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Integrating geometric programming with rough set theory

Author

Listed:
  • Rashed Khanjani Shiraz

    (University of Tabriz)

  • Hirofumi Fukuyama

    (Fukuoka University)

Abstract

Geometric programming has been applied in the problems of engineering design, economics and management science. The conventional deterministic geometric programming method requires precise single values for the coefficients and exponents of decision variables. However, there may exist uncertainty and impreciseness about the parameters as well as data in complex real-life problems. In such situations, the deterministic geometric programming method is inappropriate. In this paper, we integrate the deterministic geometric programming with rough set theory to propose a rough geometric programming method. Our proposed method has mainly three characteristics. Firstly, the coefficients in the objective function and constraints are rough variables. Secondly, the expected-value operator of rough variables is implemented. Thirdly, the method can determine both lower and upper bounds of the objective function at a specific trust level. Three illustrative examples are presented to demonstrate the efficacy of our novel method.

Suggested Citation

  • Rashed Khanjani Shiraz & Hirofumi Fukuyama, 2018. "Integrating geometric programming with rough set theory," Operational Research, Springer, vol. 18(1), pages 1-32, April.
    • Handle: RePEc:spr:operea:v:18:y:2018:i:1:d:10.1007_s12351-016-0250-0
    DOI: 10.1007/s12351-016-0250-0
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    References listed on IDEAS

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    1. Tsai, Jung-Fa & Lin, Ming-Hua & Hu, Yi-Chung, 2007. "On generalized geometric programming problems with non-positive variables," European Journal of Operational Research, Elsevier, vol. 178(1), pages 10-19, April.
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    Cited by:

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    2. Belleh Fontem, 2023. "Robust Chance-Constrained Geometric Programming with Application to Demand Risk Mitigation," Journal of Optimization Theory and Applications, Springer, vol. 197(2), pages 765-797, May.

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