Granular Fuzzy Inference System (FIS) Design by Lattice Computing

  • Vassilis G. Kaburlasos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6077)


Information granules are partially/lattice-ordered. Therefore, lattice computing (LC) is proposed for dealing with them. The granules here are Intervals’ Numbers (INs), which can represent real numbers, intervals, fuzzy numbers, probability distributions, and logic values. Based on two novel theoretical propositions introduced here, it is demonstrated how LC may enhance popular fuzzy inference system (FIS) design by the rigorous fusion of granular input data, the sensible employment of sparse rules, and the introduction of tunable nonlinearities.


Fuzzy inference system (FIS) Granular data Inclusion measure Intervals’ number (IN) Lattice computing 


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  1. 1.
    Belohlavek, R.: Fuzzy Relational Systems: Foundations & Principles. Springer, Heidelberg (2002)zbMATHGoogle Scholar
  2. 2.
    Birkhoff, G.: Lattice Theory. AMS, Colloquium Publications 25 (1967)Google Scholar
  3. 3.
    Graña, M.: State of the art in lattice computing for artificial intelligence applications. In: Nadarajan, R., Anitha, R., Porkodi, C. (eds.) Mathematical and Computational Models, pp. 233–242 (2007)Google Scholar
  4. 4.
    Graña, M.: Lattice computing: lattice-theory-based computational intelligence. In: Matsuhisa, T., Koibuchi, H. (eds.) Proc. Kosen Workshop on Mathematics, Technology, and Education (MTE), pp. 19–27 (2008)Google Scholar
  5. 5.
    Graña, M., Villaverde, I., Maldonado, J.O., Hernandez, C.: Two lattice computing approaches for the unsupervised segmentation of hyperspectral images. Neurocomputing 72(10-12), 2111–2120 (2009)CrossRefGoogle Scholar
  6. 6.
    Guillaume, S.: Designing fuzzy inference systems from data: an interpretability-oriented review. IEEE Trans. Fuzzy Systems 9(3), 426–443 (2001)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Kaburlasos, V.G.: Towards a Unified Modeling and Knowledge-Representation Based on Lattice Theory. SCI, vol. 27. Springer, Heidelberg (2006)zbMATHGoogle Scholar
  8. 8.
    Kaburlasos, V.G., Hatzimichailidis, A.G.: Improved fuzzy inference system (FIS) design based on fuzzy lattice reasoning (FLR) (submitted)Google Scholar
  9. 9.
    Kaburlasos, V.G., Papadakis, S.E.: Piecewise-linear approximation of nonlinear models based on interval numbers (INs). In: Kaburlasos, V.G., Priss, U., Graña, M. (eds.) Proc. Lattice-Based Modeling (LBM 2008) Workshop, pp. 13–22 (2008)Google Scholar
  10. 10.
    Papadakis, S.E., Kaburlasos, V.G.: Piecewise-linear approximation of nonlinear models based on probabilistically/possibilistically interpreted intervals’ numbers (INs). Information Sciences (to be published)Google Scholar
  11. 11.
    Pedrycz, W., Skowron, A., Kreinovich, V. (eds.): Handbook of Granular Computing. John Wiley & Sons, Chichester (2008)Google Scholar
  12. 12.
    Ritter, G.X., Wilson, J.N.: Handbook of Computer Vision Algorithms in Image Algebra, 2nd edn. CRC Press, Boca Raton (2000)Google Scholar
  13. 13.
    Sussner, P., Valle, M.E.: Morphological and certain fuzzy morphological associative memories for classification and prediction. In: Kaburlasos, V.G., Ritter, G.X. (eds.) Computational Intelligence Based on Lattice Theory. SCI, vol. 67, pp. 149–171. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  14. 14.
    Wang, P.P.: Mathematics of Uncertainty – Guest Editiorial. Information Sciences 177(23), 5141–5142 (2007)CrossRefMathSciNetGoogle Scholar
  15. 15.
    Xu, Y., Ruan, D., Qin, K., Liu, J.: Lattice-Valued Logic. Studies in Fuzziness and Soft Computing, vol. 132. Springer, Heidelberg (2003)zbMATHGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Vassilis G. Kaburlasos
    • 1
  1. 1.Department of Industrial InformaticsTechnological Educational Institution of KavalaKavalaGreece

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