Fuzzy Semi-Parametric Regression Based on Z-numbers

Semi-parametric regression models are highly valued for combining parametric structure with nonparametric flexibility. However, in real-world situations involving data with inherent uncertainty and variable reliability, classical fuzzy numbers are insufficient, necessitating models that incorporate reliability. This paper introduces two novel Z-number-based fuzzy semi-parametric univariate regression models. The first model, with Z-number inputs and outputs, is solved using a one-step generalized regression method incorporating Z-numberbased fuzzy clustering. The second model, with crisp inputs and Z-number outputs, employs a hybrid algorithm for simultaneous bandwidth and regression coefficient estimation. The primary innovation of this research is the introduction of a comprehensive and novel Z-number-based semi-parametric regression framework that, for the first time, enables simultaneous modeling of both data uncertainty and reliability within a semi-parametric structure. Numerical examples and a simulation study demonstrate the superior performance of the proposed methods. Compared to existing fuzzy linear regression models, our approach achieves a significant error reduction and a higher similarity measure, confirming its enhanced accuracy in handling uncertain information. The proposed models effectively capture both uncertainty and reliability within a semi-parametric framework, yielding more accurate predictions and improved interpretability. This makes them highly suitable for practical applications like medical decision-making and control systems. Future work will extend the model to multivariate cases and other imprecise data types like ZA-numbers.