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Solving First Order Linear Fuzzy Differential Equations System

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Soft Computing Applications (SOFA 2016)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 634))

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Abstract

This paper aims at solving first order linear fuzzy differential equations system by an approach called quasi-level-wise system. Some comparative examples show while some other approaches fail to obtain possible system solutions, the proposed approach is able and effective. Moreover, how the linear fuzzy differential equations system may arise in applications is explained and inverted pendulum system is given as an example. Through the example, it is also demonstrated how helpful this fuzzy linear model can be, compared to the crisp linear model.

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References

  1. Antia, H.M.: Numerical Methods for Scientists and Engineers. Springer, Berlin (2002)

    MATH  Google Scholar 

  2. Ahmadian, A., Senu, N., Larki, F., Salahshour, S., Suleiman, M., Islam, M.S.: A legendre approximation for solving a fuzzy fractional drug transduction model into the bloodstream. Adv. Intell. Syst. Comput. 287, 25–34 (2014)

    MATH  Google Scholar 

  3. Bede, B.: Mathematics of Fuzzy Sets and Fuzzy Logic. Studies in Fuzziness and Soft Computing, vol. 295. Springer, Heidelberg (2013)

    MATH  Google Scholar 

  4. Chalco-Cano, Y., Román-Flores, H.: Some remarks on fuzzy differential equations via differential inclusions. Fuzzy Sets Syst. 230, 3–20 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  5. Desoer, C., Haneda, H.: The measure of a matrix as a tool to analyze computer algorithms for circuit analysis. IEEE Trans. Circuit Theory 19, 5 (1972)

    MathSciNet  Google Scholar 

  6. Fard, O.S., Ghal-Eh, N.: Numerical solutions for linear system of first-order fuzzy differential equations with fuzzy constant coefficients. Inf. Sci. 181, 4765–4779 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  7. Gopal, M.: Modern Control System Theory. New Age International, New Delhi (1993). Automatic control

    Google Scholar 

  8. Mazandarani, M., Najariyan, M.: Differentiability of type-2 fuzzy number-valued functions. Commun. Nonlinear Sci. Numer. Simul. 19, 710–725 (2014)

    Article  MathSciNet  Google Scholar 

  9. Mazandarani, M., Najariyan, M.: A note on “A class of linear differential dynamical systems with fuzzy initial condition”. Fuzzy Sets Syst. 265, 121–126 (2014). doi:10.1016/j.fss.2014.05.018

    Article  MathSciNet  MATH  Google Scholar 

  10. Mazandarani, M., Najariyan, M.: Type-2 fuzzy fractional derivatives. Commun. Nonlinear Sci. Numer. Simul. 19, 2354–2372 (2014)

    Article  MathSciNet  Google Scholar 

  11. Mizukoshi, M.T., Barros, L.C., Chalco-Cano, Y., Román-Flores, H., Bassanezi, R.C.: Fuzzy differential equations and the extension principle. Inf. Sci. 177(17), 3627–3635 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  12. Najariyan, M., Farahi, M.H.: Optimal control of fuzzy controlled system with fuzzy initial conditions. Iran. J. Fuzzy Syst. 10, 21–35 (2013)

    MathSciNet  MATH  Google Scholar 

  13. Najariyana, M., Farahi, M.H.: A new approach for the optimal fuzzy linear time invariant controlled system with fuzzy coefficients. J. Comput. Appl. Math. 259, 682–694 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  14. Williams, R.L., Lawrence, D.A.: Linear State-Space Control Systems. Wiley, Hoboken (2007)

    Book  Google Scholar 

  15. Xu, J., Liao, Z., Hu, Z.: A class of linear differential dynamical systems with fuzzy initial condition. Fuzzy Sets Syst. 158, 2339–2358 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  16. Xu, J., Liao, Z., Nieto, J.J.: A class of linear differential dynamical systems with fuzzy matrices. J. Math. Anal. Appl. 368, 54–68 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  17. Zimmermann, H.J.: Fuzzy Set Theory and its Applications. Springer, Boston (2001)

    Book  Google Scholar 

  18. Zahreddine, Z.: Matrix measure and application to stability of matrices and interval dynamical systems. Int. J. Math. Math. Sci. 2003, 75–85 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  19. Mazandarani, M., Kamyad, A.V.: Modified fractional euler method for solving fuzzy fractional initial value problem. Commun. Nonlinear Sci. Numer. Simul. 18(1), 12–21 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  20. Najariyan, M., Farahi, M.H.: A new approach for solving a class of fuzzy optimal control systems under generalized Hukuhara differentiability. J. Franklin Inst. 352, 1836–1849 (2015)

    Article  MathSciNet  Google Scholar 

  21. Van Hoa, N.: Fuzzy fractional functional differential equations under Caputo gH-differentiability. Commun. Nonlinear Sci. Numer. Simul. 22(1–3), 1134–1157 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  22. Najariyan, M., Mazandarani, M., John, R.: Type-2 fuzzy linear systems. Granul. Comput. 2(3), 175–186 (2017). doi:10.1007/s41066-016-0037-y

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran

    Marzieh Najariyan

  2. Department of Electrical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

    Mehran Mazandarani

  3. Department of Automatics and Applied Software, Faculty of Engineering, University Aurel Vlaicu, Arad, Romania

    Valentina Emilia Balas

Authors
  1. Marzieh Najariyan
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  2. Mehran Mazandarani
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  3. Valentina Emilia Balas
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Corresponding author

Correspondence to Mehran Mazandarani .

Editor information

Editors and Affiliations

  1. Department of Automatics and Applied Informatics, Faculty of Engineering, Aurel Vlaicu University of Arad, Arad, Romania

    Valentina Emilia Balas

  2. University of Canberra, Canberra, South Australia, Australia

    Lakhmi C. Jain

  3. Universitatea Aurel Vlaicu Din Arad, Arad, Romania

    Marius Mircea Balas

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Najariyan, M., Mazandarani, M., Balas, V.E. (2018). Solving First Order Linear Fuzzy Differential Equations System. In: Balas, V., Jain, L., Balas, M. (eds) Soft Computing Applications. SOFA 2016. Advances in Intelligent Systems and Computing, vol 634. Springer, Cham. https://doi.org/10.1007/978-3-319-62524-9_26

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  • DOI: https://doi.org/10.1007/978-3-319-62524-9_26

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-62523-2

  • Online ISBN: 978-3-319-62524-9

  • eBook Packages: EngineeringEngineering (R0)

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