IDEAS home Printed from https://ideas.repec.org/a/hin/jnlmpe/280380.html
   My bibliography  Save this article

A Novel Method for Solving the Fully Fuzzy Bilevel Linear Programming Problem

Author

Listed:
  • Aihong Ren

Abstract

We address a fully fuzzy bilevel linear programming problem in which all the coefficients and variables of both objective functions and constraints are expressed as fuzzy numbers. This paper is to develop a new method to deal with the fully fuzzy bilevel linear programming problem by applying interval programming method. To this end, we first discretize membership grade of fuzzy coefficients and fuzzy decision variables of the problem into a finite number of -level sets. By using -level sets of fuzzy numbers, the fully fuzzy bilevel linear programming problem is transformed into an interval bilevel linear programming problem for each -level set. The main idea to solve the obtained interval bilevel linear programming problem is to convert the problem into two deterministic subproblems which correspond to the lower and upper bounds of the upper level objective function. Based on the th-best algorithm, the two subproblems can be solved sequentially. Based on a series of -level sets, we introduce a linear piecewise trapezoidal fuzzy number to approximate the optimal value of the upper level objective function of the fully fuzzy bilevel linear programming problem. Finally, a numerical example is provided to demonstrate the feasibility of the proposed approach.

Suggested Citation

  • Aihong Ren, 2015. "A Novel Method for Solving the Fully Fuzzy Bilevel Linear Programming Problem," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-11, March.
    • Handle: RePEc:hin:jnlmpe:280380
    DOI: 10.1155/2015/280380
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/MPE/2015/280380.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/MPE/2015/280380.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2015/280380?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hin:jnlmpe:280380. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.