a estimation of ridge-based in a type-2 fuzzy non-parametric regression

This paper focuses on estimating ridge in a type-2 fuzzy non-parametric regression model that utilizes non-fuzzy inputs, type-2 fuzzy output data, and type-2 fuzzy coefficients within a dual lagrange space. it begins with definitions of type-2 fuzzy sets (t2fss) and presents a closed parametric form for complete triangular t2fss. the proposed framework underpins a local linear smoothing method that incorporates a cross-validation procedure for optimizing ridge parameters and smoothing values. the research advances statistical modeling with type-2 fuzzy systems, offering innovative techniques for regression analysis in complex data situations. the combination of ridge estimation, local linear smoothing, and cross-validation is highlighted for its potential to yield precise results. our work is able to model complex and nonlinear relationships between variables, which more effectively deals with uncertainties and ambiguities in the data, prevents overfitting, and ultimately improves the accuracy and reliability of predictions. numerical simulations are included to validate the theoretical findings and demonstrate the method’s effectiveness.