Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Limitations of Pareto Front in Design Under Uncertainty and Their Reconciliation J. Mech. Des. 2013;135(7): doi: / Decision making with different combinations of the two types of uncertainties Figure Legend:

Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Limitations of Pareto Front in Design Under Uncertainty and Their Reconciliation J. Mech. Des. 2013;135(7): doi: / Isopreference curves over two attributes Figure Legend:

Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Limitations of Pareto Front in Design Under Uncertainty and Their Reconciliation J. Mech. Des. 2013;135(7): doi: / Pareto front over two attributes Figure Legend:

Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Limitations of Pareto Front in Design Under Uncertainty and Their Reconciliation J. Mech. Des. 2013;135(7): doi: / Pareto front over individual value functions. Negative signs indicate a minimization problem Figure Legend:

Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Limitations of Pareto Front in Design Under Uncertainty and Their Reconciliation J. Mech. Des. 2013;135(7): doi: / Process to select (a) the certainty equivalent curve or envelope for a given solution among all candidate utility functions and (b) the best solution from a given set of certainty equivalent envelopes for an attribute minimization decision problem Figure Legend:

Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Limitations of Pareto Front in Design Under Uncertainty and Their Reconciliation J. Mech. Des. 2013;135(7): doi: / Inverting a utility function in a multi-attribute problem results in a CE curve Figure Legend:

Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Limitations of Pareto Front in Design Under Uncertainty and Their Reconciliation J. Mech. Des. 2013;135(7): doi: / Performance of the solutions against all utility functions. For simplicity, only three curves in two dimensions are shown for each solution Figure Legend:

Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Limitations of Pareto Front in Design Under Uncertainty and Their Reconciliation J. Mech. Des. 2013;135(7): doi: / Best valuations (left envelope) of the CE envelopes of Fig. 7 Figure Legend:

Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Limitations of Pareto Front in Design Under Uncertainty and Their Reconciliation J. Mech. Des. 2013;135(7): doi: / Modified Pareto front and possible selections by the DM Figure Legend:

Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Limitations of Pareto Front in Design Under Uncertainty and Their Reconciliation J. Mech. Des. 2013;135(7): doi: / Contour plots of the three candidate utility functions Figure Legend:

Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Limitations of Pareto Front in Design Under Uncertainty and Their Reconciliation J. Mech. Des. 2013;135(7): doi: / (a) Certainty equivalent curves for solution μ 1 for the three utility functions and the corresponding conservative envelope. (b) Certainty equivalent curves for solution μ 2 for the three utility functions and the corresponding conservative envelope. (c) Certainty equivalent curves for solution μ 3 for the three utility functions and the corresponding conservative envelope. Figure Legend:

Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Limitations of Pareto Front in Design Under Uncertainty and Their Reconciliation J. Mech. Des. 2013;135(7): doi: / Left envelope (black solid line) of conservative certainty equivalent curves from Figs. 11(a)–11(c). The curves marked X_1, X_2 and X_3 indicate the conservative envelopes of the three designs, respectively. Figure Legend:

Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Limitations of Pareto Front in Design Under Uncertainty and Their Reconciliation J. Mech. Des. 2013;135(7): doi: / Modified Pareto front and attribute realizations for the three solutions Figure Legend:

Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Limitations of Pareto Front in Design Under Uncertainty and Their Reconciliation J. Mech. Des. 2013;135(7): doi: / Modified Pareto front and its relative position with respect to individual certainty equivalent curves Figure Legend:

Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Limitations of Pareto Front in Design Under Uncertainty and Their Reconciliation J. Mech. Des. 2013;135(7): doi: / Modified Pareto front defined by the right envelope of certainty equivalent surfaces Figure Legend:

Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Limitations of Pareto Front in Design Under Uncertainty and Their Reconciliation J. Mech. Des. 2013;135(7): doi: / A simple speed reducer (adapted from Ref. [4]) Figure Legend: