Skip to main content
SpringerLink
Log in

Research on multi-objective linear programming problem with fuzzy coefficients in constraints

  • Original Article
  • Published:
International Journal of Machine Learning and Cybernetics Aims and scope Submit manuscript

Abstract

The concepts of Q-effective solution and effective solution are extended to the model of multi-objective linear programming problem with fuzzy coefficients in constraints. Q-effective solution and effective solution are defined as fuzzy sets. The degree of an element as Q-effective solution is uniquely determined, and it fully describes the degree of solution satisfying constraints. Further, the concept of effective solution is introduced. Finally, a numerical example is given to illustrate the difference between Q-effective solution and effective solution.

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. Tian Z, Hu L (2008) The structure of solution space in fuzzy linear programming problem. Basic Sci J Textile Univ 21:161–166

    Google Scholar 

  2. Abo-Sinna MA, Amer AH, Ibrahim AS (2008) Hierarchical generation of α-Pareto optimal solutions in large-scale multi-objective non-linear systems with fuzzy parameters. Appl Math Model 32:930–957

    Article  MATH  MathSciNet  Google Scholar 

  3. Zhao R, Hao S (2010) Modeling and solving a novel class of fuzzy constraint satisfaction problems. J Syst Eng 25:415–420

    MATH  MathSciNet  Google Scholar 

  4. Baykasoglu A, Gocken T (2010) Multi-objective aggregate production planning with fuzzy parameters. Adv Eng Softw 41:1124–1131

    Google Scholar 

  5. Jimenez M, Bilbao A (2009) Pareto-optimal solutions in fuzzy multi-objective linear programming. Fuzzy Sets Syst 160:2714–2721

    Article  MATH  MathSciNet  Google Scholar 

  6. Baky IA (2010) Solving multi-level multi-objective linear programming problem through fuzzy goal programming approach. Appl Math Model 34:2377–2387

    Article  MATH  MathSciNet  Google Scholar 

  7. Ozkok BA, Tiryaki F (2011) A compensatory fuzzy approach to multi-objective linear supplier selection problem with multiple-item. Expert Syst Appl 38:11363–11368

    Article  Google Scholar 

  8. Amid A, Ghodsypour SH, O’Brien C (2011) A weighted max-min model for fuzzy multi-objective supplier selection in a supply chain. Int J Prod Econom 131:139–145

    Article  Google Scholar 

  9. Wu W, Lin YT (2010) Fuzzy-based multi-objective optimization of DMFC system efficiencies. Int J Hydrogen Energy 35:9701–9708

    Article  Google Scholar 

  10. Yu M, Goh M, Lin H (2012) Fuzzy multi-objective vendor selection under lean procurement. Eur J Oper Res 219:305–311

    Article  MATH  Google Scholar 

  11. Sakawa Masatoshi, Katagiri Hideki, Matsui Takeshi (2012) Fuzzy random bilevel linear programming through expectation optimization using possibility and necessity. Int J Mach Learn Cybern 3(3):183–192

    Article  Google Scholar 

  12. Sakawa M, Matsui T (2012) Random fuzzy bilevel linear programming through possibility-based fractile model. Int J Mach Learn Cybern. doi:10.1007/s13042-012-0145-1

  13. Katagiri H, Uno T, Kato K, Tsuda H, Tsubaki H (2012) Random fuzzy bilevel linear programming through possibility-based value at risk model. Int J Mach Learn Cybern. doi:10.1007/s13042-012-0126-4

  14. Sakawa M, Yano H (1989) Interactive decision making for multi-objective nonlinear programming problems with fuzzy parameters. Fuzzy Sets Syst 29:315–326

    Article  MATH  MathSciNet  Google Scholar 

  15. Sakawa M, Yano H (1990) An interactive fuzzy satisfying method for generalized multi-objective linear programming problems with fuzzy parameters. Fuzzy Sets Syst 35:125–142

    Article  MATH  MathSciNet  Google Scholar 

  16. Kassem M (1995) Interactive stability of multi-objective nonlinear programming problems with fuzzy parameters in the constrains. Fuzzy Sets Syst 73:235–243

    Article  MATH  MathSciNet  Google Scholar 

  17. Kassem M (1995) Stability of multi-objective nonlinear programming problems with fuzzy parameters in the constrains. Fuzzy Sets Syst 74:43–351

    Article  MathSciNet  Google Scholar 

  18. Gu J, Zhou R (2002) Multi-objective programming problem with fuzzy parameter in constrains (I)-the definition and property of solution. Nanchang Univ J 26:151–157

    Google Scholar 

  19. Gu J, Zhou R (2003) Multi-objective programming problem with fuzzy parameter in constrains (II)-the properties of constrains and image set. Nanchang Univ J 27:8–13

    Google Scholar 

  20. Gu J, Zhou R (2002) Multi-objective programming problem with fuzzy parameter in constrains (III)-the existence of solution. Nanchang Univ J 15:88–91

    Google Scholar 

Download references

Acknowledgments

This work is supported by the Natural Science Foundation of Hebei Province under Grand A2012502061.

Author information

Authors and Affiliations

  1. Information Processing and Control Institute, North China Electric Power University, Baoding, China

    Guoli Zhang & Hua Zuo

Authors
  1. Guoli Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hua Zuo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Guoli Zhang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, G., Zuo, H. Research on multi-objective linear programming problem with fuzzy coefficients in constraints. Int. J. Mach. Learn. & Cyber. 5, 403–412 (2014). https://doi.org/10.1007/s13042-013-0173-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13042-013-0173-5

Keywords

Search

Navigation