3.1.1. XGBoost feature selection.

Prior to model construction, the XGBoost method is first utilized to define the antecedent attributes. The specific procedure is outlined as follows:

A dataset containing samples and feature values is defined as:

(4)

where is the predicted value, represents the decision tree, denotes the total number of decision trees, indicates the structure of a decision tree, and represents the tree space. The objective is to minimize Equation (5).

(5)

where is the optimization objective, is the loss function, and is the regularization term. The loss function and gain function are given by Equations (6) and (7), respectively.

(6)

In the equation, represents the loss function, denotes the iteration of , is the regularization term, which represents the second-order Taylor series of at the iteration, and and indicate the first-order and second-order gradients, respectively. In this study, the gain function described in the equation uses Equation (7) as the metric for determining the optimal split node.

(7)

In equation, represents the gain function; and denote the samples in the left and right nodes after splitting; and , and are penalty parameters. The gain indicates the gain score of each split in the tree. The final feature importance score is calculated by the average gain. The average gain is defined as the total gain across all trees divided by the total number of splits for each feature. A higher feature importance score implies greater significance of the corresponding feature.

In the EBRB rule-based construction process of this study, the two most important parameters are selected for building the rule base.

3.1.2. Establishing the EBRB rule base.

As an expert system, the BRB is composed of a series of belief rules (BRs). The EBRB, as a variant of the BRB, is similarly constructed from multiple extended belief rules (EBRs). The extended belief rule (EBRB) can be expressed as:

(8)

where is the rule index. represents the antecedent attribute, denotes the number of antecedent attributes, is the reference value of the antecedent attribute, is the number of reference values, represents the matching degree of the corresponding reference value, indicates the total number of rules in the rule base, denotes the reference value of the consequent attribute, and represents the belief degree of the reference value in the consequent of the rule (if , the rule is complete; otherwise, it is incomplete). The hyperparameters in the model are and , where is the attribute weight, which represents the importance of the attribute, and is the rule weight.

The construction of the EBRB system differs from that of the BRB system in that the EBRB system is generated on the basis of existing data, with specific generation rules as follows:

Step 1: On the basis of expert knowledge, the reference values for each antecedent attribute and the consequent attributes are determined.

Step 2: Using the and generated in Step 1, the input data are transformed into a corresponding belief distribution of the following form:

(9)

Let represent the utility value of the reference value ; simultaneously, it is necessary to ensure that . Then, is calculated as follows:

(10)

For the consequent component corresponding to , the subsequent form of the belief distribution for evaluation levels can also be calculated via a method similar to Equation (9).

(11)

Through the aforementioned calculations, each piece of data is transformed into a rule form with belief distributions, thereby constructing the initial rule base.

Step 3: Determine the parameters of the EBRB system, including the attribute weights and rule weights. In the original EBRB, the rule weights and attribute weights are provided by experts.

Fig 2 illustrates the rule construction process of the NCR-EBRB model.

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Fig 2. Construction process of the NCR-EBRB rules.

https://doi.org/10.1371/journal.pone.0347303.g002

3.2.1. Neighborhood covering reduction.

First, we briefly introduce the preliminaries of neighborhood coverage reduction. [23–25]

1. Define 1. Neighborhood covering

Let be the data space of sample , and be the neighborhood of , which is defined by the formula , where is a threshold and is a distance function representing the distance between any two sample points. The complete set of all neighborhoods is denoted as , and the union of these neighborhoods forms coverage of the data space. The neighborhood coverage is denoted as .

Specifically, for each sample in the data space, its neighborhood contains all points whose distance from does not exceed the threshold . The set of neighborhoods defined in this way can cover the entire data space, meaning that all the data points belong to at least one neighborhood. This coverage method is termed neighborhood coverage.

In data coverage, neighborhoods frequently overlap, and some neighborhoods may be redundant in preserving the data distribution structure. To reveal the fundamental structure of the data space, eliminating these redundant neighborhoods is critical, thereby obtaining more compact and efficient coverage.

