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.
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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)
Mencar, C., Fanelli, A.M.: Interpretability constraints for fuzzy information granulation. Inf. Sci. 178(24), 4585–4618 (2008)
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)
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)
Zadeh, L.A.: Is there a need for fuzzy logic? Inf. Sci. 178(13), 2751–2779 (2008)
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)
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)
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)
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)
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)
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)
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)
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)
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)
Bodenhofer, U., Bauer, P.: A formal model of interpretability of linguistic variables. In: Interpretability Issues in Fuzzy Modeling, pp. 524–545. Springer, Heidelberg (2003)
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)
Ruspini, E.H.: A new approach to clustering. Inf. Control. 15(1), 22–32 (1969)
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).
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Shabelnikov, A.N., Kovalev, S.M., Sukhanov, A.V. (2019). Interpretability of Fuzzy Temporal Models. In: Abraham, A., Kovalev, S., Tarassov, V., Snasel, V., Sukhanov, A. (eds) Proceedings of the Third International Scientific Conference “Intelligent Information Technologies for Industry” (IITI’18). IITI'18 2018. Advances in Intelligent Systems and Computing, vol 874. Springer, Cham. https://doi.org/10.1007/978-3-030-01818-4_22
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DOI: https://doi.org/10.1007/978-3-030-01818-4_22
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