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A Type-1 Approximation of Interval Type-2 FLS

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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 paper presents a method for the approximation of the interval type-2 fuzzy logic system (FLS) by the type-1 FLS, when the interval type-2 FLS is assumed to perform the extended minimum Cartesian product and to have singleton consequents. The approximation error is discussed in details.

This work was partly supported by Polish Ministry of Science and Higher Education (Habilitation Project N N516 372234 2008–2011, Special Research Project 2006–2009, Polish-Singapore Research Project 2008–2010).

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References

  1. Castillo, O., Aguilar, L.T., Cazarez-Castro, N.R., Boucherit, M.S.: Application of type-2 fuzzy logic controller to an induction motor drive with seven-level diode-clamped inverter and controlled infeed. Electrical Engineering 90(5), 347–359 (2008)

    Article  Google Scholar 

  2. Castillo, O., Melin, P.: Intelligent systems with interval type-2 fuzzy logic. International Journal of Innovative Computing, Information and Control 4(4), 771–783 (2008)

    Google Scholar 

  3. Castillo, O., Melin, P.: Adaptive noise cancellation using type-2 fuzzy logic and neural networks. In: Proc. IEEE-FUZZ 2004, Budapest (July 2004)

    Google Scholar 

  4. Hagras, H.A.: A hierarchical type-2 fuzzy logic control architecture for autonomous robots. IEEE Transactions on Fuzzy Systems 12(4), 524–539 (2004)

    Article  Google Scholar 

  5. Hagras, H.: Type-2 fuzzy logic controllers: A way forward for fuzzy systems in real world environments. In: Zurada, J.M., Yen, G.G., Wang, J. (eds.) WCCI 2008. LNCS, vol. 5050, pp. 181–200. Springer, Heidelberg (2008)

    Google Scholar 

  6. Liang, Q., Mendel, J.M.: Interval type-2 fuzzy logic systems: Theory and design. IEEE Transactions on Fuzzy Systems 8, 535–550 (2000)

    Article  Google Scholar 

  7. Mendez, G.M.: Interval type-2 anfis. In: Advances in Soft Computing – Innovations in Hybrid Intelligent Systems, pp. 64–71 (2007)

    Google Scholar 

  8. Torres, P., Sáez, D.: Type-2 Fuzzy Logic Identification Applied to the Modeling of a Robot Hand. In: Proc. FUZZ-IEEE 2008, Hong Kong (June 2008)

    Google Scholar 

  9. Uncu, O., Turksen, I.B.: Discrete interval type 2 fuzzy system models using uncertainty in learning parameters. IEEE Transactions on Fuzzy Systems 15(1), 90–106 (2007)

    Article  Google Scholar 

  10. Karnik, N.N., Mendel, J.M., Liang, Q.: Type-2 fuzzy logic systems. IEEE Transactions on Fuzzy Systems 7(6), 643–658 (1999)

    Article  Google Scholar 

  11. Karnik, N.N., Mendel, J.M.: Centroid of a type-2 fuzzy set. Information Sciences 132, 195–220 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  12. Starczewski, J., Rutkowski, L.: Neuro-fuzzy systems of type 2. In: Proc. 1st Int’l Conf. on Fuzzy Systems and Knowledge Discovery, Singapore, vol. 2, pp. 458–462 (2002)

    Google Scholar 

  13. Starczewski, J.: What differs type-2 FLS from type-1 FLS? In: Rutkowski, L., Siekmann, J.H., Tadeusiewicz, R., Zadeh, L.A. (eds.) ICAISC 2004. LNCS, vol. 3070, pp. 381–387. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  14. Starczewski, J.T.: Efficient triangular type-2 fuzzy logic systems. International Journal of Approximate Reasoning (accepted for publication)

    Google Scholar 

  15. Starczewski, J.T.: Extended triangular norms. Information Sciences 179, 742–757 (2009)

    Article  MathSciNet  MATH  Google Scholar 

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Starczewski, J.T. (2009). A Type-1 Approximation of Interval Type-2 FLS. 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_36

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  • DOI: https://doi.org/10.1007/978-3-642-02282-1_36

  • 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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