Skip to main content
SpringerLink
Log in

Bi-level multi-objective programming problem with fuzzy demands: a fuzzy goal programming algorithm

  • Theoretical Article
  • Published:
OPSEARCH Aims and scope Submit manuscript

Abstract

In this paper, a fuzzy goal programming (FGP) algorithm for solving bi-level multi-objective programming problems with fuzzy demands is presented. These fuzzy demands reflect the experts' imprecise or fuzzy understandings of the nature of parameters in the problem formulation process are assumed to be characterized as fuzzy numbers. Using the level sets of fuzzy parameters, the corresponding non fuzzy bi-level programming problem is introduced. In the proposed algorithm, the membership functions for the defined fuzzy goals of all objective functions at the two levels, as well as the membership functions for the vector of decision variables controlled by FLDM are developed in the model formulation of the problem. Then FGP algorithm is used to achieve the highest degree of each of the membership goals by minimizing their deviational variables and thereby obtaining the most satisfactory solution for all decision makers. Illustrative numerical example is given to demonstrate the proposed algorithm.

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
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. Abo-Sinna, M.A., Baky, I.A.: Interactive balance space approach for solving bi-level multi-objective programming problems. Adv. Model. Anal. B 49(3–4), 43–62 (2006)

    Google Scholar 

  2. Fortuny-Amat, McCarl, B.: A representation and economic interpretation of two-level programming problem. J. Oper. Res. Soc. 32, 783–792 (1981)

    Article  Google Scholar 

  3. Baky, I.A.: Fuzzy goal programming algorithm for solving decentralized bi-level multi-objective programming problems. Fuzzy Set Syst. 160(18), 2701–2713 (2009)

    Article  Google Scholar 

  4. Baky, I.A.: Solving multi-level multi-objective linear programming problems through fuzzy goal programming approach. Appl. Math. Model. 34(9), 2377–2387 (2010)

    Article  Google Scholar 

  5. Baky, I.A.: Fuzzy goal programming procedures for multi-level multi-objective linear fractional programming problems, 6th International Conference of Mathematics and Engineering Physics. The Military Technical College, Cairo (2012)

    Google Scholar 

  6. Bialas, W.F., Karwan, M.H.: Two level linear programming. Manag. Sci. 30(8), 1004–1020 (1984)

    Article  Google Scholar 

  7. Bellman, R.E., Zadeh, L.A.: Decision-making in a fuzzy environment. Manag. Sci. 17, 141–164 (1970)

    Article  Google Scholar 

  8. Candler, W., Townsley, R.: A linear bi-level programming problem. Comput. Oper. Res. 9, 59–76 (1982)

    Article  Google Scholar 

  9. Lai, Y.J.: Hierarchical optimization: b satisfactory solution. Fuzzy Set Syst. 77, 321–335 (1996)

    Article  Google Scholar 

  10. Lee, E.S., Li, R.J.: Fuzzy multiple objective programming with Pareto optimum. Fuzzy Set Syst. 53, 275–288 (1993)

    Article  Google Scholar 

  11. Mohamed, R.H.: The relationship between goal programming and fuzzy programming. Fuzzy Set Syst. 89, 215–222 (1997)

    Article  Google Scholar 

  12. Pramanik, S., Roy, T.K.: Fuzzy goal programming approach to multi-level programming problems. Eur. J. Oper. Res. 176(2), 1151–1166 (2007)

    Article  Google Scholar 

  13. Pramanik, S., Dey, P.P.: Bi-level multi-objective programming problem with fuzzy parameters. Int. J. Comput. Appl. 30(11), 13–20 (2011)

    Google Scholar 

  14. Pal, B.B., Moitra, B.N., Maulik, U.: A goal programming procedure for fuzzy multi-objective linear fractional programming problem. Fuzzy Set Syst. 139(2), 395–405 (2003)

    Article  Google Scholar 

  15. Shih, H.S., Lai, Y.J., Lee, E.S.: Fuzzy approach for multi-level programming problems. Comput. Oper. Res. 23, 73–91 (1996)

    Article  Google Scholar 

  16. Shih, H.S., Lee, E.S.: Compensatory fuzzy multiple level decision making. Fuzzy Set Syst. 14, 71–87 (2000)

    Article  Google Scholar 

  17. Sinha, S.: Fuzzy programming approach to multi-level programming problems. Fuzzy Set Syst. 136, 189–202 (2003)

    Article  Google Scholar 

  18. Sakawa, M., Nishizaki, I., Uemura, Y.: Interactive fuzzy programming for multi-level linear programming problems with fuzzy parameters. Fuzzy Set Syst. 109(1), 03–19 (2000)

    Article  Google Scholar 

  19. Sakawa, M., Nishizaki, I.: Interactive fuzzy programming for decentralized two-level linear programming problems. Fuzzy Set Syst. 125, 301–315 (2002)

    Article  Google Scholar 

  20. Sakawa, M., Nishizaki, I., Uemura, Y.: Interactive fuzzy programming for two-level linear fractional programming problems with fuzzy parameters. Fuzzy Set Syst. 115, 93–103 (2000)

    Article  Google Scholar 

  21. Zhang, G., Lu, J., Dillon, T.: Decentralized multi-objective bi-level decision making with fuzzy demands. Knowl.-Based Syst. 20(5), 495–507 (2007)

    Article  Google Scholar 

  22. Baky, I.A., Abo-Sinna, M. A. Fuzzy goal programming procedures to bi-level multi-objective linear fractional programming problems, International Journal of Mathematics and Mathematical Sciences, Hindawi Publishing Corporation, USA, Volume 2010, Article ID 148975, 15 pages, doi:10.1155/2010/148975.

  23. Moitra B.N., Pal B.B.: A fuzzy goal programming approach for solving bi-level programming problems. Pal, N.R., Sugeno, M. (eds.) In: Advances in Soft Computing – AFSS. vol. 2275 of Lecture Notes in Computer Science, PP.91–98, Springer, Berlin, Germany (2002).

  24. Sakawa, M.: Fuzzy sets and interactive multi-objective optimization. Plenum Press, New York (1993)

    Book  Google Scholar 

  25. Steuer, R.E.: Multiple criteria optimization: theory, computations, and applications. Wiley, New York (1986)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Basic Sciences, Faculty of Engineering, Benha University, EL-Qalyoubia, Egypt

    Ibrahim A. Baky & Mohamed A. El Sayed

  2. Department of Engineering Mathematics and Physics, Faculty of Engineering-Shoubra, Benha University, EL-Qalyoubia, Egypt

    Mohamed H. Eid

Authors
  1. Ibrahim A. Baky
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohamed H. Eid
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mohamed A. El Sayed
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohamed A. El Sayed.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Baky, I.A., Eid, M.H. & El Sayed, M.A. Bi-level multi-objective programming problem with fuzzy demands: a fuzzy goal programming algorithm. OPSEARCH 51, 280–296 (2014). https://doi.org/10.1007/s12597-013-0145-2

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12597-013-0145-2

Keywords

Search

Navigation