Skip to main content
SpringerLink
Log in

Solution of Fuzzy Differential Equation of Order 2 by Intuitionistic Fuzzy Numbers (IFS)

  • Conference paper
  • First Online:
Intelligent Computing, Information and Control Systems (ICICCS 2019)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1039))

Abstract

Any real life problems can be modelled by differential equation. In this paper second order fuzzy differential equation is converted to fuzzy differential equations and solved by fuzzy sumudu transforms method with initial values as intuitionistic triangular fuzzy numbers. To understand the proposed method we solved a numerical problem with graphical representations.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Atanassov, K.T.: Intuitionistic fuzzy sets. VII ITKR’s session, Sofia (deposited in Central Science and Technical Library of the Bulgarian Academy of Sciences 1697/84) (1983)

    Google Scholar 

  2. Dubois, D., Parade, H.: Operation on fuzzy number. Int. J. Fuzzy Syst. 9, 613–626 (1978)

    MathSciNet  Google Scholar 

  3. Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20, 87–96 (1986)

    Article  Google Scholar 

  4. Zadeh, L.A.: Toward a generalized theory of uncertainty (GTU) an outline. Inf. Sci. 172, 140 (2005)

    Article  MathSciNet  Google Scholar 

  5. Dubois, D., Prade, H.: Towards fuzzy differential calculus: part 3. Differ. Fuzzy Sets Syst. 8, 225–233 (1982)

    Article  Google Scholar 

  6. Kaleva, O.: Fuzzy differential equations. Fuzzy Sets Syst. 24, 301–317 (1987)

    Article  MathSciNet  Google Scholar 

  7. Chalco-Cano, Y., Romn-Flores, H.: On the new solution of fuzzy differential equations. Chaos, Solitons Fractals 38, 112–119 (2008)

    Article  MathSciNet  Google Scholar 

  8. Gasilov, N., Amrahov, S.E., Fatullayev, A.G.: Solution of linear differential equations with fuzzy boundary values. Fuzzy Sets Syst. 257, 169–183 (2014)

    Article  MathSciNet  Google Scholar 

  9. Lata, S., Kumar, A.: A new method to solve time-dependent intuitionistic fuzzy differential equation and its application to analyze the intutionistic fuzzy reliability of industrial system. Concurrent Eng.: Res. Appl. 20, 1–8 (2012)

    Article  Google Scholar 

  10. Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20(1), 87–96 (1986)

    Article  Google Scholar 

  11. Atanassov, K.T.: Operators over interval valued intuitionistic fuzzy sets. Fuzzy Sets Syst. 64(2), 159–174 (1994)

    Article  MathSciNet  Google Scholar 

  12. De, S.K., Biswas, R., Roy, A.R.: An application of intuitionistic fuzzy sets in medical diagnosis. Fuzzy Sets Syst. 117(2), 209–213 (2001)

    Article  Google Scholar 

  13. Kharal, A.: Homeopathic drug selection using intuitionistic fuzzy sets. Homeopathy 98(1), 35–39 (2009)

    Article  Google Scholar 

  14. Mondal, S.P., Roy, T.K.: First order linear non homogeneous ordinary differential equation in fuzzy environment. Math. Theory Model 3(1), 85–95 (2013)

    Google Scholar 

  15. Mondal, S.P., Banerjee, S., Roy, T.K.: First order linear homogeneous ordinary differential equation in fuzzy environment. Int. J. Pure Appl. Sci. Technol. 14(1), 16–26 (2013)

    Google Scholar 

  16. Nirmala, V., Pandian, S.C.: Numerical approach for solving intuitionistic fuzzy differential equation under generalised differentiability concept. Appl. Math. Sci. 9(67), 3337–3346 (2015)

    Google Scholar 

  17. Ettoussi, R., Melliani, S., Elomari, M., Chadli, L.S.: Solution of intuitionistic fuzzy differential equations by successive approximations method. Notes on Intuitionistic Fuzzy Sets 21(2), 51–62 (2015)

    MATH  Google Scholar 

  18. Melliani, S., Elomari, M., Atraoui, M., Chadli, L.S.: Intuitionistic fuzzy differential equation with nonlocal condition. Notes on Intuitionistic Fuzzy Sets 21(4), 58–68 (2015)

    MATH  Google Scholar 

  19. Mondal, S.P., Roy, T.K.: System of differential equation with initial value as triangular intuitionistic fuzzy number and its application. Int. J. Appl. Comput. Math. 1, 449–474 (2015)

    Article  MathSciNet  Google Scholar 

  20. Stefanini, L., Bede, B.: Generalized Hukuhara differentiability of interval-valued functions and interval differential equations. Nonlinear Anal. 71, 1311–1328 (2009)

    Article  MathSciNet  Google Scholar 

  21. Rajkumar, A., Jesuraj, C.: Mathematical model for dengue virus infected populations with fuzzy differential equations. In: ICAICR 2018, CCIS 955, pp. 206–217. Springer, Singapore (2019)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Hindustan Institute of Technology and Science, Chennai, India

    A. Rajkumar

  2. Hindustan Institute of Technology and Science, Chennai, India

    C. Jesuraj

  3. Department of Mathematics, IFET College of Engineering, Villupuram, India

    C. Jesuraj

Authors
  1. A. Rajkumar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. Jesuraj
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to C. Jesuraj .

Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Vaigai College of Engineering, Madurai, Tamil Nadu, India

    A. Pasumpon Pandian

  2. Electrical and Computer Engineering, University of Applied Sciences, Egaleo, Attiki, Greece

    Klimis Ntalianis

  3. Department of Business Administration, The Gerald Schwartz School of Business, Antigonish, NS, Canada

    Ram Palanisamy

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Rajkumar, A., Jesuraj, C. (2020). Solution of Fuzzy Differential Equation of Order 2 by Intuitionistic Fuzzy Numbers (IFS). In: Pandian, A., Ntalianis, K., Palanisamy, R. (eds) Intelligent Computing, Information and Control Systems. ICICCS 2019. Advances in Intelligent Systems and Computing, vol 1039. Springer, Cham. https://doi.org/10.1007/978-3-030-30465-2_33

Download citation

Publish with us

Policies and ethics

Search

Navigation