The research, conducted by Tin-Chih Toly Chen of National Yang Ming Chiao Tung University in Taiwan, tackles a problem known as internal due-date assignment. Before a factory negotiates a final delivery date with a customer, it must estimate internally when a possible order would actually be completed. That estimate typically hinges on when the last job in the order would finish, a quantity that depends on a tangle of nonlinear relationships between job attributes, production conditions and the state of the factory floor at the moment of release. Machine learning and deep learning models have become popular tools for this task, but they optimize aggregate accuracy metrics such as root mean squared error, which says nothing about whether any single prediction deserves to be trusted.

Chen’s solution draws on an unusual mathematical framework called neutrosophic sets, an extension of fuzzy logic in which every statement is characterized by three degrees rather than one. A truth membership expresses the possibility that a forecast is correct, a falsity membership the possibility that it is wrong, and an indeterminacy membership quantifies the uncertainty about whether the actual value even falls within the predicted range. In the proposed approach, a fuzzy deep neural network first produces a completion-time forecast for each job, and that forecast is then converted into a triangular neutrosophic number whose three memberships carry concrete, measurable meanings.

The technical machinery is deliberate and precise. The truth and falsity memberships are derived from the global estimation accuracy of the network, measured by root mean squared error on the training data, so they reflect how well the model performs overall. The indeterminacy membership is where the method becomes genuinely local: it combines the local estimation accuracy around a specific job, computed from training examples that lie within a defined neighborhood, with the local learning sufficiency, meaning how many similar examples the network actually saw during training. Distance between jobs is calculated on normalized attributes using the Euclidean metric, and the neighborhood radius is set analytically from statistical properties of the normalized distance distribution rather than chosen arbitrarily.

Crucially, the parameters governing these membership functions are optimized rather than guessed. Chen derives bounds from domain-expert expectations, for example that the truth membership should exceed 0.99 when the forecasting error is small and fall below 0.01 when it is large, and then solves for the parameter values that best satisfy those expectations. A numerical search handles the resulting transcendental equation, and the indeterminacy scaling parameter is calibrated so that a job with average local conditions receives a moderate indeterminacy of exactly 0.5. A forecast whose indeterminacy exceeds a prespecified threshold, set at 0.5 in the case study, is declared untrustworthy, and the internal due date derived from it inherits that verdict.

The fuzzy neural network itself is trained in two stages. It is first treated as a crisp deep network and optimized with the Levenberg–Marquardt algorithm to find the cores of the fuzzy parameters. Then the output-layer parameters are fuzzified in a way that mathematically guarantees every fuzzy forecast interval contains the corresponding actual completion time, a property that most existing neutrosophic forecasting methods cannot ensure. The upper bound of each fuzzy forecast becomes the internal due date, because the last job to finish determines when the whole order is complete.

The method was tested on real production data from a wafer fabrication facility in Hsinchu Scientific Park, Taiwan, one of the most demanding manufacturing environments in the world. Two hundred possible orders of a primary memory-product type were analyzed, with 150 jobs used for training and the remainder for testing. The fuzzy deep neural network achieved a training root mean squared error of 5.88 hours and a coefficient of determination of 0.99, while on test data the error rose to 47.99 hours with a coefficient of determination of 0.91, a gap that illustrates exactly why individual predictions can diverge so sharply from aggregate performance.

The results were striking. Of the 50 test orders, 22, or 44 percent, received internal due-date assignments that were not sufficiently trustworthy, driven primarily by insufficient local learning, meaning too few similar training examples nearby, and by poor local estimation accuracy. A separate count showed that 46 percent of the possible orders had too few neighboring examples to support a confident prediction. Most practically, the study found that collecting just 16 additional similar examples for each untrustworthy case could rescue half of the untrustworthy assignments, converting an abstract reliability problem into concrete guidance for where to invest data-collection effort.

Compared with existing approaches, including a hybrid cloud-and-edge computing scheme and an immediate due-date assignment policy, the proposed method achieved higher estimation accuracy and better tightness, a measure of total tardiness, and was the only one to evaluate trustworthiness explicitly. Unlike local surrogate-model explanations such as LIME, it requires no auxiliary model, and unlike regularization or oversampling techniques, which act globally on the network, it assesses each order individually without generating synthetic data. A parametric analysis confirmed the intuition that adding neighboring examples reduces indeterminacy, though the benefit fades when local estimation accuracy is poor, signaling cases where the model itself is systematically failing in a region of the input space.

The implications reach beyond semiconductor fabs. Because the framework is general, it could be applied to other cause-and-effect forecasting problems where a single bad prediction carries real consequences, from predictive maintenance to delivery planning. Chen also notes a cognitive dimension: when users perceive an AI system as trustworthy, they shift from active monitoring to passive reliance, reducing their cognitive burden but raising the risk of over-reliance. By flagging exactly which predictions deserve skepticism, a neutrosophic approach lets human decision-makers direct their attention where it matters. The study acknowledges limitations, including the added computational cost of deriving three membership functions and the inherent subjectivity of any trustworthiness threshold, and points toward future work on alternative neutrosophic set types, collaborative forecasting methods, and validation across more diverse industrial settings.

Subject of Research: Trustworthy internal due-date assignment in manufacturing using neutrosophic neural networks

Article Title: Towards Trustworthy Internal Due-Date Assignment in Manufacturing Systems: A Neutrosophic Neural Network-Based Approach

Article References: Towards Trustworthy Internal Due-Date Assignment in Manufacturing Systems: A Neutrosophic Neural Network-Based Approach. (n.d.). https://doi.org/10.1007/s12559-026-10666-8

Image Credits: AI Generated

DOI: 10.1007/s12559-026-10666-8

Keywords: neutrosophic sets, neural networks, due-date assignment, manufacturing, wafer fabrication, fuzzy logic, deep learning, trustworthy AI, cycle time forecasting, semiconductor manufacturing, indeterminacy, predictive modeling