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Robust Optimization by Fuzzy Linear Programming

In: Managing Safety of Heterogeneous Systems

Author

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  • Masahiro Inuiguchi

    (Osaka University)

Abstract

In this paper, the possibilistic linear programming approaches, fuzzy linear programming approaches under uncertain coefficients, are reviewed in connection with robust optimization. The ideas of optimizing approaches and satisficing approaches are described rather than their technical and methodological aspects. Because the former has not been introduced in many papers, we describe the former more than the latter. As optimizing approaches, the concepts of possibly and necessarily optimal solutions are given. Among those, necessarily optimal solutions are robustly optimal solutions. However, it is frequent that such a solution does not exists. Then necessarily soft-optimal solutions are introduced. As satisficing approaches, the treatments based on necessity measures are introduced. Necessity measure optimization model, necessity fractile optimization model and symmetric model are described. Finally, the paper is concluded with giving some promising future topics.

Suggested Citation

  • Masahiro Inuiguchi, 2012. "Robust Optimization by Fuzzy Linear Programming," Lecture Notes in Economics and Mathematical Systems, in: Yuri Ermoliev & Marek Makowski & Kurt Marti (ed.), Managing Safety of Heterogeneous Systems, edition 127, pages 219-239, Springer.
    • Handle: RePEc:spr:lnechp:978-3-642-22884-1_11
    DOI: 10.1007/978-3-642-22884-1_11
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    Cited by:

    1. Guilin Gao & Xueting Zeng & Chunjiang An & Lei Yu, 2018. "A Sustainable Industry-Environment Model for the Identification of Urban Environmental Risk to Confront Air Pollution in Beijing, China," Sustainability, MDPI, vol. 10(4), pages 1-22, March.
    2. Xueting Zeng & Hua Xiang & Jia Liu & Yong Xue & Jinxin Zhu & Yuqian Xu, 2021. "Identification of Policies Based on Assessment-Optimization Model to Confront Vulnerable Resources System with Large Population Scale in a Big City," IJERPH, MDPI, vol. 18(24), pages 1-27, December.
    3. Zeng, X.T. & Huang, G.H. & Chen, H.L. & Li, Y.P. & Kong, X.M. & Fan, Y.R., 2016. "A simulation-based water-environment management model for regional sustainability in compound wetland ecosystem under multiple uncertainties," Ecological Modelling, Elsevier, vol. 334(C), pages 60-77.

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