Quadratic Fuzzy Bilevel Chance Constrained Programming with Parameters Following Weibull Distribution

  • Animesh Biswas
  • Arnab Kumar De
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8298)


This paper presents a fuzzy goal programming approach for solving quadratic fuzzy bilevel programming problems with probabilistic constraints containing Weibull distributed fuzzy random variables. In the proposed methodology the problem is first converted into an equivalent quadratic fuzzy bilevel programming model by applying chance constrained programming technique developed with the use of α –cuts in a fuzzily defined stochastic decision making situation. Then the developed model is transferred into an equivalent deterministic one by using the method of defuzzification based on probability density function of the corresponding membership functions. The individual optimal value of the objective of each decision makers is found in isolation to construct the quadratic fuzzy membership goals of each of the decision makers. The quadratic membership goals are then converted into linear goals by applying approximation techniques. A weighted minsum goal programming method is then applied to achieve the highest membership degree of each of the membership goals of decision makers in the decision making context. Finally a comparison is made on the applied approximation techniques with the help of using distance function. An illustrative numerical example is provided to demonstrate the applicability of the proposed methodology.


Bilevel programming Weibull distribution Fuzzy nonlinear programming Fuzzy Chance Constrained programming Fuzzy goal programming 


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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Animesh Biswas
    • 1
  • Arnab Kumar De
    • 2
  1. 1.Department of MathematicsUniversity of KalyaniKalyaniIndia
  2. 2.Department of MathematicsAcademy of TechnologyDist - HooghlyIndia

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