# Neuro-Fuzzy Model Evaluation for Enhanced Prediction of Mechanical Properties in AM Specimens
## 1 Introduction  
The continuous advancement of modern industry has generated a significant demand for high-performance constructions and materials with pre-designed mechanical properties. Modern industry, and thus, industry 4.0, embraces concepts such as additive manufacturing (AM) [1] and artificial intelligence (AI), among others [2]. The mechanical properties of AM parts gather great research interest [3, 4, 5, 6, 7], as the traditional approaches cannot be applied to additive-manufactured parts for predicting mechanical properties and experimentation can be time- and cost-consuming. The integration of AM and AI is of interest to the research community for mechanical properties prediction [8, 9, 10, 11, 12, 13, 14], allowing researchers to extract meaningful patterns from large datasets to accelerate material design and improve overall performance. By employing machine learning algorithms, valuable insights into material behavior can be obtained,leading to faster design iterations and enhancing material properties without extensive empirical testing. Among innovative fabrication methods, additive manufacturing (AM), or 3D printing, has emerged as a highly flexible technique. By building structures layer by layer, AM enables the production of complex geometries that are challenging to achieve with traditional manufacturing processes. This capability has broadened AM's applications across industries, allowing for the rapid prototyping and production of parts with intricate designs and customizable features. Despite its versatility, AM faces several limitations in ensuring consistent mechanical performance across manufactured parts. The mechanical properties of AM-fabricated components are influenced by various manufacturing parameters, such as layer thickness, build orientation, temperature, material selection, and more, leading to challenges in predicting the behavior of these parts. To address these challenges, artificial intelligence (AI) methodologies, particularly, adaptive neuro-fuzzy inference systems (ANFIS), offer promising solutions [8; 9; 15]. ANFIS combines the adaptability of neural networks with the interpretability of fuzzy logic, making it well-suited for modeling the nonlinear relationships in complex systems like AM. As a convergence of neural networks and fuzzy modeling, ANFIS can capture intricate input-output relationships based on experimental data and \"if-then\" rules, thereby establishing accurate predictive models for mechanical properties. This hybrid approach has already shown potential in other AI applications [16; 17; 18; 19; 20], such as automated control and decision-making systems, and it can now be applied in AM to enhance the precision and efficiency of part production. ANFIS has been effectively applied to model the relationships between inputs and outputs, combining neural network and fuzzy logic principles. It has demonstrated reliable predictive accuracy in various additive manufacturing (AM) contexts. The key advantages of this method include the following:  
* Rapid learning capability, even with limited or unevenly distributed data across the process window. * Robust modeling performance, especially effective in handling noisy data within nonlinear systems. * Ease of adaptation and application of neural network principles to specific problem domains. * Efficient processing, providing time-effective performance for complex tasks. [PERSON] and [PERSON] [21] developed a sophisticated ANFIS to predict the mechanical behavior of 3D-printed thermoset carbon fiber composites. By leveraging the neuro-fuzzy inference model, the research addresses challenges in the experimental evaluation of complex composite structures with variable fiber fractions, especially given issues like fiber aggregation and nozzle blockage at higher load levels. The model effectively predicts critical mechanical properties such as flexural stress, modulus, and elongation at break, based on real experimental data.