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Interactive fuzzy programming approach to Bi-level quadratic fractional programming problems

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  • Savita Mishra
  • Ajit Ghosh

Abstract

In this paper we propose an interactive fuzzy programming method for obtaining a satisfactory solution to a “bi-level quadratic fractional programming problem” with two decision makers (DMs) interacting with their optimal solutions. After determining the fuzzy goals of the DMs at both levels, a satisfactory solution is efficiently derived by updating the satisfactory level of the DM at the upper level with consideration of overall satisfactory balance between both levels. Optimal solutions to the formulated programming problems are obtained by combined use of some of the proper methods. Theoretical results are illustrated with the help of a numerical example. Copyright Springer Science + Business Media, Inc. 2006

Suggested Citation

  • Savita Mishra & Ajit Ghosh, 2006. "Interactive fuzzy programming approach to Bi-level quadratic fractional programming problems," Annals of Operations Research, Springer, vol. 143(1), pages 251-263, March.
    • Handle: RePEc:spr:annopr:v:143:y:2006:i:1:p:251-263:10.1007/s10479-006-7386-x
    DOI: 10.1007/s10479-006-7386-x
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    References listed on IDEAS

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    1. Nykowski, Ireneusz & Zolkiewski, Zbigniew, 1985. "A compromise procedure for the multiple objective linear fractional programming problem," European Journal of Operational Research, Elsevier, vol. 19(1), pages 91-97, January.
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    Cited by:

    1. Tajbakhsh, Alireza & Hassini, Elkafi, 2018. "Evaluating sustainability performance in fossil-fuel power plants using a two-stage data envelopment analysis," Energy Economics, Elsevier, vol. 74(C), pages 154-178.
    2. Mishra, Savita, 2007. "Weighting method for bi-level linear fractional programming problems," European Journal of Operational Research, Elsevier, vol. 183(1), pages 296-302, November.
    3. Namrata Rani & Vandana Goyal & Deepak Gupta, 2022. "FGP approach and Rouben ranking function to bi-level multi-objective quadratic fractional problem with trapezoidal fuzzy numbers and soft fuzzy constraints," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 13(1), pages 113-122, February.
    4. Vandana Goyal & Namrata Rani & Deepak Gupta, 2022. "FGP approach to quadratically constrained multi-objective quadratic fractional programming with parametric functions," OPSEARCH, Springer;Operational Research Society of India, vol. 59(2), pages 594-602, June.
    5. Rizk M. Rizk-Allah & Mahmoud A. Abo-Sinna, 2021. "A comparative study of two optimization approaches for solving bi-level multi-objective linear fractional programming problem," OPSEARCH, Springer;Operational Research Society of India, vol. 58(2), pages 374-402, June.
    6. Sujit De & Shib Sana, 2015. "Backlogging EOQ model for promotional effort and selling price sensitive demand- an intuitionistic fuzzy approach," Annals of Operations Research, Springer, vol. 233(1), pages 57-76, October.

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