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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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    1. R. E. Bellman & L. A. Zadeh, 1970. "Decision-Making in a Fuzzy Environment," Management Science, INFORMS, vol. 17(4), pages 141-164, December.
    2. Wayne F. Bialas & Mark H. Karwan, 1984. "Two-Level Linear Programming," Management Science, INFORMS, vol. 30(8), pages 1004-1020, August.
    3. Wen, Ue-Pyng & Hsu, Shuh-Tzy, 1992. "Efficient solutions for the linear bilevel programming problem," European Journal of Operational Research, Elsevier, vol. 62(3), pages 354-362, November.
    4. Pal, Bijay Baran & Nath Moitra, Bhola, 2003. "A goal programming procedure for solving problems with multiple fuzzy goals using dynamic programming," European Journal of Operational Research, Elsevier, vol. 144(3), pages 480-491, February.
    5. Richard Bellman, 1957. "On a Dynamic Programming Approach to the Caterer Problem--I," Management Science, INFORMS, vol. 3(3), pages 270-278, April.
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    3. Lachhwani, Kailash, 2015. "Modified FGP approach for multi-level multi objective linear fractional programming problems," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 1038-1049.
    4. 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.
    5. 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.
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