By removing neighborhoods that are unnecessary for representing the data distribution structure, the coverage can not only be simplified but also enhance the efficiency of data analysis and processing. A more streamlined coverage helps reduce computational complexity and provides a clearer representation of the key features and patterns inherent in the data.

1. Define 2. Neighborhood covering reduction

Let be a coverage of the data space. For a neighborhood , after removing from the neighborhood set, a new set is obtained. If the union of the remaining set still covers the entire data space, i.e.,, then the neighborhood is considered reducible; otherwise, it is irreducible.

Furthermore, if every element in the neighborhood set is irreducible, the coverage is termed irreducible; otherwise, is termed reducible.

1. Definition 3. Relative neighborhood covering reduction

Let be a neighborhood coverage, be the sample set, and be a neighborhood. If such that , then is considered a relatively reducible neighborhood with respect to ; otherwise, it is relatively irreducible. If all neighborhoods in are relatively irreducible, the neighborhood coverage is termed relatively irreducible.

1. Define 4. Measure the Sample Similarity

To establish neighborhoods within the dataset, the distances between samples are first calculated. Given that each rule in the EBRB rule base consists of numerical data, the Euclidean distance is adopted to calculate the similarity between rules.

1. Define 5. Reduction

Given a sample , its neighborhood is composed of data points close to .

(12)

where is the distance function and where is the distance threshold, which represents the radius of the neighborhood. When the neighborhood of a sample is computed, all data points whose distance from is less than or equal to are included within this neighborhood.

Relying solely on threshold-based neighborhood radius settings may introduce certain limitations. Therefore, the concepts of nearest hit and nearest miss are further introduced to enhance the granularity of analysis. For a sample , its nearest hit is defined as the closest sample belonging to the same class. If a class contains only one sample, the sample itself is designated its nearest hit. Conversely, the nearest miss is defined as the closest sample belonging to a different class from .

On the basis of the above definitions, the classification margin is defined as the difference between the distances from a sample to its nearest miss and nearest hit. Specifically, for a given data point , two critical neighbors are defined: the nearest hit and the nearest miss . The nearest hit is the closest instance sharing the same class as , whereas the nearest miss is the closest instance belonging to a different class. If a class contains only one member, the nearest hit for that member is designated as itself. Ultimately, the classification margin of the data point is determined by the difference in its distances to these two critical neighbors. The formula for calculating the classification margin is as follows:

(13)

Notably, the classification margin can potentially take negative values. These cases indicate that the sample may be misclassified when the nearest neighbor rule is used. To address this issue, any negative classification margin is adjusted to zero, i.e., is set in such cases. Fig 3 illustrates the reduction results of a dataset after nearest neighbor analysis.

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Fig 3. Neighborhood coverage reduction for noisy data: (a) original data, (b) calculation of the neighborhood coverage, (c) neighborhood coverage reduction, and (d) result.

https://doi.org/10.1371/journal.pone.0347303.g003

NCR ensures reasoning completeness by maintaining rule coverage sufficiency (i.e., all samples are covered by at least one rule). Meanwhile, NCR preserves semantic integrity by selecting rules without altering their structures (including semantic attributes and belief distributions) and prioritizes expert-defined critical decision boundary rules via classification margin analysis (Eq. 13).

3.2.2. Search the rule base.

The previous sections introduced the core relative neighborhood covering component in the rule reduction algorithm. However, generating a small set of rules that cover the original rules remains a challenging problem, as the search for a minimal rule set is an NP-hard problem [26]. Nevertheless, multiple strategies exist for searching suboptimal rule sets, such as forward search, backward search, and genetic algorithms [27]. In this study, the forward search technique is considered, which begins with an empty rule set and incrementally adds new rules one by one. At each step, the consistent neighborhood that covers the most samples is selected to generate a rule, achieving time complexity. The specific steps are as follows:

3.2.3. Reasoning of the EBRB.

Once the EBRB rule base is constructed, reasoning can be performed on the query data to obtain outputs.

Step 1: The query data are converted into the form of belief distributions, as described in Section 2.1. This ensures that the query data maintain consistency in representation format with the data in the existing rule base, thereby facilitating subsequent reasoning and analysis.

