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Simulation of fuzzy dynamical systems using the LU-representation of fuzzy numbers

Author

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  • Stefanini, Luciano
  • Sorini, Laerte
  • Guerra, Maria Letizia

Abstract

We suggest the use of the parametric LU-representation of the fuzzy numbers, introduced in Guerra and Stefanini [Guerra ML, Stefanini L. Approximate fuzzy arithmetic operations using monotonic interpolations. Fuzzy Sets Syst 2005;150:5–33] and improved in Stefanini et al. [Stefanini L, Sorini L, Guerra ML. Parametric representations of fuzzy numbers and applications. Working Paper Series EMS, 95, University of Urbino, 2004], in the simulation of fuzzy dynamical systems or fuzzy iterated maps. We show the computational advantages of the LU-representation in extending some well known standard maps to the fuzzy context, allowing the simulation by the Zadeh’s extension principle in the general case of fuzzy parameters.

Suggested Citation

  • Stefanini, Luciano & Sorini, Laerte & Guerra, Maria Letizia, 2006. "Simulation of fuzzy dynamical systems using the LU-representation of fuzzy numbers," Chaos, Solitons & Fractals, Elsevier, vol. 29(3), pages 638-652.
    • Handle: RePEc:eee:chsofr:v:29:y:2006:i:3:p:638-652
    DOI: 10.1016/j.chaos.2005.08.096
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    Citations

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    Cited by:

    1. Eslami Giski, Zahra & Ebrahimzadeh, Abolfazl & Markechová, Dagmar, 2019. "Rényi entropy of fuzzy dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 244-253.
    2. Dehghan, Mehdi & Hashemi, Behnam & Ghatee, Mehdi, 2007. "Solution of the fully fuzzy linear systems using iterative techniques," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 316-336.
    3. Luciano Stefanini & Laerte Sorini, 2007. "Representing fuzzy numbers for fuzzy calculus," Working Papers 0702, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2007.
    4. Luciano Stefanini & Laerte Sorini, 2007. "An LU-fuzzy calculator for the basic fuzzy calculus," Working Papers 0701, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2007.
    5. S. K. Gupta & Debasis Dangar, 2010. "Duality in fuzzy quadratic programming with exponential membership functions," Fuzzy Information and Engineering, Springer, vol. 2(4), pages 337-346, December.
    6. Jiří Kupka & Nicole Škorupová, 2021. "On PSO-Based Simulations of Fuzzy Dynamical Systems Induced by One-Dimensional Ones," Mathematics, MDPI, vol. 9(21), pages 1-26, October.
    7. Luciano Stefanini, 2007. "Generalized LU-fuzzy derivative and numerical solution of Fuzzy Differential Equations," Working Papers 0706, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2007.
    8. Liu, Shiang-Tai, 2009. "A revisit to quadratic programming with fuzzy parameters," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1401-1407.
    9. Liu, Shiang-Tai, 2009. "Quadratic programming with fuzzy parameters: A membership function approach," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 237-245.
    10. Sun, Yeong-Jeu, 2009. "Robust stability of uncertain T–S fuzzy time-varying systems," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1588-1594.

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