Robust fuzzy programming method for MRO problems considering location effect, dispersion effect and model uncertainty

•The robust desirability membership functions are constructed.•We present the robust fuzzy programming approach.•Proposed algorithm is used to deal with MRO problems.•Comparisons are given to further illustrate the developed method.

In this paper, considering the uncertainty associated with the fitted response surface models and the satisfaction degrees of the response values with respect to the given targets, we construct the robust membership functions of the responses in three cases and explain their practical meanings. We translate the feasible regions of multiple responses optimization (MRO) problems into ∂-level sets and incorporate the model uncertainty with the confidence intervals simultaneously to ensure the robustness of the feasible regions. Then we develop the robust fuzzy programming (RFP) approach to solve the multiple responses optimization (MRO) problems. The key advantage of the presented method is that it takes account of the location effect, dispersion effect and model uncertainty of the multiple responses simultaneously and thus can ensure the robustness of the solution. An example from literatures is illustrated to show the practicality and effectiveness of the proposed algorithm. Finally some comparisons and discussions are given to further illustrate the developed approach.