Skip to main content
SpringerLink
Log in

Solution and stability analysis of non-homogeneous difference equation followed by real life application in fuzzy environment

  • Published:
Sādhanā Aims and scope Submit manuscript

Abstract

The study fuzzy difference equation becomes very important as huge numbers of real-life problems in the field of engineering; ecology social science, etc. can be mathematically represented in the form of difference equation where impreciseness is inherently involved. In this paper, we have focused on the solution techniques of non-homogeneous fuzzy linear difference equation with different cases involving fuzzy initial conditions, fuzzy forcing function and fuzzy coefficient. The idea of fuzzy equilibrium point is introduced and its stability analysis has been performed. The whole theoretical work is followed by real-life applications which show the impact of fuzzy concepts in mathematical modelling for better understanding the behaviour of the system in an elegant manner.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12
Figure 13
Figure 14
Figure 15
Figure 16
Figure 17
Figure 18

Similar content being viewed by others

References

  1. Zadeh L A 1965 Fuzzy sets. Inf. Control 8: 338–353

    Article  MathSciNet  MATH  Google Scholar 

  2. Chang S S L and Zadeh L A 1972 On fuzzy mappings and control. IEEE Trans. Syst. Man Cybern. 2: 30–34

    Article  MathSciNet  MATH  Google Scholar 

  3. Lakshmikatham V and Vatsala A S 2002 Basic theory of fuzzy difference equations. J. Differ. Equ. Appl. 8: 957–968

    Article  MathSciNet  MATH  Google Scholar 

  4. Papaschinopoulos G and Papadopoulos B K 2002 On the fuzzy difference equation \( x_{n + 1} = A + B/x_{n} \). Soft Comput. 6: 456–461

    Article  Google Scholar 

  5. Papaschinopoulos G and Papadopoulos B K 2002 On the fuzzy difference equation \( x_{n + 1} = A + {\raise0.7ex\hbox{${x_{n} }$} \!\mathord{\left/ {\vphantom {{x_{n} } {x_{n - m} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${x_{n - m} }$}} \). Fuzzy Sets Syst. 12(9): 73–81

    Article  Google Scholar 

  6. Papaschinopoulos G and Schinas C J 2000 On the fuzzy difference equation \( x_{n + 1} \mathop \sum \nolimits_{k = 0}^{k = 1} {\raise0.7ex\hbox{${Ai}$} \!\mathord{\left/ {\vphantom {{Ai} {x_{n - i}^{pi} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${x_{n - i}^{pi} }$}} + {\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 {x_{n - k}^{pk} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${x_{n - k}^{pk} }$}} \). J. Differ. Equ. Appl. 6(7): 85–89

    Google Scholar 

  7. Stefanidou G, Papaschinopoulos G and Schinas C J 2010 On an exponential-type fuzzy difference equation. Adv. Differ. Equ. 2010: 196920

    Article  MathSciNet  MATH  Google Scholar 

  8. Din Q 2015 Asymptotic behavior of a second-order fuzzy rational difference equations. J. Discrete Math, 2015: 524931

    Article  MathSciNet  MATH  Google Scholar 

  9. Zhang Q H,Yang L H and Liao D X 2012 Behaviour of solutions of to a fuzzy nonlinear difference equation. Iran. J. Fuzzy Syst. 9(2): 1–12

    MATH  Google Scholar 

  10. Memarbashi R and Ghasemabadi A 2013 Fuzzy difference equations of volterra type. Int. J. Nonlinear Anal. Appl. 4: 74–78

    MATH  Google Scholar 

  11. Papaschinopoulos G and Stefanidou G 2003 Boundedness and asymptotic behavior of the Solutions of a fuzzy difference equation. Fuzzy Sets Syst. 140: 523–539

    Article  MathSciNet  MATH  Google Scholar 

  12. Stfanidou G and Papaschinopoulos G 2005 A fuzzy difference equation of a rational form. J. Nonlinear Math. Phys. 12(supplement 2): 300–315

    Article  MathSciNet  MATH  Google Scholar 

  13. Deeba E Y, De Korvin A and Koh E L 1996 A fuzzy difference equation with an application. J. Differ. Equ. Appl. 2: 365–374

    Article  MathSciNet  MATH  Google Scholar 

  14. Deeba E Y and De Korvin A 1999 Analysis by fuzzy difference equations of a model of CO2 level in the blood. Appl. Math. Lett. 12: 33–40

    Article  MATH  Google Scholar 

  15. Umekkan S A, Can E and Bayrak M A 2014 Fuzzy difference equation in finance. IJSIMR 2(8): 729–735

    Google Scholar 

  16. Chrysafis K A, Papadopoulos B K and Papaschinopoulos G 2008 On the fuzzy difference equations of finance. Fuzzy Sets Syst 159: 3259–3270

    Article  MathSciNet  MATH  Google Scholar 

  17. De Barros L C, Bassanezi R C and Lodwick W A 2017 The extension principle of zadeh and fuzzy numbers. In: A First Course in Fuzzy Logic, Fuzzy Dynamical Systems, and Biomathematics Springer, Berlin, pp. 23–41

  18. Román-Flores H, Barros L C and Bassanezi R C 2001A note on Zadeh’s extensions. Fuzzy Sets Syst. 117(3): 327–331

    Article  MathSciNet  MATH  Google Scholar 

  19. Diamond P and Kloeden P 1994 Metric spaces of fuzzy sets, World Scientific, Singapore

    MATH  Google Scholar 

  20. Jensen A 2011 Lecture notes on difference equation, Department of mathematical science, Aalborg University, Denmark, July 18

  21. Khastan A 2016 New solutions for first order linear fuzzy difference equations. J. Comput. Appl. Math. 312: 156–166

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Science, Maulana Abul Kalam Azad University of Technology, West Bengal, Nadia, Haringhata, West Bengal, 741249, India

    Abdul Alamin & Sankar Prasad Mondal

  2. Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, 711103, India

    Shariful Alam

  3. Department of Mathematics, Indian Institute of Technology, Kharagpur, Kharagpur, India

    Adrijit Goswami

Authors
  1. Abdul Alamin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sankar Prasad Mondal
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shariful Alam
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Adrijit Goswami
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sankar Prasad Mondal.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Alamin, A., Mondal, S.P., Alam, S. et al. Solution and stability analysis of non-homogeneous difference equation followed by real life application in fuzzy environment. Sādhanā 45, 185 (2020). https://doi.org/10.1007/s12046-020-01422-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12046-020-01422-1

Keywords

Search

Navigation