Robust Multiobjective Optimization with Robust. Consensus. Kaustuv Nag, Member, IEEE, Tandra Pal, Senior Member, IEEE, Rajani K. Mudi, and Nikhil R. Pal, ...
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S UPPLEMENTARY M ATERIALS
Robust Multiobjective Optimization with Robust Consensus Kaustuv Nag, Member, IEEE, Tandra Pal, Senior Member, IEEE, Rajani K. Mudi, and Nikhil R. Pal, Fellow, IEEE
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Fig. S-1. Original and Type I robust Pareto Front of the Test Problem with δ = δ 1 = (0.007, 0.014, 0.014, 0.014, 0.014).
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Fig. S-2. Contour plots of different definitions of consensus and the corresponding obtained solutions with δ = 0 when Gaussian membership functions are used to denote the DMs’ preferences.
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Fig. S-3. Surface plots of different definitions of consensus and the corresponding obtained solutions with δ = 0 when Gaussian membership functions are used to denote the DMs’ preferences.
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Fig. S-4. Contour plots of different definitions of consensus and the corresponding obtained solutions with δ = 0 when triangular membership functions are used to denote the DMs’ preferences.
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Fig. S-5. Contour plots of different definitions of consensus and the corresponding obtained solutions with δ = δ 1 = (0.007, 0.014, 0.014, 0.014, 0.014) when Gaussian membership functions are used to denote the DMs’ preferences.
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Fig. S-6. Contour plots of different definitions of consensus and the corresponding obtained solutions with δ = δ 1 = (0.007, 0.014, 0.014, 0.014, 0.014) when triangular membership functions are used to denote the DMs’ preferences.
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Fig. S-7. Contour plots of different definitions of consensus and the obtained solutions considering different specificities of the preferences (provided by the decision makers) with δ = 0 and φ(·) = min(·). Preferences are provided using Gaussian membership functions.
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Fig. S-8. Contour plots of different definitions of consensus and the obtained solutions considering different specificities of the preferences (provided by the decision makers) with δ = δ1 = (0.007, 0.014, 0.014, 0.014, 0.014) and φ(·) = min(·). Preferences are provided using Gaussian membership functions.
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Fig. S-9. Contour plots of different definitions of consensus and the obtained solutions considering different weights associated with the decision makers. δ = δ 1 = (0.007, 0.014, 0.014, 0.014, 0.014) and φ(·) = min(·) are used. Preferences are provided using Gaussian membership functions.
