Skip to main content
SpringerLink
Log in

An Interval-Parameter Fuzzy Approach for Multiobjective Linear Programming Under Uncertainty

  • Published:
Journal of Mathematical Modelling and Algorithms

Abstract

An interval-parameter fuzzy linear programming method (IFMOLP) is proposed in this study for multiple objective decision-making under uncertainty. As a hybrid of interval-parameter and fuzzy methodologies, the IFMOLP incorporates interval-parameter linear programming and fuzzy multiobjective programming approaches to form an integrated optimization system. The method inherits advantages of interval-parameter programming, and allows uncertainties and decision-makers’ aspirations to be effectively communicated into its programming processes and resulting solutions. Membership functions for both objectives and constraints are formulated to reflect uncertainties in different system components and their interrelationships. An interactive solution procedure has been developed based on solution approaches of the interval-parameter and fuzzy programming techniques, plus necessary measures for handling the multiobjective feature. A didactic example is provided in the paper to illustrate the detailed solution process. Possibilities of further improvements by seeking Pareto optimum and incorporating flexible preference within constraints are also discussed.

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. Benayoun, R., de Montgolfier, J., Tergny, J., Larichev, O.: Linear programming with multiple objective functions: STEP method (STEM). Math. Program. 1, 366–375 (1971)

    Article  MATH  Google Scholar 

  2. Chang, N.B., Yeh, S.C., Wu, G.C.: Stability analysis of grey compromise programming and its application to watershed land-use planning. Int. J. Syst. Sci. 30(6), 571–582 (1999)

    Article  MATH  Google Scholar 

  3. Goicoechea, A., Hansen, D.R., Duckstein L.: Multiobjective Decision Analysis with Engineering and Business Applications. Wiley, New York (1982)

    Google Scholar 

  4. Huang, G.H.: IPWM: An interval parameter water management model. Eng. Optim. 26, 79–103 (1996)

    Google Scholar 

  5. Huang, G.H., Baetz, B.W., Patry, G.G.: A grey linear programming approach for municipal solid waste management planning under uncertainty. Civ. Eng. Syst. 9, 319–335 (1992)

    Google Scholar 

  6. Huang, G.H., Baetz, B.W., Patry, G.G.: Waste flow allocation under independent stipulation uncertainties. Civ. Eng. Syst. 11, 209–243 (1994)

    Google Scholar 

  7. Lai, Y.J., Hwang, C.L.: Fuzzy Multiple Objective Decision Making – Methods and Applications. Springer, Berlin Heidelberg New York (1994)

    MATH  Google Scholar 

  8. Luhandjula, M.K.: Compensatory operators in fuzzy linear programming with multiple objectives. Fuzzy Sets Syst. 8, 245–252 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  9. Luhandjula, M.K.: Multiobjective programming problems with possibilistic coefficients. Fuzzy Sets Syst. 21, 135–145 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  10. Rommelfanger, H.: Fuzzy linear programming and applications. Eur. J. Oper. Res. 92, 512–527 (1996)

    Article  MATH  Google Scholar 

  11. Sakawa, M., Kato, K., Nishizaki, I.: An interactive fuzzy satisficing method for multiobjective stochastic linear programming problems through an expectation model. Eur. J. Oper. Res. 145(3), 665–672 (2003)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  13. Slowinski, R., Teghem, J. (eds.): Stochastic versus Fuzzy Approaches to Multiobjective Mathematical Programming under Uncertainty. Kluwer, Dordrecht (1990)

    MATH  Google Scholar 

  14. Stanciulescu, C., Fortemps, P., Installe, M., Wertz, V.: Multiobjective fuzzy linear programming problems with fuzzy decision variables. Eur. J. Oper. Res. 149(3), 654–675 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  15. Teghem, J., Dufrasne, D., Thauvoye, M., Kunsch P.: STRANGE: An interactive method for multiobjective linear programming under uncertainty. Eur. J. Oper. Res. 26(1), 65–82 (1986)

    Article  MATH  Google Scholar 

  16. Urli, B., Nadeau, R.: Multiobjective stochastic linear programming with incomplete information: A general methodology. In: Slowinski, R., Teghem, J. (eds.) Stochastic vs. Fuzzy Approaches to Multiobjective Mathematical Programming Under Uncertainty, pp. 131–161. Kluwer, Dordrecht (1990)

    Google Scholar 

  17. Yeomans, J.S., Huang, G.H.: An evolutionary grey, hop, skip, and jump approach: Generating alternative policies for the expansion of waste management facilities. J. Environ. Inform. 1, 37–51 (2003)

    Google Scholar 

  18. Zimmermann, H.J.: Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst. 1, 45–55 (1978)

    Article  MATH  Google Scholar 

  19. Zimmermann, H.J.: Fuzzy Sets and Decision Analysis. Elsevier, Amsterdam, Holland (1984)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Engineering, University of Regina, Regina, Saskatchewan, S4S 0A2, Canada

    Simon Wu & Guo H. Huang

Authors
  1. Simon Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Guo H. Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Simon Wu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wu, S., Huang, G.H. An Interval-Parameter Fuzzy Approach for Multiobjective Linear Programming Under Uncertainty. J Math Model Algor 6, 195–212 (2007). https://doi.org/10.1007/s10852-006-9042-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10852-006-9042-5

Key words

Mathematics Subject Classifications (2000)

Search

Navigation