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Uninorm Based Fuzzy Network for Tree Data Structures

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Fuzzy Logic and Applications (WILF 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5571))

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Abstract

The aim of this study is to introduce a fuzzy model to process structured data. A structured organization of information is typically required by symbolic processing. Most connectionist models assume that data are organized in a form of relatively simple structures such as vectors or sequences. In this work, we propose a connectionist model that can directly process labeled trees. The model is based on a new category of logic connectives and logic neurons that use the concept of uninorms. Uninorms are a generalization of t-norms and t-conorms used for aggregating fuzzy sets. Using a back-propagation algorithm we optimize the parameters of the model (relations and membership functions). The learning issues are presented and some experimental results obtained for synthetic realistic data, are reported.

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References

  1. Calvo, T., Mesiar, R.: Continuous Generate Associative Aggregation Operators. Fuzzy Sets and Systems 126, 191–197 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bianchini, M., Maggini, M., Martinelli, E., Sarti, L., Scarselli, F.: Recursive Neural Networks for Processing Graphs with Labelled Edges: Theory and Applications. Neural Networks 18, 1040–1050 (2005)

    Article  Google Scholar 

  3. Ciaramella, A., Pedrycz, W., Tagliaferri, R.: The Genetic Development of Ordinal Sums. Fuzzy Sets and Systems 151, 303–325 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  4. Ciaramella, A., Pedrycz, W., Tagliaferri, R.: OR/AND Neurons for Fuzzy Set Connectives Using Ordinal Sums and Genetic Algorithms. In: Bloch, I., Petrosino, A., Tettamanzi, A.G.B. (eds.) WILF 2005. LNCS (LNAI), vol. 3849, pp. 188–194. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  5. Ciaramella, A., Pedrycz, W., Tagliaferri, R.: The Genetic Development of Uninorms Based Neurons. In: Masulli, F., Mitra, S., Pasi, G. (eds.) WILF 2007. LNCS, vol. 4578, pp. 69–76. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  6. Fodor, J.C., Yager, R.R., Rybalov, A.: Structure of Uninorms. Int. J. of Uncertainty, Fuzziness and Knowledge-Based Systems 5, 411–427 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  7. Frasconi, P., Gori, M., Sperduti, A.: A General Framework for Adaptive Processing of Data Structures. IEEE Transaction on Neural Networks 9(5), 768–786 (1998)

    Article  Google Scholar 

  8. Gori, M., Petrosino, A.: Encoding Nondeterministic Fuzzy Tree Automata Into Recursive Neural Networks. IEEE Transactions on Neural Networks 15(6), 1435–1449 (2004)

    Article  Google Scholar 

  9. Hirota, K., Pedrycz, W.: OR/AND Neuron in Modeling Fuzzy Set Connectives. IEEE Transaction on Fuzzy Systems 2, 151–161 (1994)

    Article  Google Scholar 

  10. Kuchler, A., Goller, C.: Inductive Learning in Symbolic Domains Using Structure-Driven Recurrent Neural Networks. In: Görz, G., Hölldobler, S. (eds.) KI 1996. LNCS, vol. 1137, pp. 183–197. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  11. Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer Academic Publishers, Dordrecht (2001)

    MATH  Google Scholar 

  12. Pedrycz, W.: Logic-Based Fuzzy Neurocomputing with Unineurons. IEEE Transaction on Fuzzy Systems 14(6), 860–873 (2006)

    Article  Google Scholar 

  13. Sperduti, A., Starita, A.: Supervised Neural Networks for the Classification of Structures. IEEE Transaction on Neural Networks 8(3) (1997)

    Google Scholar 

  14. Yager, R.R.: Uninorms in Fuzzy Systems Modeling. Fuzzy Sets and Systems 122, 167–175 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  15. Zuckerman, M.-M.: Ordinal Sum-Sets. Proceedings of Americal Mathematical Society 35(1), 242–248

    Google Scholar 

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Ciaramella, A., Pedrycz, W., Petrosino, A. (2009). Uninorm Based Fuzzy Network for Tree Data Structures. In: Di Gesù, V., Pal, S.K., Petrosino, A. (eds) Fuzzy Logic and Applications. WILF 2009. Lecture Notes in Computer Science(), vol 5571. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02282-1_10

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  • DOI: https://doi.org/10.1007/978-3-642-02282-1_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02281-4

  • Online ISBN: 978-3-642-02282-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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