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Architecting a fully fuzzy information model for multi-level quadratically constrained quadratic programming problem

Author

Listed:
  • Hawaf AbdAlhakim

    (Helwan University)

  • O. E. Emam

    (Helwan University)

  • A. A. Abd El-Mageed

    (Helwan University)

Abstract

Fully fuzzy quadratic programming became emerge naturally in numerous real-world applications. Therefore, an effective model based on the bound and decomposition method and the separable programming method is proposed in this paper for solving Fully Fuzzy Multi-Level Quadratically Constrained Quadratic Programming (FFMLQCQP) problem, where the objective function and the constraints are quadratic, also all the coefficients and variables of both objective functions and constraints are described fuzzily as fuzzy numbers. The bound and decomposition method is recommended to decompose the given (FFMLQCQP) problem into series of crisp Quadratically Constrained Quadratic Programming (QCQP) problems with bounded variable constraints for each level. Each (QCQP) problem is then solved independently by utilizing the separable programming method, which replaces the quadratic separable functions with linear functions. At last, the fuzzy optimal solution to the given (FFMLQCQP) problem is obtained. The effectiveness of the proposed model is illustrated through an illustrative numerical example.

Suggested Citation

  • Hawaf AbdAlhakim & O. E. Emam & A. A. Abd El-Mageed, 2019. "Architecting a fully fuzzy information model for multi-level quadratically constrained quadratic programming problem," OPSEARCH, Springer;Operational Research Society of India, vol. 56(2), pages 367-389, June.
    • Handle: RePEc:spr:opsear:v:56:y:2019:i:2:d:10.1007_s12597-019-00368-1
    DOI: 10.1007/s12597-019-00368-1
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    References listed on IDEAS

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    1. R. E. Bellman & L. A. Zadeh, 1970. "Decision-Making in a Fuzzy Environment," Management Science, INFORMS, vol. 17(4), pages 141-164, December.
    2. M. S. Osman & O. E. Emam & M. A. El Sayed, 2017. "Stochastic Fuzzy Multi-level Multi-objective Fractional Programming Problem: A FGP Approach," OPSEARCH, Springer;Operational Research Society of India, vol. 54(4), pages 816-840, December.
    3. Izaz Ullah Khan & Tahir Ahmad & Normah Maan, 2013. "A Simplified Novel Technique for Solving Fully Fuzzy Linear Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 159(2), pages 536-546, November.
    4. N. Ranarahu & J. K. Dash & S. Acharya, 2017. "Multi-objective bilevel fuzzy probabilistic programming problem," OPSEARCH, Springer;Operational Research Society of India, vol. 54(3), pages 475-504, September.
    5. David P. Baron, 1972. "Quadratic programming with quadratic constraints," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 19(2), pages 253-260, June.
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    Cited by:

    1. Namrata Rani & Vandana Goyal & Deepak Gupta, 2021. "A solution procedure for multi-objective fully quadratic fractional optimization model," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 12(6), pages 1447-1458, December.

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