Comparison of fuzzy logic based models for the multi-response surface problems with replicated response measures

Abstract

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.