A nonlinear modeling with linear fuzzy numbers for replicated response measures. (English) Zbl 07552614

Summary: In this study, it is aimed to present a flexible modeling approach for replicated response measured data set via linear fuzzy numbers (LFNs), e.g. pentagonal linear fuzzy numbers (PLFNs), trapezoidal linear fuzzy numbers (TrLFNs), and triangular linear fuzzy numbers (TLFNs). For this purpose, a fuzzification formula of replicated measures was proposed with calculating quartile based descriptive statistics. The model parameters were also assumed as LFNs whereas the input variable was crisp. In order to obtain the predicted fuzzy nonlinear regression model, least squares (LS) approach and hybrid optimization algorithm, hybrid of Genetic Algorithm and Quasi-Newton algorithm (GA-QN), were used as estimation and optimization methods, respectively. Two data sets were chosen from the literature for application purpose. It is seen from the obtained results that the predicted fuzzy nonlinear functions, obtained with PLFNs, TrLFNs, TLFNs, have equal performance according to the nonparametric statistical tests. However, it is seen from the medians of prediction errors that the predicted fuzzy nonlinear model with PLFNs is the most preferable one.


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