Obtaining interval estimates of nonlinear model parameters based on combined soft computing tools

Obtaining interval estimates of nonlinear model parameters is as important as point estimates of model parameters. Because the estimated value of the parameters cannot always be expressed as a single numerical quantity exactly. In this study, it is aimed to propose an interval estimation procedure for nonlinear model parameters with combining soft computing methods instead of using probabilistic assumptions. For this purpose, response and model parameters were presented as triangular fuzzy numbers (TFNs) in nonlinear regression model. The errors were defined as intervals through alpha-cut operations and minimized according to the least absolute deviation (LAD) metric. The novelty of the study is achieving the minimization in a multi-objective framework in which the objective functions are lower and upper bound of interval type error functions. The NSGA-II (Non-dominated Sorting Genetic Algorithm-II) and the TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) methods were used for multi-objective optimization (MOO) and multi-criteria decision making (MCDM) stages, respectively. Innovatively, in order to obtain reasonable interval estimates, predefined sized compromise solution set was composed and the fuzzy C-means (FCM) clustering algorithm was applied to the compromise set of interval estimates according to the predicted alpha-cut values. The proposed interval estimation approach is applied on a synthetic and a real data sets for application purpose.