Journal of Applied Science and Engineering

Published by Tamkang University Press

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Uncertainty Analysis of 3D-Printed Dental Models Using a Hybrid Fuzzy Bayesian Model

 2026

 Volume 35

Jie Wu, Shuang Zhao, Xiaoguang Li

Stomatology College of Jiamusi University, Jiamusi 154000, China

Received: July 21, 2026
Accepted: August 19, 2026
Publication Date: September 06, 2026

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Hybrid fuzzy Bayesian uncertainty-modeling process for 3D-printed dental models

 Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.

Download Citation: BibTeX | http://dx.doi.org/10.6180/jase.202612_35.015

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This study proposes a hybrid fuzzy Bayesian model for analyzing the deviation field of 3D-printed dental models. The model represents the dental-model surface as a signed three-dimensional deviation field and integrates printing-process variables, local geometric features, and fuzzy memberships for low-error, medium-error, and high-risk states at each sampled surface point. A Student-t mixture likelihood is then used to identify latent error mechanisms, including low-error behavior, material shrinkage, local warping, and registration or measurement noise. Error-field reconstruction, latent-mode probabilities, and threshold-exceedance risks are estimated through Bayesian posterior inference. A simulation-driven benchmark dataset of 3D dental-model surfaces is constructed, and the proposed method is compared with linear regression, Gaussian mixture regression, Gaussian process regression, and a conventional Bayesian hierarchical model. The proposed model achieves the best overall performance in RMSE, MAE, CRPS, 95% interval coverage, and risk AUC. Specifically, its RMSE is 0.031 mm, its CRPS is 0.019, and its 95% interval coverage is 94.7%. Visualizations of the 3D dental-model surface show that the model reconstructs high-gradient deviations in cusps, margins, and support-adjacent regions more accurately while also generating posterior risk maps for quality control. These findings suggest that hybrid fuzzy Bayesian modeling is suitable for uncertainty quantification, scientific computing, and parameter-level decision support in digital dental additive manufacturing. The benchmark is simulation-driven and should therefore be interpreted as methodological validation rather than direct clinical evidence.

Keywords: 3D printing; dental model; uncertainty quantification; fuzzy Bayesian model; hybrid model; deviation field; posterior simulation; additive manufacturing.

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