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Integrating geometric programming with rough set theory

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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.

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Acknowledgments

The first author was partially supported by the Grant from the University of Tabriz.

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Authors and Affiliations

  1. School of Mathematical Science, University of Tabriz, Tabriz, Iran

    Rashed Khanjani Shiraz

  2. Faculty of Commerce, Fukuoka University, Fukuoka, Japan

    Hirofumi Fukuyama

Authors
  1. Rashed Khanjani Shiraz
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  2. Hirofumi Fukuyama
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Correspondence to Rashed Khanjani Shiraz.

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Shiraz, R.K., Fukuyama, H. Integrating geometric programming with rough set theory. Oper Res Int J 18, 1–32 (2018). https://doi.org/10.1007/s12351-016-0250-0

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  • DOI: https://doi.org/10.1007/s12351-016-0250-0

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