Step 2: The activation weight for each rule in the rule base due to data input is calculated, as all the rules in the rule base are activated upon data input. The distance between the input data and the rules is computed via the Euclidean distance method, as shown below:

(14)

Here, , ; if , this implies that the rule is not activated.

Step 3: For rules satisfying the evidential reasoning algorithm is employed to fuse them, thereby generating the inference result .

(15)

where

(16)

(17)

For classification problems, the final result is determined via the following approach:

(18)

3.3.1. Optimization of the evidence reasoning (ER) approach.

Prior to parameter optimization, the original ER reasoning engine must be optimized. This is because although the NCR-EBRB rule base established in Section 3.2 can effectively replace the original redundant rule base with fewer rules, this does not guarantee the absence of redundant rules in the constructed rule base. Therefore, further optimization of the reasoning engine is needed.

In traditional EBRB systems, when the rule base is established and the input data to be evaluated are provided, the rules in the rule base are activated. For rules satisfying , the ER reasoning engine is employed for inference. However, during the rule fusion process in classification EBRB systems, the following issue arises: a rule with a high matching degree and numerous redundant rules with extremely low matching degrees are simultaneously activated and fused. Intuitively, the inference result should align with the rule of a high degree of matching. However, the presence of many redundant rules with low matching degrees leads to inaccuracies in the final inference. Therefore, a method must be adopted to restrict the number of activated rules. In this study, a threshold is applied to limit the number of rules. can represent either the specific quantity of rules to be fused or the percentage of rules to be fused relative to the total activated rules.

3.3.2. Optimization of NCR-EBRB parameters via P-CMA-ES.

In traditional EBRB models, rule weights , attribute weights and consequent attributes are typically manually assigned by experts. However, in practical applications, as the number of rules increases, it becomes challenging for experts to provide precise values for each parameter. Therefore, the introduction of a parameter training mechanism becomes particularly critical. Through iterative optimization of the learning directions, more accurate information can be effectively aggregated, thereby significantly enhancing the performance of the NCR-EBRB model.

Since the model proposed in this study is applied to classification tasks, the consequent attribute is determined by the category to which the samples belong; thus, parameter optimization is not performed on the consequent attribute .

(19)

where 𝑃 denotes the parameters of the NCR-EBRB. The parameter optimization model of the NCR-EBRB system is as follows:

(20)

Here, represents the loss function, whereas and are the rule weights and attribute weights mentioned above.

in Eq. (19) is the well-known cross-entropy loss function. The advantage of the cross-entropy loss function lies in its sensitivity to mispredictions: compared with the mean squared error, it imposes a greater penalty on incorrect predictions, thereby driving the model to learn rapidly. In this study, the cross-entropy loss function is selected as the objective function of the model:

(21)

Here, is a binary variable (0 or 1), which takes a value of 1 when the sample belongs to the class, represents the number of classes, represents the number of samples, and denotes the predicted probability of the sample for the class.

The model proposed in this study employs the P-CMA-ES method for parameter optimization. This is because, compared with other algorithms such as random search [28], gradient descent [29], and Bayesian optimization [30], P-CMA-ES can generate solutions within the feasible region, ensuring that the solutions strictly satisfy the equality constraints [31,32]. The steps are as follows:

1. Step 1: Parameter initialization:

The initial parameter set is defined as follows:

(22)

1. Step 2: Sampling

Sampling operations are performed to generate a population:

(23)

where represents the solution in the offspring of the generation, denotes the mean of the population, is the step size, denotes the normal distribution, and is the covariance matrix of the generation.

1. Step 3: Prediction

Projection operations are performed to satisfy the following constraints:

(24)

The hyperplane can be expressed as , where represents the number of variables in the equality constraints of the solution , denotes the number of equality constraints in the solution and is the parameter vector.

1. Step 4: Selection

Selection operations are performed to update the population mean , where represents the solution among solutions in the generation denotes the offspring population size.

1. Step 5: Adaptation operations

Adaptation operations are executed to update the covariance matrix.

The above optimization process is recursively iterated until the optimal solution is obtained. The optimal EBRB model can then be constructed.

