: A formal model of interpretability of linguistic variables. In: Casillas, J., Cordón, O., Herrera, F., Magdalena, L. (eds.) Interpretability Issues in Fuzzy Modeling. Studies in Fuzziness and Soft Computing, vol. 128, pp. 524–545. Springer, Berlin, Heidelberg (2003)

    Google Scholar 

  10. Botta, A., Lazzerini, B., Marcelloni, F., Stefanescu, D.C.: Context adaptation of fuzzy systems through a multi-objective evolutionary approach based on a novel interpretability index. Soft Comput. 13(5), 437–449 (2009)

    Article  Google Scholar 

  11. Casillas, J., Cordón, O., Herrera, F., Magdalena, L.: Accuracy improvements to find the balance interpretability-accuracy in linguistic fuzzy modeling: an overview. In: Casillas, J., Cordon, O., Herrera, F., Magdalena, L. (eds.) Accuracy Improvements in Linguistic Fuzzy Modeling, pp. 3–24. Springer, Berlin, Heidelberg (2003)

    Google Scholar 

  12. Casillas, J., Cordón, O., Herrera, F., Magdalena, L.: Interpretability improvements to find the balance interpretability-accuracy in fuzzy modeling: an overview. In: Casillas, J., Cordón, O., Herrera, F., Magdalena, L. (eds.) Interpretability Issues in Fuzzy Modeling, pp. 3–22. Springer, Berlin, Heidelberg (2003)

    Google Scholar 

  13. Cordon, O.: A historical review of evolutionary learning methods for Mamdani-type fuzzy rule-based systems: designing interpretable genetic fuzzy systems. Int. J. Approx. Reason. 52, 894–913 (2011)

    Article  Google Scholar 

  14. Cordón, O., Herrera, F.: A three-stage evolutionary process for learning descriptive and approximate fuzzy logic controller knowledge bases from examples. Int. J. Approx. Reason. 17(4), 369–407 (1997)

    Article  Google Scholar 

  15. Cordon, O., Herrera, F., Magdalena, L., Villar, P.: A genetic learning process for the scaling factors, granularity and contexts of the fuzzy rule-based system data base. Inf. Sci. 136(1–4), 85–107 (2001)

    Article  Google Scholar 

  16. Fayyad, U., Piatetsky-Shapiro, G., Smyth, P.: From data mining to knowledge discovery in databases. AI Mag. 17(3), 37–53 (1996)

    Google Scholar 

  17. Fazzolari, M., Alcala, R., Nojima, Y., Ishibuchi, H., Herrera, F.: A review of the application of multi-objective evolutionary fuzzy systems: current status and further directions. IEEE Trans. Fuzzy Syst. 21(1), 45–65 (2013)

    Article  Google Scholar 

  18. Gacto, M.J., Alcala, R., Herrera, F.: A multi-objective evolutionary algorithm for tuning fuzzy rule-based systems with measures for preserving interpretability. In: Proceedings of IFSA-EUSFLAT 2009, pp. 1146–1151. Lisbon, Portugal (2009)

    Google Scholar 

  19. Gacto, M.J., Alcala, R., Herrera, F.: Integration of an index to preserve the semantic interpretability in the multiobjective evolutionary rule selection and tuning of linguistic fuzzy systems. IEEE Trans. Fuzzy Syst. 18(3), 515–531 (2010)

    Article  Google Scholar 

  20. Gacto, M.J., Alcala, 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 

  21. Laugel, T., Lesot, M., Marsala, C., Renard, X., Detyniecki, M.: Comparison-based inverse classification for interpretability in machine learning. Commun. Comput. Inf. Sci. 853 (2018)

    Google Scholar 

  22. Magdalena, L.: Fuzzy rule based systems. In: Kacprzyk, J., Pedrycz W. (eds.) Springer Handbook of Computational Intelligence, pp. 203–218. Springer (2015)

    Google Scholar 

  23. Mencar, C., Castellano, G., Fanelli, A.M.: Some fundamental interpretability issues in fuzzy modeling. In: Proceedings—4th Conference of the European Society for Fuzzy Logic and Technology and 11th French Days on Fuzzy Logic and Applications, EUSFLAT-LFA 2005 Joint Conference, pp. 100–105 (2005)

