Multi-response problems with replicated response measures are considered.Fuzzy least squares regression (FLSR) and fuzzy clustering based modeling methods, switching fuzzy C-regression (SFCR) and Takagi-Sugeno (TS) fuzzy model, were used for modeling of multi-response experiment data with replicated response measures.In this paper, the SFCR is used for the first time to model the replicated response measured data sets.It was seen that the SFCR had the better prediction performance rather than FLSR and TS fuzzy model according to the root mean square error (RMSE). A replicated multi-response experiment is a process that includes more than one responses with replications. One of the main objectives in these experiments is to estimate the unknown relationship between responses and input variables simultaneously. In general, classical regression analysis is used for modeling of the responses. However, in most practical problems, the assumptions for regression analysis cannot be satisfied. In this case, alternative modeling methods such as fuzzy logic based modeling approaches can be used. In this study, fuzzy least squares regression (FLSR) and fuzzy clustering based modeling methods, which are switching fuzzy C-regression (SFCR) and Takagi-Sugeno (TS) fuzzy model, are preferred. The novelty of the study is presenting the applicability of SFCR to the multi-response experiment data set with replicated response measures. Three real data set examples are given for application purposes. In order to compare the prediction performance of modeling approaches, root mean square error (RMSE) criteria is used. It is seen from the results that the SFCR gives the better prediction performance among the other fuzzy modeling approaches for the replicated multi-response experimental data sets.
['Özlem Türkşen', 'Nevin Güler']
Comparison of fuzzy logic based models for the multi-response surface problems with replicated response measures