4.1.1. Experiment definition.

To validate the effectiveness of the proposed NCR-EBRB diabetes diagnosis model, this section conducts an experimental analysis using real-world clinical diabetes diagnostic data. [33]. The data were collected from Iraqi society, as they were acquired from the laboratory of Medical City Hospital and (the Specializes Center for Endocrinology and Diabetes-Al-Kindy Teaching Hospital).

The dataset comprises 1000 patients and covers three classes, namely, diabetic, nondiabetic, and predicted diabetic, with 844, 103, and 53 patients, respectively. Detailed information on the data parameters is presented in Table 1.

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Table 1. Overview of Patient Distribution and Data Parameters in the Study Dataset.

https://doi.org/10.1371/journal.pone.0347303.t001

In the experiments of this section, comparative experiments are conducted with decision trees, two ensemble models of decision trees (Bagging Tree and Boosting Tree), K-Nearest Neighbor (KNN), Support Vector Machine (SVM), and the single EBRB model to demonstrate the advancement of the proposed model.

4.1.2. Model construction and parameter setting.

Equations (7)-(10) demonstrate the generation process of the EBRB rules. Among the subjectively set parameters are the attribute weights , rule weights , and utility values . In the original EBRB, the attribute weights and rule weights are assigned by experts. In the experiments of this study, the original values are set to 1. For , the utility values are generated through clustering from the data, with the quantity set to three.

The modeling steps of the NCR-EBRB applied to diabetes prediction can be described as follows:

1. Step 1: Dataset partitioning

To demonstrate the effectiveness of the proposed model, the dataset is divided into training and testing sets using a 70%:30% split. The test set is extracted from each class of data to ensure balanced representation.

1. Step 2: Feature Selection

For the NCR-EBRB model, the XGBoost feature selection technique is employed to evaluate feature importance. The evaluation results are shown in Table 2, where the importance of the most critical feature is set to 1, and the importance scores of other features are derived relative to this baseline.

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Table 2. Feature Importance Assessment Results.

https://doi.org/10.1371/journal.pone.0347303.t002

1. Step 3: Setting Reference Values for the EBRB Model to Generate the Rule Base

Antecedent reference values are determined based on the selected features. Consequent reference values are determined by the classes. Since the dataset contains three classes, the reference values for the classes are set as follows: the reference values of classes are set as .

1. Step 4: Parameter initialization

In the original EBRB model, rule weights , attribute weights , and the belief distributions of rule consequents are assigned by experts.

In this study, the initial parameters and are set to 1. are determined by the sample classes. The hyperparameter is set to 0.2.

1. Step 5: Rule reduction

After completing the configuration of the relevant parameters, the input data are processed to generate the original rule base. The NCR method proposed in Section 3.2 is subsequently applied to reduce the rule base, thereby generating a smaller and more refined new rule base.

1. Step 6: Parameter Optimization

The P-CMA-ES algorithm is utilized to optimize the parameters of the NCR-EBRB model established in Step 5. Finally, the optimized NCR-EBRB model is obtained.

The parameters of the NCR-EBRB model established in Step 5 are optimized using the P-CMA-ES. The algorithm employs a population size of (where is the number of decision variables), an initial step size of , and runs for a maximum of function evaluations as the termination criterion. The resulting optimized NCR-EBRB model is then used for inference.

For Step 2, the XGBoost feature analysis technique is employed for feature selection to construct a highly interpretable model. However, whether less important features should be included as input attributes for the model remains a question worth exploring. To address this, this study further investigates the impact of varying numbers of input attributes on model performance. Importantly, regardless of the number of input attributes, the selected features are always based on the importance ranking determined by the XGBoost feature analysis technique—i.e., the top features are sequentially selected according to their importance scores from highest to lowest. Table 2 presents the corresponding evaluation results, while Fig 4 illustrates the experimental outcomes for input attribute quantities of 2, 3, 4, and 5. Through comparative analysis, the relationship between the number of input attributes and model performance is more clearly revealed, thereby providing a more scientifically sound basis for feature selection.

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Fig 4. Impact of the input attribute quantity on the performance of the NCR-EBRB model.

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As evidenced by the experimental results, the model exhibits optimal performance when the number of premise attributes is 2 or 4, whereas its effectiveness is relatively inferior when 3 or 5 attributes are used. This phenomenon suggests that, for complex data, the relationship between model performance and the number of input attributes is not a simple linear correlation but rather a more intricate nonlinear or composite relationship.

However, from the perspective of model interpretability, the NCR-EBRB, as an expert system model, inherently emphasizes its core strength in simulating the decision-making processes of human experts and presenting reasoning outcomes in a transparent and intuitive manner. When fewer input attributes are used, the system’s decision logic becomes more concise and interpretable. This not only enhances user understanding and trust in the model but also reduces operational complexity in practical applications.

Therefore, in the context of applying the proposed NCR-EBRB model to diabetes diagnosis, a balanced consideration of experimental results and interpretability leads to the final selection of HbA1c (glycated hemoglobin) and BMI (body mass index) as the premise attributes. These two attributes are not only widely recognized in medical practice as critical indicators for diabetes diagnosis [34] but also capture the core characteristics of the disease in the most streamlined manner. This ensures robust model performance while maximizing transparency and practical utility.

4.1.3. Experimental analysis.

After the NCR-EBRB model is established, the model parameters are altered due to rule reduction and parameter optimization. On the one hand, the number of rules is significantly reduced from 702 to 125. On the other hand, the rule weights and attribute weights are modified: the attribute weights are adjusted to 1 and 0.8893. The changes in rule weights are illustrated in Fig 5 (the original settings for both rule weights and attribute weights were 1).

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Fig 5. Numerical distribution of rule weights optimized by the P-CMA-ES.

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To demonstrate the superiority of the proposed NCR-EBRB model, it is first compared with the original EBRB model. Owing to the presence of class imbalance in the dataset, a confusion matrix is employed to present the experimental results. The experimental results are shown in Fig 6.

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Fig 6. Comparative performance analysis of the NCR-EBRB model and the original EBRB model.

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The experimental results in Fig 6 show that the NCR-EBRB outperforms the EBRB model in predicting Class 0 and Class 2 while achieving performance identical to that of the EBRB model for Class 1. This is because the original data for Class 1 contain less noise, and the rule reduction process does not enhance model accuracy in this case.

To further verify the effectiveness of the proposed NCR-EBRB model, comparative experiments are conducted against five representative classifiers including Support Vector Machine (SVM), Decision Tree, K-Nearest Neighbor (KNN), Bagging Tree, Boosting Tree, and the single EBRB model. For reproducibility, all comparative models are implemented under fixed configurations without individual hyper-parameter tuning. Specifically, SVM adopts linear multi-class learning; Decision Tree is configured with moderate tree complexity; KNN employs a neighborhood size of five; Bagging Tree aggregates twenty base decision trees; and Boosting Tree is trained with decision trees as weak learners. Such configurations correspond to commonly used baseline settings and ensure a fair comparison framework.

Given the inherent class imbalance in the diabetes dataset, relying solely on globally aggregated true positives and false positives (i.e., micro-averaging) may mask the model’s performance on minority classes. To provide a stringent and fair evaluation, the evaluation metrics in this study include overall accuracy, macro-averaged precision, and macro-averaged recall.

First, the overall accuracy is calculated to evaluate the holistic correctness across the entire dataset. Then, for precision and recall, we calculate the specific metrics for each individual class as follows:

(25)

Where and represent the true positives, false positives, and false negatives for the class, respectively. The final macro-averaged precision and recall are then obtained by computing the arithmetic mean of these class-specific metrics across all classes:

(26)

This macro-averaging strategy ensures that each diagnostic category (e.g., healthy vs. diabetic) is treated with equal weight, thereby providing a more rigorous assessment of the model’s diagnostic robustness. The computed results are presented in Table 3.

