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A revisit to quadratic programming with fuzzy parameters

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  • Liu, Shiang-Tai

Abstract

Quadratic programming has been widely applied to solving real-world problems. Recently, Liu describes a solution method for solving a class of fuzzy quadratic programming problems, where the cost coefficients of the linear terms in objective function, constraint coefficients, and right-hand sides are fuzzy numbers [Liu ST. Quadratic programming with fuzzy parameters: a membership function approach. Chaos, Solitons & Fractals 2009;40:237–45]. In this paper, we generalize Liu’s method to a more general fuzzy quadratic programming problem, where the cost coefficients in objective function, constraint coefficients, and right-hand sides are all fuzzy numbers. A pair of two-level mathematical programs is formulated to calculate the upper bound and lower bound of the objective values of the fuzzy quadratic program. Based on the duality theorem and by applying the variable transformation technique, the pair of two-level mathematical programs is transformed into a family of conventional one-level quadratic programs. Solving the pair of quadratic programs produces the fuzzy objective values of the problem. With the ability of calculating the fuzzy objective value developed in this paper, it might help initiate wider applications.

Suggested Citation

  • Liu, Shiang-Tai, 2009. "A revisit to quadratic programming with fuzzy parameters," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1401-1407.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:3:p:1401-1407
    DOI: 10.1016/j.chaos.2008.04.061
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    References listed on IDEAS

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    1. Liu, Shiang-Tai, 2009. "Quadratic programming with fuzzy parameters: A membership function approach," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 237-245.
    2. Stefanini, Luciano & Sorini, Laerte & Guerra, Maria Letizia, 2006. "Simulation of fuzzy dynamical systems using the LU-representation of fuzzy numbers," Chaos, Solitons & Fractals, Elsevier, vol. 29(3), pages 638-652.
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    5. Dehghan, Mehdi & Hashemi, Behnam & Ghatee, Mehdi, 2007. "Solution of the fully fuzzy linear systems using iterative techniques," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 316-336.
    6. Soleimani-damaneh, M., 2008. "Fuzzy upper bounds and their applications," Chaos, Solitons & Fractals, Elsevier, vol. 36(2), pages 217-225.
    7. Nieto, Juan J. & Rodríguez-López, Rosana, 2006. "Bounded solutions for fuzzy differential and integral equations," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1376-1386.
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    9. Abdel-Malek, Layek L. & Areeratchakul, Nathapol, 2007. "A quadratic programming approach to the multi-product newsvendor problem with side constraints," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1607-1619, February.
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    Cited by:

    1. Amin Mansoori & Sohrab Effati & Mohammad Eshaghnezhad, 2018. "A neural network to solve quadratic programming problems with fuzzy parameters," Fuzzy Optimization and Decision Making, Springer, vol. 17(1), pages 75-101, March.

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