Skip to main content
SpringerLink
Log in

Some new solution concepts in generalized fuzzy multiobjective optimization problems

  • Foundations
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

Some new solution concepts to a general fuzzy multiobjective nonlinear programming problem are introduced in this research, and four scalarization techniques are proposed to obtain them. Then, the relation between the set of defined optimal solutions and the set of optimal solutions of the scalarized problems are studied. Moreover, a general scalarized problem is given and shown that these four techniques can be drawn from this problem. Adequate number of numerical examples have been solved to illustrate the techniques.

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

Fig. 1

Similar content being viewed by others

References

  • Abo-Sinna MA, Abo-Elnaga YY, Mousa AA (2014) An interactive dynamic approach based on hybrid swarm optimization for solving multiobjective programming problem with fuzzy parameters. Appl Math Model 38:2000–2014

    Article  MathSciNet  Google Scholar 

  • Charnes A, Cooper WW (1961) Management models and industrial applications of linear programming. Wiley, New York

    MATH  Google Scholar 

  • Cheng H, Huanga W, Zhoub Q, Caic J (2013) Solving fuzzy multi-objective linear programming problems using deviation degree measures and weighted max–min method. Appl Math Model 37:6855–6869

    Article  MathSciNet  Google Scholar 

  • Ehrgott M (2005) Multicriteria optimization. Springer, Berlin

    MATH  Google Scholar 

  • Kuhn HW, Tucker AW (1951) Nonlinear programming. In: Proceedings of the second Berkeley symposium on mathematical statistics and probability, Berkeley, pp 481–492

  • Kotinis M (2014) Improving a multi-objective differential evolution optimizer using fuzzy adaptation and K-medoids clustering. Soft Comput 18:757–771

    Article  Google Scholar 

  • Luhandjula MK, Rangoaga MJ (2014) An approach for solving a fuzzy multiobjective programming problem. Eur J Oper Res 232:249–255

  • Mansoori A, Effati S, Eshaghnezhad M (2016) An efficient recurrent neural network model for solving fuzzy non-linear programming problems. Appl Intell. doi:10.1007/s10489-016-0837-4

    Google Scholar 

  • Mansoori A, Effati S, Eshaghnezhad M (2016) A neural network to solve quadratic programming problems with fuzzy parameters. Fuzzy Optim Decis Mak. doi:10.1007/s10700-016-9261-9

  • Mishra B, Nishad AK, Singh SR (2014) Fuzzy multi-fractional programming for land use planning in agricultural production system. Fuzzy Inf Eng 6:245–262

    Article  MathSciNet  Google Scholar 

  • Neumann V, Morgenstern O (1944) Theory of games and economic behavior, 1st edn. Princeton University Press, Princeton

    MATH  Google Scholar 

  • Pandian P (2013) Multi-objective programming approach for fuzzy linear programming problems. Appl Math Sci 7:1811–1817

    MathSciNet  Google Scholar 

  • Pareto V (1896) Manual di’economie politique. F. Rouge, Lausanne (in French)

    Google Scholar 

  • Sakawa M, Nishizaki I, Katagiri H (1993) Fuzzy stochastic multiobjective programming. Springer, New York

    MATH  Google Scholar 

  • Thapar A, Pandey D, Gaur SK (2012) Satisficing solutions of multi-objective fuzzy optimization problems using genetic algorithm. Appl Soft Comput 12:2178–2187

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Mathematical Sciences and Statistics, University of Birjand, Birjand, Iran

    Fatemeh Fayyaz Rouhbakhsh & Hassan Hassanpour

  2. Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran

    Sohrab Effati

  3. Center of Excellence of Soft Computing and Intelligent Information Processing (SCIIP), Ferdowsi University of Mashhad, Mashhad, Iran

    Sohrab Effati

Authors
  1. Fatemeh Fayyaz Rouhbakhsh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hassan Hassanpour
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sohrab Effati
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fatemeh Fayyaz Rouhbakhsh.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Additional information

Communicated by A. Di Nola.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (lg4 4 KB)

Supplementary material 2 (lg4 5 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fayyaz Rouhbakhsh, F., Hassanpour, H. & Effati, S. Some new solution concepts in generalized fuzzy multiobjective optimization problems. Soft Comput 22, 3261–3270 (2018). https://doi.org/10.1007/s00500-017-2787-0

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-017-2787-0

Keywords

Search

Navigation