## 4 Discussion  
This study integrated the PFA theory with various quantitative analysis methods to systematically investigate the decision-making process in machine tool product design, providing scientific and reasonable ways of thinking for industrial design practices. As per the research findings, the following conclusions could be drawn:  
(1) Introduction and validation of the PFA-SEM model  
Figure 5 reveals that in traditional methods, when using entropy weighting as an objective weighting approach, errors in weight allocation may occur, particularly for certain indicators that exhibit significant discrepancies with the original expert opinions. However, the PFA-SEM evaluation method proposed in this paper demonstrates its uniqueness in handling multi-factor and multi-level decision-making problems. Compared to traditional methods, the PFA-SEM approach is more reliable. Traditional methods typically rely on expert experience, with direct modeling to determine weights, while PFA-SEM employs an a priori validation method to determine the effects of each factor before conducting weight calculations. This approach helps mitigate potential errors in weight allocation due to differences in expert opinions, thereby enhancing the accuracy and reliability of decision making. PFA-SEM leverages the theoretical support of PFA theory for paradigm collection, aiding in the more comprehensive collection of data and information, thus providing a more reliable data foundation for the evaluation model. This method is particularly crucial when dealing with complex information from various domains in the decision-making process for machine tool product design. Figure 6: Improvement design drawing for vertical quenching machine tool industrial styling (**a–d**). Furthermore, another significant innovation of the PFA-SEM model is its combination of objective weights from SEM with subjective weights from GRA, thus taking both subjective and objective factors into account. Compared to traditional methods, PFA-SEM provides a more comprehensive and precise method for weight calculation, fully considering the relative importance of different factors. This results in more accurate and trustworthy evaluation outcomes. Finally, compared to traditional methods that only consider information entropy, PFA-SEM is better at avoiding biases in weight allocation caused by outliers. Outliers can have adverse effects on traditional methods, while the a priori validation method used by PFA-SEM helps to eliminate potential outliers, increasing the stability of the evaluation results. Through this comparison, we can emphasize the innovativeness of PFA-SEM in the design decision-making process and how it addresses some limitations of traditional methods, thus providing more scientific, accurate, and reliable decision support. (2) Comprehensive evaluation of machine tool design elements  
Based on PFA-SEM path coefficients and a combination of subjective and objective weighting methods, the impact ranking of design elements was determined as follows: design domain > physical domain > functional domain > technological domain. This finding suggested that industrial styling and man-machine interaction are the aspects in which current machine tool products require the most optimization. In contrast to the traditional focus on functionality in machine tools, the significance of the design domain stands out, which is closely associated with the evolving demand for personalized and user-friendly products in today's market. From a comprehensive perspective, more attention should be given to the visual appearance of machine tools, such as materials and color schemes, and product families should utilize similar design elements to enhance the brand image and recognition of machine tool products. Additionally, the physical structure of machine tools is relatively important, highlighting the need for a rational approach to physical component structuring in machine tool styling design.