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Robust-Soft Solutions in Linear Optimization Problems with Fuzzy Parameters

In: Robustness Analysis in Decision Aiding, Optimization, and Analytics

Author

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  • Masahiro Inuiguchi

    (Osaka University)

Abstract

Linear optimization linear programming problems with fuzzy parameters were studied deeply and widely. Many of the approaches to fuzzy problems generate robust solutions. However, they were based on satisficing approaches so that the solutions do not maintain the optimality or suboptimality against the fluctuations in the coefficients. In this chapter, we describe a robust solution maintaining the suboptimality against the fluctuations in the coefficients. We formulate the problem as an extension of the minimax regret/maximin achievement rate problem and investigate a solution procedure based on a bisection method and a relaxation method. It is shown that the proposed solution procedure is created well so that both bisection and relaxation methods converge simultaneously.

Suggested Citation

  • Masahiro Inuiguchi, 2016. "Robust-Soft Solutions in Linear Optimization Problems with Fuzzy Parameters," International Series in Operations Research & Management Science, in: Michael Doumpos & Constantin Zopounidis & Evangelos Grigoroudis (ed.), Robustness Analysis in Decision Aiding, Optimization, and Analytics, chapter 0, pages 171-190, Springer.
    • Handle: RePEc:spr:isochp:978-3-319-33121-8_8
    DOI: 10.1007/978-3-319-33121-8_8
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