IDEAS home Printed from https://ideas.repec.org/h/spr/lnechp/978-3-540-85646-7_18.html
   My bibliography  Save this book chapter

Solving a Fuzzy Multiobjective Linear Programming Problem Through the Value and the Ambiguity of Fuzzy Numbers

In: Multiobjective Programming and Goal Programming

Author

Listed:
  • Mariano Jiménez

    (Universidad del País Vasco.)

  • Mar Arenas

    (Universidad de Oviedo.)

  • Amelia Bilbao

    (Universidad de Oviedo.)

  • Ma Victoria Rodíguez

    (Universidad de Oviedo.)

Abstract

In this paper we solve multiobjective programming problems with fuzzy parameters and flexible constraints. To work with fuzzy numbers we use two real indices, the value and the ambiguity. In order to rank two fuzzy numbers a lexicographic ranking procedure can be used: in the first step the values of fuzzy numbers are compared, if these values are ‘approximately equal’ then we compare their ambiguities. In this paper we apply this ranking procedure to a fuzzy programming problem with fuzzy coefficients. In the first step we solve a model in which the fuzzy coefficients have been defuzzified by its corresponding value. Now the question is to determine when two solutions of the first step are approximately equal. In order to answer this question we propose to reflect the decision makers (DMs) preferences through the natural language, establishing a semantic correspondence for the different satisfaction degrees. We consider as approximately equal all the solutions whose global satisfaction degrees belong to the same linguistic label. Then, in the second step, among all the solutions that belong to the same linguistic label as the solution obtained in the first step, we find those with minimum (or maximum) ambiguity, depending on DMs attitude when faced with the risk. We use one example to illustrate this procedure.

Suggested Citation

  • Mariano Jiménez & Mar Arenas & Amelia Bilbao & Ma Victoria Rodíguez, 2009. "Solving a Fuzzy Multiobjective Linear Programming Problem Through the Value and the Ambiguity of Fuzzy Numbers," Lecture Notes in Economics and Mathematical Systems, in: Vincent Barichard & Matthias Ehrgott & Xavier Gandibleux & Vincent T'Kindt (ed.), Multiobjective Programming and Goal Programming, pages 187-195, Springer.
    • Handle: RePEc:spr:lnechp:978-3-540-85646-7_18
    DOI: 10.1007/978-3-540-85646-7_18
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    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:spr:lnechp:978-3-540-85646-7_18. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.