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Robustness-based approach for fuzzy multi-objective problems

  • S.I.: MOPGP 2017
  • Published:
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Abstract

In recent years, reasoning under uncertainty in multi-objective problems has become an active research area. However, solving this kind of problems reveals many performance and robustness issues that have been so far been neglected. Most of existing studies in this area are focused on dealing with robustness in the field of mono-objective optimization. The aim of the present paper is to address robustness of multi-objective optimization problems over uncertain inputs data. In particular, we focus on the specific case of fuzziness propagation to the multiple objectives in such problems. Then in order to avoid the loss of efficiency of fuzzy-valued objective values, we introduce new robustness techniques combining fuzziness and multi-objective context.

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Notes

  1. Let \(x, y \in {\mathbb {R}}^n \times {\mathbb {R}}^n\) where \(x = (x_1,\dots ,x_n)\) and \(y = (y_1,\dots ,y_n)\), then:   \(x \le y\)   iff \(x = y\)   or   \(x_i < y_i\)   for \(1\le i \le n\).

  2. defined as the difference between the best minimum cost and the second minimum for every problem solution.

  3. Big-oh O is the most popularly used complexity measure which denotes the asymptotic upper bound.

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  1. Centre de Recherche Inria Lille - Nord Europe, 172 Avenue de Bretagne, 59000, Lille, France

    Oumayma Bahri & El-Ghazali Talbi

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  1. Oumayma Bahri
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  2. El-Ghazali Talbi
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Correspondence to Oumayma Bahri.

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Bahri, O., Talbi, EG. Robustness-based approach for fuzzy multi-objective problems. Ann Oper Res 296, 707–733 (2021). https://doi.org/10.1007/s10479-020-03567-y

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