Random fuzzy bilevel linear programming through possibility-based value at risk model

  • Hideki KatagiriEmail author
  • Takeshi Uno
  • Kosuke Kato
  • Hiroshi Tsuda
  • Hiroe Tsubaki
Original Article


This article considers bilevel linear programming problems where random fuzzy variables are contained in objective functions and constraints. In order to construct a new optimization criterion under fuzziness and randomness, the concept of value at risk and possibility theory are incorporated. The purpose of the proposed decision making model is to optimize possibility-based values at risk. It is shown that the original bilevel programming problems involving random fuzzy variables are transformed into deterministic problems. The characteristic of the proposed model is that the corresponding Stackelberg problem is exactly solved by using nonlinear bilevel programming techniques under some convexity properties. A simple numerical example is provided to show the applicability of the proposed methodology to real-world hierarchical problems.


Bilevel linear programming Random fuzzy variable Stackelberg solutions Possibility Value at risk 


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Hideki Katagiri
    • 1
    Email author
  • Takeshi Uno
    • 2
  • Kosuke Kato
    • 3
  • Hiroshi Tsuda
    • 4
  • Hiroe Tsubaki
    • 5
  1. 1.Faculty of EngineeringHiroshima UniversityHigashi-HiroshimaJapan
  2. 2.Institute of Socio-Arts and SciencesThe University of TokushimaTokushimaJapan
  3. 3.Faculty of Applied Information ScienceHiroshima Institute of TechnologyHiroshimaJapan
  4. 4.Faculty of Science and EngineeringDoshisha UniversityKyotanabeJapan
  5. 5.The Institute of Statistical MathematicsTachikawaJapan

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