Skip to main content

Solution of Dual Fuzzy Equations Using a New Iterative Method

  • Conference paper
  • First Online:
Intelligent Information and Database Systems (ACIIDS 2018)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10752))

Included in the following conference series:

Abstract

In this paper, a new hybrid scheme based on learning algorithm of fuzzy neural network (FNN) is offered in order to extract the approximate solution of fully fuzzy dual polynomials (FFDPs). Our FNN in this paper is a five-layer feed-back FNN with the identity activation function. The input-output relation of each unit is defined by the extension principle of Zadeh. The output from this neural network, which is also a fuzzy number, is numerically compared with the target output. The comparison of the feed-back FNN method with the feed-forward FNN method shows that the less error is observed in the feed-back FNN method. An example based on applications are given to illustrate the concepts, which are discussed in this paper.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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. Jin, L., Gupta, M.M.: Stable dynamic backpropagation learning in recurrent neural networks. IEEE Trans. Neural Networks 10(6), 1321–1334 (1999)

    Article  Google Scholar 

  2. Jafari, R., Yu, W., Li, X.: Numerical solution of fuzzy equations with Z-numbers using neural networks. Intell. Autom. Soft Comput. 1–7 (2017)

    Google Scholar 

  3. Jafari, R., Yu, W., Li, X., Razvarz, S.: Numerical solution of fuzzy differential equations with Z-numbers using bernstein neural networks. Int. J. Comput. Intell. Syst. 10(1), 1226–1237 (2017)

    Article  Google Scholar 

  4. Jafari, R., Yu, W.: Fuzzy differential equation for nonlinear system modeling with Bernstein neural networks. IEEE Access (2017). https://doi.org/10.1109/access.2017.2647920

  5. Jafari, R., Yu, W.: Uncertainty nonlinear systems modeling with fuzzy equations. Math. Probl. Eng. (2017). https://doi.org/10.1155/2017/8594738

  6. Jafarian, A., Jafari, R., Mohamed Al Qurashi, M., Baleanud, D.: A novel computational approach to approximate fuzzy interpolation polynomials. Springer Plus 5, 14–28 (2016)

    Article  Google Scholar 

  7. Ishibuchi, H., Kwon, K., Tanaka, H.: A learning of fuzzy neural networks with triangular fuzzy weights. Fuzzy Sets Syst. 71(3), 277–293 (1995)

    Article  Google Scholar 

  8. Abbasbandy, S., Otadi, M.: Numerical solution of fuzzy polynomials by fuzzy neural network. Appl. Math. Comput. 181(2), 1084–1089 (2006)

    MathSciNet  MATH  Google Scholar 

  9. Jafarian, A., Measoomynia, S.: Solving fuzzy polynomials using neural nets with a new learning algorithm. Aust. J. Basic Appl. Sci. 5(9), 2295–2301 (2011)

    Google Scholar 

  10. Friedman, M., Ming, M., Kandel, A.: Fuzzy linear systems. Fuzzy Sets Syst. 96(1), 201–209 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  11. Friedman, M., Ma, M., Kandel, A.: Duality in fuzzy linear systems. Fuzzy Sets Syst. 109(1), 55–58 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  12. Otadi, M.: Fully fuzzy polynomial regression with fuzzy neural networks. Neurocomputing 142, 486–493 (2014)

    Article  Google Scholar 

  13. Abbasbandy, S., Asady, B.: Newton’s method for solving fuzzy nonlinear equations. Appl. Math. Comput. 159(2), 356–379 (2004)

    MathSciNet  MATH  Google Scholar 

  14. Dehghan, M., Hashemi, B.: Iterative solution of fuzzy linear systems. Appl. Math. Comput. 175(1), 645–674 (2006)

    MathSciNet  MATH  Google Scholar 

  15. Rouhparvar, H.: Solving fuzzy polynomial equation by ranking method. In: First Joint Congress on Fuzzy and Intelligent Systems. Ferdowsi University of Mashhad, Iran (2007)

    Google Scholar 

  16. Rahman, N.A., Abdullah, L.: An interval type-2 dual fuzzy polynomial equations and ranking method of fuzzy numbers. Int. J. Math. Comput. Phys. Electr. Comput. Eng. 8(1), 92–99 (2014)

    Google Scholar 

  17. Muzzioli, S., Reynaerts, H.: The solution of fuzzy linear systems by non-linear programming: a financial application. Eur. J. Oper. Res. 177(2), 1218–1231 (2007)

    Article  MATH  Google Scholar 

  18. Amirfakhrian, M.: Numerical solution of algebraic fuzzy equations with crisp variable by Gauss-Newton method. Appl. Math. Model. 32(9), 1859–1868 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  19. Kumar, A., Bansal, A., Babbar, N.: Solution of fully fuzzy linear system with arbitrary coefficients. Int. J. Appl. Math. Comput. 3(3), 232–237 (2011)

    Google Scholar 

  20. Ezzati, R.: Solving fuzzy linear systems. Soft. Comput. 15(1), 193–197 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  21. Allahviranloo, T., Mikaeilvand, N.: Non zero solutions of the fully fuzzy linear systems. Appl. Comput. Math. 10(2), 271–282 (2011)

    MathSciNet  MATH  Google Scholar 

  22. Waziri, M.Y., Majid, Z.A.: A new approach for solving dual fuzzy nonlinear equations using Broyden’s and Newton’s methods. Adv. Fuzzy Syst. 2012(1), 1–5 (2012)

    MathSciNet  MATH  Google Scholar 

  23. Otadi, M., Mosleh, M.: Solution of fuzzy polynomial equations by modified Adomian decomposition method. Soft. Comput. 15(1), 187–192 (2011)

    Article  MATH  Google Scholar 

  24. Allahviranloo, T., Gerami Moazam, L.: The solution of fully fuzzy quadratic equation based on optimization theory. Sci. World J. 2014(1), 1–6 (2014)

    Article  Google Scholar 

  25. Babbar, N., Kumar, A., Bansal, A.: Solving fully fuzzy linear system with arbitrary triangular fuzzy numbers (m, α, β). Soft Comput. 17(4), 691–702 (2013)

    Article  MATH  Google Scholar 

  26. Oh, S.K., Pedrycz, W., Roh, S.B.: Genetically optimized fuzzy polynomial neural networks with fuzzy set-based polynomial neurons. Inf. Sci. 176(23), 3490–3519 (2006)

    Article  MATH  Google Scholar 

  27. Wang, C.C., Tsai, C.F.: Fuzzy processing using polynomial bidirectional hetero-associative network. Inf. Sci. 125(1–4), 167–179 (2000)

    Article  MATH  Google Scholar 

  28. Zadeh, L.A.: Toward a generalized theory of uncertainty (GTU) an outline. Inf. Sci. 172(1–2), 1–40 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  29. Beer, F.P., Johnston, E.R.: Mechanics of Materials, 2nd edn. Mcgraw-Hill, New York (1992)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Raheleh Jafari .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Razvarz, S., Jafari, R., Granmo, OC., Gegov, A. (2018). Solution of Dual Fuzzy Equations Using a New Iterative Method. In: Nguyen, N., Hoang, D., Hong, TP., Pham, H., Trawiński, B. (eds) Intelligent Information and Database Systems. ACIIDS 2018. Lecture Notes in Computer Science(), vol 10752. Springer, Cham. https://doi.org/10.1007/978-3-319-75420-8_23

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-75420-8_23

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-75419-2

  • Online ISBN: 978-3-319-75420-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics