Hybrid fuzzy-SVM collaborative reasoning framework for intelligent CNC turning process planning

Introduction: The optimization of machining process decision-making remains a major challenge in intelligent manufacturing due to the uncertainty of process information, incompleteness of rule bases, and the tendency of traditional algorithms to converge to local optima. Therefore, enhancing the adaptability and robustness of decision-making systems is a crucial task for achieving efficient and reliable computer numerical control (CNC) process planning.

Methods: This study proposes a hybrid decision-making approach that integrates fuzzy theory with support vector machines (SVM) to address uncertainty and incomplete knowledge representation in CNC turning. An Analytic Hierarchy Process (AHP) is used to determine the relative importance of influencing factors, and trapezoidal membership functions are designed to determine the credibility of fuzzy reasoning rules. When the credibility value falls below a defined threshold, a linear-kernel SVM model is activated to provide alternative decisions which formed a fuzzy-SVM collaborative reasoning mechanism.

Results: Experimental validation demonstrates that the proposed hybrid fuzzy-SVM collaborative method achieves remarkable classification accuracy on the test dataset. The system maintains stable performance even under low-credibility or incomplete rule conditions. The SVM module effectively compensates for the limitations of the fuzzy reasoning process, thereby improving the robustness of decision inference compared to single-model approaches.

Conclusion: The proposed fuzzy-SVM collaborative reasoning framework enhances the adaptability, stability, and interpretability of CNC machining process decision-making. These findings offer a practical and scalable solution for intelligent process planning in complex and uncertain manufacturing environments.

1 Introduction

With the continuous advancement of modern manufacturing, computer numerical control (CNC) machining technology has achieved remarkable development. As a representative and core component of advanced manufacturing, CNC machining continues to play a pivotal role in the production industry (Xu and Newman, 2006). Consequently, the optimization of CNC machining process routes has become a central research focus aimed at improving efficiency, precision, and automation in modern manufacturing systems.

In early studies, from the perspective of intelligent optimization, Bo et al. developed a dual-linked list-based genetic algorithm that ensures solution feasibility and provides an effective method for process route generation and sequencing (Bo et al., 2006). Guo et al. carried out an in-depth investigation into process route decision-making and established a feature-based decision-making mechanism for shaft component machining processes, laying a foundation for feature-driven CAPP (Computer-Aided Process Planning) systems (Guo et al., 2021). To tackle the challenges of process inference and decision-making in CAPP environments, Afif and Sarhan constructed a process information knowledge base and implemented automatic optimization and sequencing of machining routes using a forward reasoning-based process priority algorithm (Afif and Sarhan, 2025). Building on knowledge reasoning approaches, Jing et al. proposed a 3D CAPP intelligent process route inference engine supported by a process knowledge database and validated its feasibility through keyway feature machining experiments (Jing et al., 2020). Subsequent research has focused on optimization algorithms for improving process planning precision. Zhang et al. formulated the machining process route planning problem as a constrained optimization model and innovatively applied Hopfield neural networks to sequence and solve the optimization process (Zhang et al., 2024). Butdee and Kunhirunbawon introduced fuzzy logic-based feature recognition to classify and identify machining features from geometric and process information, achieving more accurate process route design and parameter selection (Butdee and Kunhirunbawon, 2020).

To enhance process simulation and verification, Hu et al. utilized CAXA CNC Lathe software to simulate machining motion, generate CNC programs, and integrate component similarity analysis to optimize the process analysis workflow, thereby significantly improving process formulation efficiency (Hu et al., 2024). Similarly, Li et al. proposed a CAPP process sequencing algorithm based on genetic edge-selection encoding, and introduced a numerical model that integrates three-dimensional polar radius surface moments and bounding boxes to construct structured process data from key machining parameters (Li et al., 2025). In parallel, advances in signal processing and intelligent feature extraction have contributed to improved fault diagnosis, with Fourier–Bessel–based methods such as empirical Fourier–Bessel heuristic denoising (EFBHD) and shrinkage sliding Fourier–Bessel packet (SSFBP) enabling adaptive spectrum segmentation and accurate extraction of fault-information-rich narrowband features from noisy and non-stationary signals (Zhou et al., 2025; Zhou et al., 2026). In recent years, the introduction of artificial intelligence and large language models (LLMs) has further advanced data-driven process planning research (Li et al., 2024). Zheng Xiaohu proposed a knowledge recommendation method for process decision-making within the LangChain framework, achieving over 90% recommendation accuracy by integrating domain-specific knowledge bases and semantic reasoning (Zheng Xiaohu, 2025). Meanwhile, Su et al. presented a data and knowledge driven decision-making approach that effectively addresses mismatches between designed process routes and real-world manufacturing conditions, improving adaptability and robustness in dynamic production environments (Su et al., 2024).

Although substantial progress has been made in process route decision-making by scholars worldwide, several enduring challenges persist-such as the formalization of knowledge acquisition, the susceptibility of algorithms to local optima, and inefficient transmission of process information (Kaur et al., 2025). To address these issues, this study focuses on the CNC turning process and proposes a novel process decision-making method that integrates fuzzy theory with SVM. By leveraging the strength of fuzzy theory in managing uncertainty and the superior classification capability of SVM, the proposed hybrid approach effectively handles fuzzy information in process decision-making. This integration enhances decision robustness and accuracy, mitigates the tendency of traditional algorithms to converge to local optima, and provides an improved and intelligent decision-making framework for complex machining process environments.

The novelty of this study lies in the development of a fuzzy–SVM collaborative reasoning framework that significantly improves the adaptability, stability, and interpretability of CNC machining process decision-making. The main contributions are summarized as follows:

1. A hybrid process decision-making method that integrates fuzzy theory with SVM is proposed to effectively handle uncertainty and incomplete knowledge representation in CNC turning.

2. The relative importance of the influencing factors is quantified using the Analytic Hierarchy Process, providing a structured basis for decision weighting.

3. Trapezoidal membership functions are designed to compute the credibility of fuzzy reasoning rules, enabling more reliable and interpretable reasoning outcomes.

The rest of the paper is structured as follows: Section 2 elaborates the fuzzy logic theory in decision -making, Section 3 covers the results of decision inference model and case verification of collaborative reasoning model and its discussion. Section 4 concludes this paper.

2 Methodology

2.1 Preliminary analysis for CNC turning process decision-making

CNC turning technology, while rooted in conventional turning processes, exhibits distinct characteristics due to its automated nature. The high efficiency and automation level of CNC lathes necessitate comprehensive analysis of these features and related knowledge when developing machining plans. Prior to CNC turning operations, process planners must program machine tool movements, workpiece processes, tool selection, cutting parameters, and tool paths into the system. During process planning formulation, critical considerations including machining route During process planning formulation, critical considerations including machining route determination, tool selection, and equipment configuration must comprehensively address product quality, production efficiency, safety compliance, and environmental sustainability.

The development of machining process routes for mechanical components constitutes a critical phase in process planning. This phase primarily involves selecting appropriate machining methods for target surfaces, rationally staging manufacturing processes, and scientifically sequencing operations to ensure both processing efficiency and dimensional accuracy. Under standard production conditions, the attainable accuracy range achievable through cost-effective means is defined as the machining method’s economic accuracy. This accuracy range encompasses three key parameters which are economic accuracy and surface roughness for cylindrical turning, economic accuracy and surface roughness for bore machining, economic accuracy and surface roughness for face milling. Detailed specifications are provided in Table 1.

Table 1

Table 1. Economic accuracy and surface roughness of processing methods.

CNC lathes impose stringent requirements on cutting tools. These tools must exhibit not only superior wear resistance, extended tool life, high reliability, precision, rigidity, and durability, but also demonstrate ease of installation, adjustment and effective chip evacuation. When selecting cutting inserts, the following factors require consideration:

a. Cutting inserts material. Cutting tool cutting inserts exhibit significant material diversity, with cemented carbide and coated carbide variants demonstrating the widest industrial adoption owing to their superior performance characteristics. When selecting blade materials, comprehensive consideration of multiple factors is essential, including: the workpiece material, required dimensional tolerances, and specified surface finish requirements.

b. Cutting inserts size. Determining blade dimensions requires comprehensive consideration of critical parameters, including effective cutting edge length, depth of cut, and tool lead angle, to optimize the trade-off between machining efficiency and quality.

c. Cutting inserts shape. The selection of blade geometry is governed by multiple factors, including: workpiece surface topography, machining methodology, targeted tool longevity, and number of insert indexing positions during operations. Comprehensive evaluation of these parameters enables optimal geometry determination for specific machining requirements. Corresponding relationships between machined surface profiles and recommended insert configurations are illustrated in Figure 1.

d. Cutting inserts economy. Tool selection must incorporate comprehensive economic evaluation. When machining accuracy and quality requirements are satisfied, cost-effective inserts should be prioritized to maximize value efficiency.

e. Other. Occupational safety and environmental compliance must be integral to blade selection. This necessitates adherence to industrial safety standards, implementation of hazard mitigation protocols, and preferential use of sustainable tool materials with eco-conscious manufacturing processes to minimize environmental impact.

Figure 1

Figure 1. The shape of the surface to be processed and its applicable blade diagram.

This study focuses on CNC lathes, with processing plans formulated exclusively based on the turning characteristics. When selecting CNC equipment, critical considerations include part machining accuracy, workpiece clamping capacity, specific energy consumption, and capital investment cost.

2.2 Fuzzy reasoning and rule generation mechanism

Process planning decisions involve multifaceted considerations with non-unique solution spaces, necessitating optimal rule selection methodologies. This study employs fuzzy-theoretic production rules to formulate process decision logic, offering dual advantages, i.e., enhanced interpretability and inherent capability for handling ambiguous and uncertain parameters, as represented in Equation 1.

$IF{E}_i\left({\theta }_i,{\lambda }_i\right)THENH\left(CF\left(H\right)\right)(1)$

Where, E_i is the conditional part (known fact), θ_i is the degree of influence of this fact on processing process decisions, λ_i is the degree of membership (credibility) of this fact, H is the result that conforms to this fact, and CF (H) is the credibility of the entire rule.

Owing to the multifactorial nature of process planning decisions, solution spaces are inherently constrained by concurrent parameters. Thus, Equation 1 is extended to derive Equation 2 for enhanced representational completeness.

$IF{E}_1\left({\theta }_1,{\lambda }_1\right)\text{\hspace{0.17em}AND }{E}_2\left({\theta }_2,{\lambda }_2\right)\cdots THENH\left(CF\left(H\right),\beta \right)(2)$

Where: E₁, E₂… are known facts, θ₁, θ₂… are the degree of influence of each fact on processing process decisions, λ₁, λ₂ are the degree of membership (credibility) of each fact, and β is the threshold of this rule.

2.2.1 Determination of degree of influence θ_i by hierarchical analysis

The AHP is a multi-criteria decision-making method that facilitates both qualitative and quantitative analysis in complex decision frameworks to identify optimal solutions. In this study, it has been employed to determine criteria weighing coefficients for process planning decisions. To ensure the scientificity and credibility of the judgment matrix, this study adopted the Delphi method combined with expert consultation, inviting an expert panel consisting of five experts with intermediate or higher professional titles in the field of manufacturing technology and CNC machining. All members of the expert panel have more than 10 years of industry experience or teaching and research background, and are familiar with CNC turning process planning and decision-making processes. Through two rounds of anonymous questionnaire surveys and feedback discussions, the panel members finally reached a consensus on the relative importance of various influencing factors and constructed a judgment matrix (as shown in Equation 3). This method effectively integrates multiple expert opinions, reduces subjective biases, and enhances the empirical basis of the weight coefficients.

During the process of processing technology decision-making, it will be affected by many factors. In this study, we consider five factors to be determined by the knowledge acquisition and finishing results as the credibility evaluation factors, which are dimensional accuracy S0, surface roughness value S1, hardness value of the processed material (HB) S2, diameter of the rod material S3, and length of the rod material S4. In production environments, statistically significant variations exist in the weighting coefficients of these five factors. To quantify these coefficients with precision, establishing a pairwise comparison scale constitutes the foundational step, as defined in Table 2.

Table 2

Table 2. Pairwise comparison scale.

Subsequently, pairwise comparisons of the five criteria were conducted using the established scale. This systematic comparison elucidates the relative importance and interdependencies among the criteria, yielding comparison matrix A as follows:

$A=\left(\begin{array}{ccc}\begin{array}{l}1\\ 1\\ 1/2\\ \begin{array}{l}1/3\\ 1/4\end{array}\end{array}& \begin{array}{l}\begin{array}{l}1\\ 1\end{array}\\ 1/2\\ 1/3\\ 1/4\end{array}& \begin{array}{cc}\begin{array}{cc}\begin{array}{l}\begin{array}{l}2\\ 2\end{array}\\ 1\\ 1/2\\ 1/2\end{array}& \begin{array}{l}\begin{array}{l}3\\ 3\end{array}\\ 2\\ 1\\ 1\end{array}\end{array}& \begin{array}{l}\begin{array}{l}4\\ 4\end{array}\\ 2\\ 1\\ 1\end{array}\end{array}\end{array}\right)(3)$

Based on the comparison matrix A, the maximum eigenvalue λ_max = 5.013 is obtained, and the eigenvector ω corresponding to the maximum eigenvalue = [0.64, 0.64, 0.34, 0.19, 0.17] is obtained. The weight coefficients are obtained by normalizing the eigenvector ω corresponding to the maximum eigenvalue, as defined in Table 3 and Figure 2.

Table 3

Table 3. Weight coefficients of factors affecting processing technology decision.

Figure 2

Figure 2. Feature weight bar chart.

In this paper, a Consistency Index (CI) was computed and then the consistency criterion was applied to assess the acceptability of the matrix. The CI is determined to test the employment of criterion using Equations 4, 5. Based on the order of the judgment matrix, the average Random Consistency Index (RI) has also been determined. The RI values are obtained from Table 4.

$CI=\frac{{\lambda }_{\max }-n}{n-1}(4)$

Table 4

Table 4. Mean stochastic consistency indicator.

In Equation 4, λ_max denotes the maximum eigenvalue of the judgment matrix and n represents its order.

$\text{CR}=\frac{CI}{RI}(5)$

where R_I is an average random consistency index.

According to Equations 4, 5 and Tables 1, 2, the consistency index CR 0.003 has been selected, which is less than 0.1, and passes the consistency test.

2.2.2 Membership function

The membership function in fuzzy logic quantifies the degree to which an element belongs to a fuzzy set. Given that the problem domain described in this study exhibits a trapezoidal distribution, the trapezoidal membership function was selected for calculating membership degrees. Its mathematical Equation 6 is given as follows.

$u\left(x\right)=\left\{\begin{array}{l}0,x<a_1\text{\hspace{0.17em}or\hspace{0.17em}}x>b_2\\ \frac{x-a_1}{a_2-a_1},a_1\le x\le a_2\\ 1,a_2\le x\le b_1\\ \frac{b_2-x}{b_2-b_1},b_1\le x\le b_2\end{array}\right.(6)$

Under the condition of a1<a2<b1<b2, this function defines a trapezoidal membership function with output values ranging from 0 to 1, representing the membership degree of input x in the fuzzy set. A higher value of u(x) indicates a stronger degree of membership, while a lower value signifies weaker membership. In practical applications, membership degrees may exhibit low or high values depending on specific problem contexts, necessitating detailed case-by-case analysis.

The parameter β_g denotes the integrated credibility, reflecting the aggregated confidence level obtained from multi-source evidence. In this study, the integrated credibility for each reasoning rule is computed according to the following Equation 7.

${\beta }_g=CF\left(H\right)\times {\displaystyle \sum _{i=1}^n}\left({\theta }_i\times {\lambda }_i\right)(7)$

The comprehensive confidence of each rule calculated can be used in the inference process in the fuzzy inference system to obtain the final output.

2.3 Process rule reasoning mechanism based on credibility calculation

Process engineers conduct extensive process analysis and verification when designing CNC lathe machining schemes. First, they thoroughly analyze part design specifications from technical drawings or 3D models, including geometric requirements, dimensional tolerances, and surface roughness parameters. Second, they process this technical information using manufacturing knowledge and empirical expertise to make engineering judgments. This decision-making methodology parallels elements of the structural design reasoning process. Consequently, the machining process reasoning system employs a forward chaining control strategy. To address the inherent fuzziness in manufacturing decisions, this study introduces a credibility-based forward chaining mechanism (FBCM) incorporating integrated credibility calculations, as illustrated in Figure 3. The process of the FBCM as follows:

Figure 3

Figure 3. The process of forward reasoning mechanism based on credibility.

Step 1: The process information is extracted from the parts and converted into input parameters of the forward reasoning mechanism for the confidence calculation.

Step 2: Determine whether the rule set is empty. If it is not empty, start to reason, otherwise it ends.

Step 3: The comprehensive confidence βg for each rule is calculated and compared with the preset threshold β. If βg is greater than β, the conclusion of the rule is extracted and arranged in descending order according to the size of βg.

Step 4: Determine whether the rule set has been read. If all rules in the set are read, the reasoning ends, and the reasoning continues.

2.4 Case reasoning description

As an illustrative example, representative rules from the machining decision rule base are selected for case analysis, with typical instances summarized in Table 5.

Table 5

Table 5. Partial rules for processing technology decision making.

From Table 5, the given input parameters are dimensional accuracy grade “IT7”, surface roughness grade “Ra 3.2 μm”, material hardness “180 HB”, rod diameter “D = 50 mm”, and rod length “L = 220 mm”. The membership functions quantify the credibility of each input fact for subsequent rule matching. As shown in Table 5, the weight coefficients (θ) of process decision factors are [0.32, 0.32, 0.17, 0.10, 0.09]. These weights enable calculation of the integrated credibility (βg) for Rules 1-3 using Equations 8–10.

${\beta }_{g1}=0.9\times \left(\begin{array}{l}0.32\times 0+0.32\times 0+0.17\times 1\\ +0.1\times 1+0.09\times 1\end{array}\right)=0.324(8)$

${\beta }_{g2}=0.95\times \left(\begin{array}{l}0.32\times 1+0.32\times 1+0.17\times 1\\ +0.1\times 1+0.09\times 1\end{array}\right)=0.95(9)$

${\beta }_{\mathrm{g}3}=0.95\times \left(\begin{array}{l}0.32\times 1+0.32\times 1+0.17\times 1\\ +0.1\times 0.71+0.09\times 0.73\end{array}\right)=0.89(10)$

The determined integrated credibility values indicate that Rule 2 achieves β_g = 0.95, exceeding both the credibility threshold of 0.85 and the values of Rules 1 and 3. Consequently, only Rule 2 fires, executing its conclusion. The resulting machining sequence is: (1) rough turning, (2) semi-finish turning, and (3) precision turning. The selected machine tool is a CAK50135 lathe, using T-shaped blade.

2.5 Case reasoning description

The confidence heatmap visually presents the data confidence level in terms of color depth, with red representing high confidence and blue representing low confidence, helping to quickly identify reliable areas.

In order to visually demonstrate the confidence performance of different rules under different input parameters and enhance the visualization and interpretability of the results, this study designed a 3-row x 12 column heatmap, as shown in Figure 4. This figure shows the comprehensive confidence heatmap of three typical rules under different input parameter combinations. The depth of colors in the figure reflects the credibility of the rules, with darker colors indicating higher confidence. From the graph, it can be seen that Rule 2 maintains a high confidence level (close to 0.95) under most parameter combinations, while Rule 1 and Rule 3 have low confidence levels or even close to 0 under certain parameter combinations. This indicates that Rule 2 has stronger adaptability and reliability under given input conditions. The heatmap provides an intuitive validation of the effectiveness of the credibility-based inference mechanism in rule screening and offers a clear visual basis for triggering the subsequent SVM-based inference module.

Figure 4

Figure 4. Rule confidence heatmap.

3 Process decision inference model based on fuzzy theory and SVM

Although the credibility-based process rule reasoning mechanism provides interpretable decision logic and effectively handles uncertainties in machining process planning, its limitations become evident when confronted with low-credibility rules or rule base incompleteness. Under such conditions, the mechanism fails to generate reliable process solutions. To overcome this limitation, an SVM-based inference model is introduced as a complementary decision-making module. When the fuzzy reasoning mechanism becomes inoperative, the SVM model activates to provide alternative decisions, thereby enhancing the expert system’s robustness while mitigating the inherent limitations of rule-based credibility approaches.

3.1 SVM-based inference model for process decision-making

The fundamental principle of SVM is to identify an optimal hyperplane that partitions the feature space while maximizing the margin between distinct classes. For linearly separable cases, SVM constructs a hyperplane that perfectly segregates the two classes. When linear separability is unattainable, it employs soft-margin optimization. This approach permits controlled classification errors through the introduction of slack variables. The SVM formulation is as follows.

Hyperplane as shown Equation 11:

$w^T·x+b=0(11)$

Where: w is the normal vector, b is the intercept, and x is the eigenvector.

Optimize target as shown Equation 12:

$\min \frac{1}{2}{‖w‖}^2+C·\sum _{i=1}^n{\epsilon }_i(12)$

Where: C is a regularization parameter, it is the slack variable of the ith sample.

Constraints as shown Equations 13, 14:

$y_i·\left(w^T·x+b\right)\ge 1-{\epsilon }_i,\forall i(13)$

${\epsilon }_i\ge 0,\forall i(14)$

Where: y_i is the real label of the ith sample.

3.2 Design of SVM inference model

3.2.1 Process data collection and enhancement

The dataset collected in this study includes a total of 30 independent CNC turning process decision samples, each consisting of five input features (dimensional accuracy level, surface roughness, material hardness, bar diameter, and bar length) and a five digit digital output decision label (corresponding to the machining process, machine tool, and cutting tool). The combination of data sources with the production experience of partner enterprises, domain expert knowledge, and basic rule data generated from standard process manuals ensures the rationality and logical foundation of the project.

However, a dataset size of only 30 independent samples is not statistically sufficient to validate intelligent decision models. The results generated from the small sample test set have high variance and low confidence. However, collecting large-scale industrial data is very difficult, and this study must use data augmentation techniques (SMOTE method) to expand the dataset to 200 samples to demonstrate the robustness of model performance, rather than unexpected or overfitting results on micro datasets.

SMOTE is a classic technique for synthesizing minority class oversampling, used to solve class imbalance problems. It is based on the nearest neighbor relationship in the feature space and synthesizes new samples by linear interpolation between minority class samples, thereby increasing dataset diversity and avoiding overfitting caused by simple replication. This method can effectively improve the generalization ability and statistical significance of machine learning models under small sample conditions.

3.2.2 Comparative analysis of inference model construction and algorithm performance

The SVM receives preprocessed feature vectors rather than raw input data. This study requires not only preprocessing of input parameters but also conversion of textual labels into numerical representations to facilitate SVM model training. The architecture of the SVM inference model is presented in Figure 5. The procedure of Fuzzy-SVM is described as follows:

Figure 5

Figure 5. SVM inference model.

The 5-digit encoding scheme simplifies initial validation of a hybrid reasoning framework for CNC turning, capturing core decision logic like machining stage selection, machine tool choice, and insert type. It isolates and evaluates the core collaborative reasoning mechanism (fuzzy logic and SVM) without full-scale process planning complexities. While real-world process planning for complex components involves more, the framework is extensible. The output code structure can expand by enriching the rule base and SVM training data. The main contribution is establishing a robust decision-switching logic between knowledge-driven and data-driven modules, serving as a foundation for future practical systems.

Step 1: The data is divided using 70% training set and 30% test sets.

Step 2: Text-based outputs are converted into numerical labels to ensure effective model training. Each label uses a five-digit code: Digits 1–3 denote the presence of rough, semi-finishing, and precision machining (1/0), while Digits 4 and 5 index the machine tool model and cutting-insert type. This structured encoding transforms descriptive information into machine-readable form, improving training efficiency and classification performance. The scheme is illustrated in Figure 6.

Figure 6

Figure 6. All meanings of labels.

Step 3: The training set and test set data are normalized, and the normalization method is shown in Formula 15.

$X_{scale}=\frac{X-X_{\min }}{X_{\max }-X_{\min }}(15)$

Step 4: The model is trained based on the training set data and the trained model is saved.

Step 5: The trained model is verified using the test set and finally the results are evaluated.

To determine the superiority of the support vector machine algorithm in small sample prediction cases within the framework of this study, this paper adopts a comparative analysis method combining horizontal and vertical comparisons, systematically studying the performance of different algorithms under various parameter configurations. In terms of horizontal comparison, the performance variation patterns of the linear kernel function (Equation 16) and radial basis kernel function (Equation 17) under different parameter settings are analyzed separately. In terms of vertical comparison, the prediction accuracy of the BP neural network algorithm is compared.

$K\left(x_i,x_j\right)=x_i·x_j(16)$

Where: x_i is the input variable and x_j is the input variable.

$K\left(x,\mathrm{z}\right)=\exp \left(-\gamma ·{‖x-\mathrm{z}‖}^2\right)(17)$

Where, x is the input vector, z is the input vector, γ is a positive scalar parameter, ‖x - z‖ is the Euclidean distance between x and z.

In this study, we utilized the Python language for algorithm development. Furthermore, by utilizing the scikit-learn library, we obtained the accuracy comparison charts for the SVM training and testing sets with the linear kernel function, as illustrated in Figure 7. Additionally, we obtained the accuracy comparison charts for the SVM training and testing sets with the radial basis function, as depicted in Figure 8. Lastly, we also obtained the accuracy comparison charts for the training and testing sets of the Bp neural network, as shown in Figure 9.

Figure 7

Figure 7. Comparison of accuracy of SVM training set and test set of linear kernel functions.

Figure 8

Figure 8. Comparison of accuracy of SVM training set and test set of radial basis function.

Figure 9

Figure 9. Comparison of accuracy between training set and test set of Bp neural network.

By comparing the parameter tuning results of the three models, linear kernel SVM exhibits significant comprehensive advantages. When the regularization parameter C is at 0.9, the highest testing accuracy can reach 0.88, which is significantly better than the 0.75 of RBF kernel SVM and the 0.66 of BP neural network. Meanwhile, the training and testing accuracy curves are close, indicating good generalization ability and no significant overfitting. In terms of parameter adjustment, linear kernel SVM maintains stability and high accuracy over a wide range of C, with low sensitivity and intuitive and reliable parameter tuning.

In contrast, RBF kernel SVM is extremely sensitive to the gamma parameter, and the training accuracy continues to increase with the increase of gamma. However, the improvement in testing accuracy is limited, and it is prone to overfitting or underfitting, making tuning difficult. The BP neural network is significantly affected by its structure, with significant performance fluctuations under different layers and neuron configurations. The testing accuracy ranges from 0.58 to 0.73, and its stability and reproducibility are weak. Additionally, the network structure adjustment is complex and the computational cost is high.

In summary, linear kernel SVM performs the best in terms of testing accuracy, generalization performance, parameter stability, and computational efficiency, making it particularly suitable for practical engineering applications. RBF kernel SVM has strong sensitivity to parameters, and the optimization of BP neural network structure is complex and the results fluctuate greatly. Therefore, on the dataset of this study, linear kernel SVM is the optimal choice.

In addition, the linear SVM model designed in this study can be expressed in the form of f (x) = w^Tx + b, where w is the weight vector, as shown in Figure 10.

Figure 10

Figure 10. Feature weight histogram.

3.3 Performance evaluation of SVM model

To rigorously evaluate the generalization ability of the Support Vector Machine (SVM) model and avoid making overly optimistic estimates of its performance, we conducted a 5-fold cross-validation on the entire dataset. The dataset was randomly divided into 5 equally sized folds. In each iteration, 4 folds were used for training, while the remaining 1 fold served as the test set. This process was repeated 5 times, with each fold being used exactly once as the test set. Finally, all prediction results were combined, and a confusion matrix (Figure 11) was generated to gain a deeper understanding of its performance, especially in identifying any potential class imbalance or specific misclassifications.

Figure 11

Figure 11. SVM model confusion matrix.

By analyzing the confusion matrix, it can be seen that the SVM model exhibits good classification performance in eight types of tasks. For categories such as 10112 and 11112, this model can achieve correct classification of all or most samples without misclassification. However, there are cases of misclassification between categories with high feature similarity, such as between categories 11112 and 11113, and between categories 11122 and 11123. This indicates that the separability of these category combinations in the input feature space is relatively weak, or that existing features cannot provide sufficient discriminative information. In addition, the distribution differences in sample size between different categories may have a certain impact on the performance evaluation of the model. According to calculations, the overall accuracy of the model on the test set is approximately 0.88, indicating that the model has achieved good results under the current data and feature conditions. In the future, data resampling can be used to improve class balance, further optimize feature engineering, adjust model hyperparameters, or introduce ensemble learning strategies to further enhance the classification robustness and accuracy of the model.

3.4 Fuzzy-SVM collaborative reasoning mechanism and case verification

3.4.1 Comparative analysis of reasoning strategies

In order to further clarify the role of each module, a comparative analysis was conducted among three reasoning strategies: the pure fuzzy reasoning system, the pure SVM-based approach, and the proposed hybrid framework.

1. Pure fuzzy reasoning system: This system relies entirely on the credibility of predefined rules. In cases where the credibility of all candidate rules falls below the predefined threshold, the system results in decision failures (i.e., no valid output) rather than misclassifications. This limitation highlights its dependency on complete and high-credibility rule sets.

2. Pure SVM-based approach: While this data-driven model can provide decisions under all input conditions and achieves an accuracy of 0.88 in our test set, its main drawback is the lack of explicit process logic and interpretability. The decision process is opaque, making it difficult to explain or validate in engineering terms.

3. Proposed hybrid framework: Our framework effectively combines the strengths of both methods. It maintains the interpretability of fuzzy logic for high-credibility scenarios, while seamlessly switching to the SVM module to avoid decision failures when rule credibility is low. This design ensures decision continuity and robustness without sacrificing transparency, thereby achieving a superior balance between performance and explainability.

3.4.2 Fuzzy-SVM collaborative reasoning mechanism

From the perspective of knowledge representation, the proposed collaborative reasoning framework integrates two complementary forms of knowledge: the fuzzy reasoning module embodies explicit knowledge derived from domain experts and standardized practices, while the SVM-based module captures implicit (tacit) knowledge—experiential decision patterns learned from historical data that are difficult to formalize. This dual-knowledge design provides a theoretical foundation for the hybrid approach, where explicit knowledge ensures transparency and interpretability in high-confidence scenarios, while implicit knowledge enhances system adaptability when rule reasoning becomes uncertain. Consequently, the framework functions not merely as a credibility-based switching mechanism but fundamentally as a knowledge complementarity mechanism, theoretically explaining its superiority over approaches that rely solely on rule-based or data-driven reasoning.

In summary, each of the two reasoning mechanisms possesses distinct advantages. Therefore, this paper integrates both approaches into a dynamic collaborative framework, primarily utilizing fuzzy theory-based reasoning while employing the SVM model as a compensatory mechanism. The operational process of this collaborative reasoning mechanism is depicted in Figure 12. When fuzzy reasoning fails due to low rule credibility or an incomplete knowledge base, the system automatically switches to the SVM module. Based on the patterns learned from historical data, SVM provides statistical support for decision-making and ensures robust performance through high classification accuracy validated by cross-validation. Consequently, SVM and fuzzy reasoning complement each other, jointly constructing a hybrid system that combines expert knowledge interpretability with data-driven reliability, significantly enhancing the credibility and adaptability of process decision-making in intelligent manufacturing environments.

Figure 12

Figure 12. Cooperative reasoning mechanism operation process.

3.4.3 Case validation one

Case One employs selected rules from Table 5 as a case demonstration of the collaborative reasoning process. Given the input parameters-dimensional accuracy level 12, surface roughness Ra 12.3, material hardness (HB) 150, rod diameter D = 50 mm, and rod length L = 220 mm, the comprehensive credibility is calculated using Equation 7.

According to Table 6, the comprehensive credibility of all three rules falls below the threshold value, indicating that none is credible. Consequently, the SVM inference model is utilized, yielding an output of [1,0,0,1,1]. This binary vector corresponds to the machining solution “rough turning - CAK50135 - W-shaped blade”.

Table 6

Table 6. The credibility calculation result of the rule.

3.4.4 Case validation two

To fully verify the ability of the proposed fuzzy SVM collaborative reasoning mechanism to handle complex real-world parts, Case 2 introduces a stepped shaft part containing multiple machining features as a comprehensive case. This type of shaft component includes two sections of outer cylindrical surface, one relief groove, and one external thread. With diverse features and clear technical requirements, it is suitable for demonstrating the system’s processing strategy and automatic switching logic for different features on the same component.

Standard feature processing (dominated by fuzzy reasoning): For outer circular surfaces and threads, the system found highly matching rules in the rule library. For example, for the Φ60h7 outer circle surface, the comprehensive credibility of its input parameters and high-precision outer circle machining rules in the rule library (Formula 7) β_g is calculated to be 0.91, which is higher than the threshold (β = 0.85). Therefore, the system adopts a fuzzy reasoning module to quickly output detailed process decisions including multiple processes (rough turning semi precision turning precision turning), equipment (CAK50135), and cutting tools (T-shaped blades). The same applies to other standard features as shown in Table 7.

Table 7

Table 7. Complex staircase axis feature list and processing strategy.

Nonstandard feature processing (SVM automatic switching): When the system processes the return groove feature, due to the lack of clear and highly reliable rules in the rule library for the specific size combination of “3×Φ48” return grooves, the calculated comprehensive credibility β_g is only 0.52, which is lower than the set threshold. According to the collaborative reasoning process shown in Figure 12, the system automatically triggers the SVM compensation reasoning module. The SVM model receives feature vectors such as size, tolerance, and roughness of the return groove, predicts based on historical data patterns, and outputs decision codes. After decoding, the process plan obtained is “slotting”, the recommended equipment is “CAK50135”, and the cutting tool is “slotting blade”.

Overall, this chapter develops a hybrid decision inference framework that combines credibility-based fuzzy reasoning with an SVM auxiliary model. The results confirm that fuzzy reasoning performs well under high-credibility conditions, while the SVM model effectively compensates when rule credibility is low or the rule base is incomplete. Together, the two mechanisms provide a robust and reliable foundation for intelligent CNC process decision-making.

4 Conclusion

This paper proposes a hybrid inference framework based on collaborative fuzzy theory and SVM to address critical challenges in CNC turning process planning, such as knowledge uncertainty and rule incompleteness. By quantifying factor weights via the AHP and defining rule credibility through trapezoidal membership functions, we constructed a transparent and interpretable fuzzy inference mechanism.

To address the limitations of rule coverage, a Linear-SVM model was introduced as a dynamic compensatory mechanism. Validated through cross-validation, this model achieved high classification accuracy and effectively solved decision failures in low-credibility scenarios. The case study demonstrates that the proposed credibility-based switching strategy allows the system to handle non-conventional parameters robustly. While the current study validates the feasibility of this data-knowledge dual-driven framework on a typical engineering dataset, future work will focus on expanding the dataset size and exploring comparisons with a broader range of algorithms to further enhance the system’s scalability.

Data availability statement

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

Author contributions

HQ: Writing – original draft, Methodology. RR: Formal Analysis, Project administration, Writing – review and editing. LZ: Methodology, Writing – original draft. JZ: Software, Visualization, Data curation, Writing – review and editing.

Funding

The author(s) declared that financial support was received for this work and/or its publication. The authors declare that the research is supported by Specialized Intelligent Manufacturing Engineering Laboratory, Platform ID: PT2022TS02.

Conflict of interest

Author JZ was employed by Liao Shen Industries Group Co. Ltd.

The remaining author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Generative AI statement

The author(s) declared that generative AI was not used in the creation of this manuscript.

Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.

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