    Google Scholar 

  24. Mencar, C., Castiello, C., Cannone, R., Fanelli, A.: Design of fuzzy rule-based classifiers with semantic cointension. Inf. Sci. 181(20), 4361–4377 (2011)

    Article  Google Scholar 

  25. Mencar, C., Castiello, C., Cannone, R., Fanelli, A.: Interpretability assessment of fuzzy knowledge bases: a cointension based approach. Int. J. Approx. Reason. 52(4), 501–518 (2011)

    Article  MathSciNet  Google Scholar 

  26. Michalski, R.S.: A theory and methodology of inductive learning. Artif. Intell. 20(2), 111–161 (1983)

    Article  MathSciNet  Google Scholar 

  27. Miller, G.A.: The magical number seven, plus or minus two: some limits on our capacity for processing information. Psychol. Rev. 63, 81–97 (1956)

    Google Scholar 

  28. Pancho, D., Alonso, J.M., Cordon, O., Quirin, A., Magdalena, L.: Fingrams: visual representations of fuzzy rule-based inference for expert analysis of comprehensibility. IEEE Trans. Fuzzy Syst. 21(6), 1133–1149 (2013)

    Article  Google Scholar 

  29. Pedrycz, W.: Fuzzy Modelling: Paradigms and Practice. Kluwer Academic Press (1996)

    Google Scholar 

  30. Ribeiro, M.T., Singh, S., Guestrin, C.: “Why should I trust you?”: explaining the predictions of any classifier. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD ’16, pp. 1135–1144. ACM, New York, NY, USA (2016)

    Google Scholar 

  31. Robnik-Šikonja, M., Likas, A., Constantinopoulos, C., Kononenko, I., Štrumbelj, E.: Efficiently explaining decisions of probabilistic RBF classification networks. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6593 LNCS, PART 1 (2011)

    Google Scholar 

  32. Roubos, H., Setnes, M.: Compact and transparent fuzzy models and classifiers through iterative complexity reduction. IEEE Trans. Fuzzy Syst. 9(4), 516–524 (2001)

    Article  Google Scholar 

  33. Setnes, M., Babuska, R., Verbruggen, H.: Rule-based modeling: precision and transparency. IEEE Trans. Syst. Man Cybern. Part C (Appl. Rev.) 28(1), 165–169 (1998)

    Google Scholar 

  34. Setnes, M., Babuška, R., Verbruggen, H.B.: Complexity reduction in fuzzy modeling. Math. Comput. Simul. 46(5–6), 509–518 (1998)

    Google Scholar 

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

    Article  Google Scholar 

  36. Tarski, A., Mostowsk, A., Robinson, R.: Undecidable Theories. North-Holland (1953)

    Google Scholar 

  37. Zadeh, L.A.: Outline of a new approach to the analysis of complex systems and decision processes. IEEE Trans. Syst. Man Cybern. SMC-3(1), 28–44 (1973)

    Google Scholar 

  38. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning—I. Inf. Sci. 8, 199–249 (1975)

    Article  MathSciNet  Google Scholar 

  39. Zadeh, L.A.: Fuzzy systems theory: a framework for the analysis of humanistic systems. In: Systems Methodology in Social Science Research. Frontiers in Systems Research (Implications for the social sciences), vol. 2. Springer (1982)

    Google Scholar 

  40. Zadeh, L.A.: Is there a need for fuzzy logic? Inf. Sci. 178(13), 2751–2779 (2008)

    Article  MathSciNet  Google Scholar 

  41. Zhang, Q.S., Zhu, S.C.: Visual interpretability for deep learning: a survey. Front. Inf. Technol. Electron. Eng. 19(1), 27–39 (2018)

    Google Scholar 

  42. Zhou, S., Gan, J.: Low-level interpretability and high-level interpretability: a unified view of data-driven interpretable fuzzy system modelling. Fuzzy Sets Syst. 159(23), 3091–3131 (2008)

    Article  MathSciNet  Google Scholar 

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Correspondence to Luis Magdalena .

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Magdalena, L. (2021). Fuzzy Systems Interpretability: What, Why and How. In: Lesot, MJ., Marsala, C. (eds) Fuzzy Approaches for Soft Computing and Approximate Reasoning: Theories and Applications. Studies in Fuzziness and Soft Computing, vol 394. Springer, Cham. https://doi.org/10.1007/978-3-030-54341-9_10

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