A Comparative Study of Full Z Number–Based Semi Parametric Regression Models: Accuracy, Structural Consistency, and Data Heterogeneity

Abstract

Simultaneous modeling of uncertainty and reliability in real-world data is one of the major challenges in regression analysis under uncertain conditions. Z-numbers, as a two-component framework, enable the concurrent representation of an imprecise value and the associated degree of confidence. However, developing Z-number-based regression models that possess adequate numerical accuracy, structural consistency, and the ability to cope with data heterogeneity remains challenging. In this study, for the first time, a fully semiparametric regression model based on Z-numbers is introduced, and three distinct solution methods are proposed. The first method, referred to as the baseline approach, provides a simple modeling framework by integrating the uncertainty and reliability components. The second method, referred to as the improved baseline method, explicitly separates the $A$ and $B$ components and applies inconsistency control mechanisms to preserve the conceptual coherence of Z-numbers. The third method, referred to as the clustered method, addresses data heterogeneity by proposing a Z-number-based clustering approach that enhances predictive accuracy through local model fitting. The results of the case study indicate that although the baseline model is structurally simpler and the improved baseline method provides satisfactory numerical stability, the clustered method exhibits the best performance in terms of error and similarity measures due to its ability to model data heterogeneity. Overall, the results demonstrate a trade-off among numerical accuracy, preservation of the conceptual structure of Z-numbers, and robustness against data heterogeneity; therefore, the proposed framework enables an informed selection of the appropriate method according to the application objectives and the nature of the data.