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Simultaneous Learning of Fuzzy Sets

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Neural Approaches to Dynamics of Signal Exchanges

Part of the book series: Smart Innovation, Systems and Technologies ((SIST,volume 151))

Abstract

We extend a procedure based on support vector clustering and devoted to inferring the membership function of a fuzzy set to the case of a universe of discourse over which several fuzzy sets are defined. The extended approach learns simultaneously these sets without requiring as previous knowledge either their number or labels approximating membership values. This data-driven approach is completed via expert knowledge incorporation in the form of predefined shapes for the membership functions. The procedure is successfully tested on a benchmark.

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Notes

  1. 1.

    Note that even with this careful setting, there is no guarantee that the three clusters will get associated injectively with the three available classes. We simply re-executed the iterations in which these cases occurred.

References

  1. Afify, A.: FuzzyRULES-II: a new approach to fuzzy rule induction from numerical data. Front. Artif. Intell. Appl. 281, 91–100 (2016)

    Google Scholar 

  2. Apolloni, B., Bassis, S., Gaito, S., Malchiodi, D.: Bootstrapping complex functions. Nonlinear Anal.: Hybrid Syst. 2(2), 648–664 (2008)

    MathSciNet  MATH  Google Scholar 

  3. Apolloni, B., Bassis, S., Gaito, S., Malchiodi, D., Zoppis, I.: Controlling the losing probability in a monotone game. Inf. Sci. 176(10), 1395–1416 (2006)

    Article  MathSciNet  Google Scholar 

  4. Apolloni, B., Bassis, S., Malchiodi, D., Pedrycz, W.: Interpolating support information granules. Proceeding of the 16th International Conference on Artificial Neural Networks - Part II. ICANN’06, pp. 270–281. Springer-Verlag, Berlin, Heidelberg (2006)

    Chapter  Google Scholar 

  5. Apolloni, B., Iannizzi, D., Malchiodi, D., Pedrycz, W.: Granular regression. In: Neural nets: 16th italian workshop on neural nets, WIRN2005 and international workshop on natural and artificial immune systems, NAIS 2005, vol. 3931 LNCS, pp. 147–156. Springer (2006)

    Google Scholar 

  6. Apolloni, B., Malchiodi, D., Valerio, L.: Relevance regression learning with support vector machines. Nonlinear Anal., Theory, Methods Appl. 73(9), 2855–2864 (2010)

    Article  MathSciNet  Google Scholar 

  7. Ben-Hur, A., Horn, D., Siegelmann, H.T., Vapnik, V.: Support vector clustering. J. Mach. Learn. Res. 2(Dec), 125–137 (2001)

    Google Scholar 

  8. Dubois, D., Hájek, P., Prade, H.: Knowledge-driven versus data-driven logics. J. Log., Lang. Inf. 9(1), 65–89 (2000)

    Google Scholar 

  9. Dubois, D., Prade, H.: The three semantics of fuzzy sets. Fuzzy Sets Syst. 90, 141–150 (1997)

    Article  MathSciNet  Google Scholar 

  10. Hong, T.P., Lee, C.Y.: Induction of fuzzy rules and membership functions from training examples. Fuzzy Sets Syst. 84(1), 33–47 (1996)

    Article  MathSciNet  Google Scholar 

  11. Lo Presti, M., Poluzzi, R., Zanaboni, A.M.: Synthesis of fuzzy controllers through neural networks. Fuzzy Sets Syst. 71, 47–70 (1995)

    Article  MathSciNet  Google Scholar 

  12. Malchiodi, D., Pedrycz, W.: Learning membership functions for fuzzy sets through modified support vector clustering. In: Masulli, F. Pasi, G., Yager R.R. (eds.) Fuzzy Logic and Applications - 10th International Workshop, WILF 2013, Genoa, Italy, November 19–22, 2013. Proceedings, vol. LNCS 8256, pp. 52–59. Springer (2013)

    Google Scholar 

  13. Malchiodi, D., Tettamanzi, A.G.B.: Predicting the possibilistic score of OWL axioms through modified support vector clustering. In: SAC 2018: Symposium on Applied Computing, April 9–13, 2018, Pau, France. ACM, New York, NY, USA (2018). https://doi.org/10.1145/3167132.3167345

  14. Mottaghi-Kashtiban, M., Khoei, A., Hadidi, K.: Optimization of rational-powered membership functions using extended kalman filter. Fuzzy Sets Syst. 159(23), 3232–3244 (2008)

    Article  MathSciNet  Google Scholar 

  15. Nguyen, H., Walker, E.: A First Course in Fuzzy Logic. CRC Press, Boca Raton, Chapman Hall (1999)

    MATH  Google Scholar 

  16. de Oliveira, J.V.: Semantic constraints for membership function optimization. IEEE Trans. Syst., Man, Cybern.-Part A: Syst.Humans 29(1), 128–138 (1999)

    Google Scholar 

  17. Pedrycz, W.: Granul. Comput.: Anal. Des. Intell. Syst. CRC Press/Francis Taylor, Boca Raton (2013)

    Google Scholar 

  18. Setnes, M., Babuska, R., Verbruggen, H.B.: Transparent fuzzy modelling. Int. J. Hum.-Comput. Stud. 49(2), 159–179 (1998)

    Article  Google Scholar 

  19. Wu, J.N., Cheung, K.C.: An efficient algorithm for inducing fuzzy rules from numerical data. In: Proceedings of the Eleventh International FLAIRS Conference, pp. 221–224. AAAI (1998)

    Google Scholar 

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Acknowledgements

The authors would like to thank Angelo Ciaramella and Antonino Staiano for the fruitful discussion concerning the organization of the experimental phase.

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Authors and Affiliations

  1. Dipartimento di Informatica, Università degli Studi di Milano, Milan, Italy

    Luca Cermenati, Dario Malchiodi & Anna Maria Zanaboni

Authors
  1. Luca Cermenati
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  2. Dario Malchiodi
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  3. Anna Maria Zanaboni
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Corresponding author

Correspondence to Dario Malchiodi .

Editor information

Editors and Affiliations

  1. Department of Psychology, University of Campania Luigi Vanvitelli, Caserta, Italy

    Anna Esposito

  2. Tecnocampus, Mataró, Spain

    Marcos Faundez-Zanuy

  3. Department of Civil, Environment, Energy and Materials Engineering, Mediterranea University of Reggio Calabria, Reggio Calabria, Italy

    Francesco Carlo Morabito

  4. Dipartimento di Elettronica e Telecomunicazioni, Politecnico di Torino, Turin, Italy

    Eros Pasero

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Cermenati, L., Malchiodi, D., Zanaboni, A.M. (2020). Simultaneous Learning of Fuzzy Sets. In: Esposito, A., Faundez-Zanuy, M., Morabito, F., Pasero, E. (eds) Neural Approaches to Dynamics of Signal Exchanges. Smart Innovation, Systems and Technologies, vol 151. Springer, Singapore. https://doi.org/10.1007/978-981-13-8950-4_16

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