Skip to main content
SpringerLink
Log in

Quadratic Form Optimization with Fuzzy Number Parameters: Multiobjective Approaches

  • Published:
International Journal of Fuzzy Systems Aims and scope Submit manuscript

Abstract

Problems in daily life can be modeled into mathematical forms, one of them is the optimization of the quadratic form where the objective functions are the quadratic function. There are many real problems involving variables that cannot be stated numerically so that fuzzy logic appears. The purpose of this research is to optimize the quadratic form with all its parameters in the form of a fuzzy number by using the method of a triangular fuzzy number. This research resulted in a new completion method by utilizing definitions and arithmetic on the triangular fuzzy numbers. The resulted method is by changing a single fuzzy quadratic program becomes a simple quadratic multiobjective program. By using Sum of Objective Method, the multiobjective problem can be changed into single optimization problem. This single optimization problem is then completed using Karush–Kuhn–Tucker method, resulting in three optimal values which will form optimal values in the form of triangular fuzzy numbers.

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

Similar content being viewed by others

References

  1. Peressini, A.L., Sullivan, F.E., Uhl, J.J.: The Mathematics of Nonlinear Programming. Springer, New York (1988)

    Book  Google Scholar 

  2. Silva, R.C., Cruz, C., Yamakami, A.: A parametric method to solve quadratic programming probles with fuzzy costs. IFSA-EUSFLAT. 1398–1403, (2009)

  3. Javanmard, M., Nehi, H.M.: A solving method for fuzzy linear programming problem with interval type-2 fuzzy number. Int J Fuzzy Syst (2019). https://doi.org/10.1007/s40815-018-0591-3

    Article  MathSciNet  MATH  Google Scholar 

  4. Ghaznavi, M., Soleimani, F., Hoseinpoor, N.: Parametric analysis in fuzzy number linear programming problems. Int J Fuzzy Syst (2016). https://doi.org/10.1007/s40815-015-0123-3

    Article  MathSciNet  MATH  Google Scholar 

  5. Ammar, E., Khalifa, H.A.: Fuzzy portfolio optimization a quadratic programming approach. Chaos Solitons Fractals (2003). https://doi.org/10.1016/S0960-0779(03)00071-7

    Article  MathSciNet  MATH  Google Scholar 

  6. Liu, S,-T.: Solving quadratic programming with fuzzy parameters based on extension principle (2007)

  7. Liu, S.-T.: A revisit to quadratic programming with fuzzy parameters. Chaos Solitons Fractal (2009). https://doi.org/10.1016/j.chaos.2008.04.061

    Article  MathSciNet  MATH  Google Scholar 

  8. Allahviranloo, T., Moazam, L.G.: The solution of fully quadratic equation based on optimization theory. Scientific World J (2014). https://doi.org/10.1155/2014/156203

    Article  Google Scholar 

  9. Mirmohseni, S.M., Nasseri, S.H.: a quadratic programming with triangular fuzzy number. J Appl Math Phys (2017). https://doi.org/10.4236/jamp.2017.511181

    Article  Google Scholar 

  10. Dhanasekar, S., Hariharan, S., Sekar, P.: Fuzzy Hungarian MODI to solve fully fuzzy transportation problems. Int J Fuzzy Syst (2016). https://doi.org/10.1007/s40815-016-0251-4

    Article  Google Scholar 

  11. Dourado, A.D.P., Lobato, F.S., Cavalini Jr., A.A., Steffen Jr., V.: Fuzzy reliability-based optimization for engineering system design. Int J Fuzzy Syst (2019). https://doi.org/10.1007/s40815-019-00655-5

    Article  Google Scholar 

  12. Ghanbari, R., Moghadam, K.G.: Solving fuzzy quadratic programming problems based on ABS algorithm. Soft Comput (2019). https://doi.org/10.1007/s00500-019-04013-3

    Article  Google Scholar 

  13. Nezhad, N.A.T.: A solution approach for solving fully fuzzy quadratic programming problems. J Appl Res Ind Eng (2018). https://doi.org/10.22105/jarie.2018.111797.1028

    Article  Google Scholar 

  14. Yang, Y., Zhao, J., Xia, J., Zhuang, G., Zhang, W.: Multiobjective optimization control for uncertain nonlinear stochastic system with state-delay. Int J Fuzzy Syst (2018). https://doi.org/10.1007/s40815-018-0541-0

    Article  Google Scholar 

  15. Pourjavad, E., Mayorga, R.V.: Multi-objective fuzzy programming of closed-loop supply chain considering sustained measures. Int J Fuzzy Syst (2018). https://doi.org/10.1007/s40815-018-0551-y

    Article  Google Scholar 

  16. Rout, P.K., Nanda, S., Acharya, S.: Multi-objective fuzzy probabilistic quadratic programming problem. Int J Oper Res 34, 387–408 (2019)

    Article  MathSciNet  Google Scholar 

  17. Gani, A.N., Saleem, R.A.: Solving fuzzy sequential quadratic programming algorithm for fuzzy non-linear programming. J Phys Sci 23, 89–96 (2018)

    MathSciNet  Google Scholar 

  18. Pandian, P.: A simple approach for finding a fair solution to multiobjective programming problems. Bull Math Sci Appl (2012). https://doi.org/10.18052/www.scipress.com/BMSA.2.21

    Article  Google Scholar 

  19. Mirzei, N., Mahmoodirad, A., Niroomand, S.: An uncertain multi-objective assembly line balancing problem: a credibility-based fuzzy modeling approach. Int J Fuzzy Syst (2019). https://doi.org/10.1007/s40815-019-00734-7

    Article  MathSciNet  Google Scholar 

  20. Kecskes, I., Ordy, P.: Multi-scenario multi-objective optimization of a fuzzy motor controller for the Szabad(ka)-II hexapod robot. Acta Polytech Hung 15, 157–178 (2018)

    Google Scholar 

  21. Chong, E.K.P., Zak, S.H.: An Introduction to Optimization, 2nd edn. Wiley-Interscience Publication, Hoboken (2001)

    MATH  Google Scholar 

  22. Jaimes, A.L., Martinez, S.Z., Coello, C.A.: An Introduction to Multiobjective Optimization Techniques. McGraw-Hill Companies Inc., New York (2009)

    Google Scholar 

  23. Hanss, M.: Applied Fuzzy Arithmatic. Springer, New York (2005)

    MATH  Google Scholar 

Download references

Acknowledgements

We are grateful for support from Department of Mathematics, Faculty of Science and Applied Technology, Ahmad Dahlan University.

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science and Applied Technology, Ahmad Dahlan University, Yogyakarta, Indonesia

    Niswatus S. Al-Mumtazah & Sugiyarto Surono

Authors
  1. Niswatus S. Al-Mumtazah
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sugiyarto Surono
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sugiyarto Surono.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Al-Mumtazah, N.S., Surono, S. Quadratic Form Optimization with Fuzzy Number Parameters: Multiobjective Approaches. Int. J. Fuzzy Syst. 22, 1191–1197 (2020). https://doi.org/10.1007/s40815-020-00808-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-020-00808-x

Keywords

Search

Navigation