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Interpretability of Fuzzy Temporal Models

  • Alexander N. Shabelnikov
  • Sergey M. Kovalev
  • Andrey V. Sukhanov
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 874)

Abstract

The paper presents a new approach to assessment of interpretability of fuzzy models. The approach differs from conventional ones, which consider interpretability from the point of structural complexity of both fuzzy model and its elements. In terms of developed approach, the interpretability means the ability of fuzzy model to reflect the same information presented in different forms to different users. Different forms of fuzzy model are given by use of specific inference system, which provides equivalent transformations of fuzzy rules from knowledge base on the linguistic level.

In our work, the inference system providing the equivalent transformations of fuzzy rules is developed for the specific class of fuzzy-temporal models. The necessary and sufficient conditions for properties of fuzzy rules are found. Such conditions provide semantic equivalence for equations obtained during fuzzy inference.

The formalized criterion is presented for interpretability of fuzzy model. The criterion is based on ability of model to keep information semantics on the fuzzy sets level when it is changed on the linguistic level.

Keywords

Assesment of fuzzy models Cointension Fuzzy interpretation of subjective information 

Notes

Acknowledgement

The work was supported by RFBR (Grants No. 17-20-01040 ofi_m_RZD, No. 16-07-00032-a and No. 16-07-00086-a).

References

  1. 1.
    Zadeh, L.: From computing with numbers to computing with words - from manipulation of measurements to manipulation of perceptions. In: IEEE Transactions on Circuits and Systems - I: Fundamental Theory and Applications, pp. 81–117. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  2. 2.
    Mencar, C., Fanelli, A.M.: Interpretability constraints for fuzzy information granulation. Inf. Sci. 178(24), 4585–4618 (2008)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Delgado, M.R., Zube, F.V.: Interpretability issues in fuzzy modelingstudies in fuzziness and soft computing. In: Hierarchical Genetic Fuzzy Systems: Accuracy, Interpretability and Design Autonomy, pp. 379–405. Physica-Verlag, New York (2003)CrossRefGoogle Scholar
  4. 4.
    Bargiela, A., Pedrycz, W.: Granular computing. In: Handbook on Computational Intelligence: Fuzzy Logic, Systems, Artificial Neural Networks, and Learning Systems, vol. 1, pp. 43–66 (2016)CrossRefGoogle Scholar
  5. 5.
    Zadeh, L.A.: Is there a need for fuzzy logic? Inf. Sci. 178(13), 2751–2779 (2008)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Zhou, S.M., Gan, J.Q.: Extracting Takagi-Sugeno fuzzy rules with interpretable submodels via regularization of linguistic modifiers. IEEE Trans. Knowl. Data Eng. 21(8), 1191–1204 (2009)CrossRefGoogle Scholar
  7. 7.
    Alonso, J.M., Magdalena, L.: Combining user’s preferences and quality criteria into a new index for guiding the design of fuzzy systems with a good interpretability-accuracy trade-off. In: 2010 IEEE International Conference on Fuzzy Systems (FUZZ), pp. 961–968 (2010)Google Scholar
  8. 8.
    Mencar, C., Castellano, G., Fanelli, A.M.: On the role of interpretability in fuzzy data mining. Int. J. Uncertain., Fuzziness Knowl.-Based Syst. 15(05), 521–537 (2007)CrossRefGoogle Scholar
  9. 9.
    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)CrossRefGoogle Scholar
  10. 10.
    Ishibuchi, H., Nojima, Y.: Analysis of interpretability-accuracy tradeoff of fuzzy systems by multiobjective fuzzy genetics-based machine learning. Int. J. Approx. Reason. 44(1), 4–31 (2007)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Marquez, A.A., Marquez, F.A., Peregrin, A.: A multi-objective evolutionary algorithm with an interpretability improvement mechanism for linguistic fuzzy systems with adaptive defuzzification. In: IEEE International Conference on Fuzzy Systems (FUZZ), pp. 277–283 (2010)Google Scholar
  12. 12.
    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)CrossRefGoogle Scholar
  13. 13.
    Riid, A., Rustern, E.: Interpretability improvement of fuzzy systems: reducing the number of unique singletons in zeroth order Takagi-Sugeno systems. In: IEEE International Conference on Fuzzy Systems (FUZZ), pp. 2013–2018 (2010)Google Scholar
  14. 14.
    Mencar, C., Castiello, C., Cannone, R., Fanelli, A.M.: Interpretability assessment of fuzzy knowledge bases: a cointension based approach. Int. J. Approx. Reason. 52(4), 501–518 (2011)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Bodenhofer, U., Bauer, P.: A formal model of interpretability of linguistic variables. In: Interpretability Issues in Fuzzy Modeling, pp. 524–545. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  16. 16.
    Kovalev, S.M., Tarassov, V.B., Dolgiy, A.I., Dolgiy, I.D., Koroleva, M.N., Khatlamadzhiyan, A.E.: Towards intelligent measurement in railcar on-line monitoring: from measurement ontologies to hybrid information granulation system. In: International Conference on Intelligent Information Technologies for Industry, pp. 169–181. Springer, Cham (2017)Google Scholar
  17. 17.
    Ruspini, E.H.: A new approach to clustering. Inf. Control. 15(1), 22–32 (1969)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Alexander N. Shabelnikov
    • 1
  • Sergey M. Kovalev
    • 1
  • Andrey V. Sukhanov
    • 1
  1. 1.Rostov State Transport UniversityRostov-on-DonRussia

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