IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v42y2009i3p1677-1683.html
   My bibliography  Save this article

Fuzzy differential invariant (FDI)

Author

Listed:
  • Nadjafikhah, M.
  • Bakhshandeh-Chamazkoti, R.

Abstract

In this paper, we have tried to apply the concepts of fuzzy set to Lie groups and fuzzy differential invariant (FDI) in order to provide suitable conditions for applying Lie symmetry method in solving fuzzy differential equations (FDEs). For this, we define a C1-fuzzy submanifold and fuzzy immersion with some examples. In main section, we defined the fuzzy Lie group and some its relative concepts such as fuzzy transformation group and fuzzy G-invariant. The goal of this paper is to introduce and study new defining for fuzzy Lie group and fuzzy differential invariant (FDI). Also, some illustrative examples are given.

Suggested Citation

  • Nadjafikhah, M. & Bakhshandeh-Chamazkoti, R., 2009. "Fuzzy differential invariant (FDI)," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1677-1683.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:3:p:1677-1683
    DOI: 10.1016/j.chaos.2009.03.070
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007790900188X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2009.03.070?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Khastan, A. & Ivaz, K., 2009. "Numerical solution of fuzzy differential equations by Nyström method," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 859-868.
    2. Nieto, Juan J. & Rodríguez-López, Rosana, 2006. "Bounded solutions for fuzzy differential and integral equations," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1376-1386.
    3. Chalco-Cano, Y. & Román-Flores, H., 2008. "On new solutions of fuzzy differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 112-119.
    4. M. Oberguggenberger & S. Pittschmann, 1999. "Differential Equations With Fuzzy Parameters," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 5(3), pages 181-202, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chalco-Cano, Y. & Román-Flores, H., 2008. "On new solutions of fuzzy differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 112-119.
    2. Animesh Mahata & Sankar Prasad Mondal & Ali Ahmadian & Fudiah Ismail & Shariful Alam & Soheil Salahshour, 2018. "Different Solution Strategies for Solving Epidemic Model in Imprecise Environment," Complexity, Hindawi, vol. 2018, pages 1-18, May.
    3. A. Rufián-Lizana & Y. Chalco-Cano & G. Ruiz-Garzón & H. Román-Flores, 2014. "On some characterizations of preinvex fuzzy mappings," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 771-783, July.
    4. Ho Vu, 2017. "Random Fuzzy Differential Equations with Impulses," Complexity, Hindawi, vol. 2017, pages 1-11, June.
    5. Mawia Osman & Yonghui Xia & Omer Abdalrhman Omer & Ahmed Hamoud, 2022. "On the Fuzzy Solution of Linear-Nonlinear Partial Differential Equations," Mathematics, MDPI, vol. 10(13), pages 1-49, June.
    6. U. M. Pirzada & V. D. Pathak, 2013. "Newton Method for Solving the Multi-Variable Fuzzy Optimization Problem," Journal of Optimization Theory and Applications, Springer, vol. 156(3), pages 867-881, March.
    7. Sankar Prasad Mondal & Tapan Kumar Roy, 2017. "Solution of second order linear fuzzy ordinary differential equation by Lagrange multiplier method with application in mechanics," OPSEARCH, Springer;Operational Research Society of India, vol. 54(4), pages 766-798, December.
    8. Jin, Ting & Sun, Yun & Zhu, Yuanguo, 2020. "Time integral about solution of an uncertain fractional order differential equation and application to zero-coupon bond model," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    9. Thanh-Lam Nguyen, 2017. "Methods in Ranking Fuzzy Numbers: A Unified Index and Comparative Reviews," Complexity, Hindawi, vol. 2017, pages 1-13, July.
    10. Eman Hussain & Ayad Ali, 2013. "Homotopy Analysis Method for Solving Fuzzy Integro-Differential Equations," Modern Applied Science, Canadian Center of Science and Education, vol. 7(3), pages 1-15, March.
    11. Nguyen Dinh Phu, 2016. "On Nonlocal Initial Problems for Fuzzy Differential Equations and Environmental Pollution Problems," Academic Journal of Applied Mathematical Sciences, Academic Research Publishing Group, vol. 2(8), pages 77-92, 08-2016.
    12. Yilmaz, Yilmaz, 2009. "Fréchet differentiation of nonlinear operators between fuzzy normed spaces," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 473-484.
    13. Zhang, Chuanlin & Ye, Guoju & Liu, Wei & Liu, Xuelong, 2024. "Upwind difference scheme for fuzzy convection–diffusion equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 351-367.
    14. Alijani, Zahra & Baleanu, Dumitru & Shiri, Babak & Wu, Guo-Cheng, 2020. "Spline collocation methods for systems of fuzzy fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    15. Liu, Shiang-Tai, 2009. "A revisit to quadratic programming with fuzzy parameters," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1401-1407.
    16. Harb, Ahmad M. & Smadi, Issam A., 2009. "Tracking control of DC motors via mimo nonlinear fuzzy control," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 702-710.
    17. Hoang Viet Long & Haifa Bin Jebreen & Y. Chalco-Cano, 2020. "A New Continuous-Discrete Fuzzy Model and Its Application in Finance," Mathematics, MDPI, vol. 8(10), pages 1-15, October.
    18. Luciano Stefanini & Barnabas Bede, 2008. "Generalized Hukuhara Differentiability of Interval-valued Functions and Interval Differential Equations," Working Papers 0803, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2008.
    19. Ahmadian, A. & Salahshour, S. & Ali-Akbari, M. & Ismail, F. & Baleanu, D., 2017. "A novel approach to approximate fractional derivative with uncertain conditions," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 68-76.
    20. Rao, T.D. & Chakraverty, S., 2021. "Forward and inverse techniques for fuzzy fractional systems applied to radon transport in soil chambers," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:42:y:2009:i:3:p:1677-1683. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.