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Interactive fuzzy goal programming approach for bilevel programming problem

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  • Arora, S.R.
  • Gupta, Ritu

Abstract

This paper presents an interactive fuzzy goal programming (FGP) approach for bilevel programming problems with the characteristics of dynamic programming (DP). In the proposed approach, the tolerance membership functions in fuzzy sets for measuring the degree of satisfactions of the objectives of both the decision makers and degree of achievement of the decision vector controlled by the leader is defined first. Then the dynamic fuzzy goal programming model for achievement of highest degree (unity) to the extent possible to each of the defined membership functions for the fuzzy goal is developed to solve the decisions of the interrelated stages. A satisfactory solution is derived efficiently by updating the satisfactory degrees of the decision makers with the consideration of overall satisfactory balance between both the levels. Illustrative numerical examples are provided to demonstrate the feasibility of the proposed method.

Suggested Citation

  • Arora, S.R. & Gupta, Ritu, 2009. "Interactive fuzzy goal programming approach for bilevel programming problem," European Journal of Operational Research, Elsevier, vol. 194(2), pages 368-376, April.
    • Handle: RePEc:eee:ejores:v:194:y:2009:i:2:p:368-376
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    References listed on IDEAS

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    3. Nacéra Maachou & Mustapha Moulaï, 2022. "Branch and cut method for solving integer indefinite quadratic bilevel programs," Annals of Operations Research, Springer, vol. 316(1), pages 197-227, September.
    4. Abdul Sattar Safaei & Saba Farsad & Mohammad Mahdi Paydar, 2020. "Emergency logistics planning under supply risk and demand uncertainty," Operational Research, Springer, vol. 20(3), pages 1437-1460, September.
    5. Zhang, Xiaodong & Vesselinov, Velimir V., 2016. "Energy-water nexus: Balancing the tradeoffs between two-level decision makers," Applied Energy, Elsevier, vol. 183(C), pages 77-87.
    6. Ma, Y. & Li, Y.P. & Huang, G.H. & Zhang, Y.F. & Liu, Y.R. & Wang, H. & Ding, Y.K., 2022. "Planning water-food-ecology nexus system under uncertainty: Tradeoffs and synergies in Central Asia," Agricultural Water Management, Elsevier, vol. 266(C).
    7. Hong Wang & Xiaodong Zhang, 2018. "A Decentralized Bi-Level Fuzzy Two-Stage Decision Model for Flood Management," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 32(5), pages 1615-1629, March.
    8. Dempe, S., 2011. "Comment to "interactive fuzzy goal programming approach for bilevel programming problem" by S.R. Arora and R. Gupta," European Journal of Operational Research, Elsevier, vol. 212(2), pages 429-431, July.
    9. Firoz Ahmad, 2022. "Interactive neutrosophic optimization technique for multiobjective programming problems: an application to pharmaceutical supply chain management," Annals of Operations Research, Springer, vol. 311(2), pages 551-585, April.
    10. Xu, Jiuping & Song, Xiaoling & Wu, Yimin & Zeng, Ziqiang, 2015. "GIS-modelling based coal-fired power plant site identification and selection," Applied Energy, Elsevier, vol. 159(C), pages 520-539.
    11. 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.
    12. M. A. El Sayed & Ibrahim A. Baky & Pitam Singh, 2020. "A modified TOPSIS approach for solving stochastic fuzzy multi-level multi-objective fractional decision making problem," OPSEARCH, Springer;Operational Research Society of India, vol. 57(4), pages 1374-1403, December.
    13. M. S. Osman & O. E. Emam & M. A. El Sayed, 2017. "Stochastic Fuzzy Multi-level Multi-objective Fractional Programming Problem: A FGP Approach," OPSEARCH, Springer;Operational Research Society of India, vol. 54(4), pages 816-840, December.
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