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Table 3. Experimental Results under Different Testing Set Partitioning Strategies.

https://doi.org/10.1371/journal.pone.0347303.t003

From the experimental results, it is evident that the proposed NCR-EBRB model outperforms the original EBRB model across all the evaluation metrics, demonstrating its superior performance. Particularly in scenarios with limited test sample sizes, the NCR method is more accurate than other benchmark models are. However, as the scale of the test set expands and the volume of training data diminishes, the accuracy of the NCR-EBRB model gradually decreases. This phenomenon is attributed primarily to the application of the NCR rule reduction algorithm. While this algorithm effectively streamlines the rule base, it may also lead to an insufficient number of rules, thereby negatively impacting the model’s overall accuracy.

4.1.4. Ablation study.

To rigorously validate the individual contributions of the NCR module and P-CMA-ES optimization, a comprehensive ablation study was conducted across varying test set proportions (20%–40%), comparing three configurations: (1) Pure EBRB (no rule reduction/optimization), (2) NCR-EBRB without optimization (rule reduction only), and (3) the full NCR-EBRB (with both components).

As shown in Table 4, the NCR module alone improved the accuracy over the Pure EBRB at the 20% test split (0.9394 vs. 0.9343), reflecting effective rule pruning while preserving decision fidelity. Incorporating P-CMA-ES further enhanced performance significantly, increasing the accuracy to 0.9747 compared to 0.9394 for the unoptimized NCR-EBRB at the same split, indicating its necessity for fine-grained parameter adaptation.

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Table 4. Ablation Study of NCR-EBRB under Varying Test Set Partitioning Ratios.

https://doi.org/10.1371/journal.pone.0347303.t004

Notably, the full NCR-EBRB model achieved its peak performance at the 25% split with an accuracy of 0.9759, outperforming the Pure EBRB (0.9197) by 5.62 percentage points. This confirms that both modules are indispensable for optimal predictive performance. Overall, the ablation results verify that NCR provides efficient structural reduction while P-CMA-ES unlocks additional optimization potential, and their combination yields robust performance across different partitioning ratios.

4.2.1. Experimental definition.

To further validate the generalizability and adaptability of the NCR-EBRB method, four publicly available datasets are selected from the UCI Machine Learning Repository for experimental testing. Table 5 details the fundamental information of the selected datasets, including dataset names, the number of input attributes, the number of classes, and the total sample size. In this section, the NCR-EBRB model is compared with several classical machine learning methods, specifically Decision Tree, Bagging Tree, Boosting Tree, k-Nearest Neighbor (k-NN), and Support Vector Machine (SVM). The experimental modeling workflow and parameter settings remain consistent with those in the previous section to ensure the fairness of the comparison.

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Table 5. Dataset overview.

https://doi.org/10.1371/journal.pone.0347303.t005

4.2.2. Analysis results.

The experimental results are presented in Table 6. As shown in the table, the proposed NCR-EBRB model outperforms the other benchmark models across the four datasets (Newthyroid, Ecoli, Iris, and Banknote), demonstrating satisfactory classification performance. Therefore, in certain specific application scenarios, the NCR-EBRB can serve as an effective classification method to achieve desirable classification outcomes.

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Table 6. Results of comparative research.

https://doi.org/10.1371/journal.pone.0347303.t006

4.2.3. Discussion of the value of the hyperparameter .

In the proposed NCR-EBRB system, a hyperparameter is introduced to control the number of fused rules. To further investigate the impact of this parameter on model performance, the four datasets from Section 4.2 are selected to evaluate the effects of varying values on system performance. In each experiment, the parameter is adjusted as the independent variable, while all other parameters remain fixed to ensure experimental controllability and result comparability.

The experimental results are shown in Fig 7, where the horizontal axis represents the values of the hyperparameter , and the vertical axis indicates the classification accuracy of the NCR-EBRB system. The figure shows that for the Iris, Newthyroid, and Ecoli datasets, the system’s classification accuracy tends to fluctuate as varies, with multiple local maxima emerging during the process. Overall, the model achieves optimal classification performance when for the Banknote dataset; however, the accuracy curve displays only one distinct maximum, reaching peak accuracy at .

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Fig 7. Effects of the parameter on the experimental performance.

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This experiment further explores the impact of the parameter on system performance, validating the complexity and necessity of its selection process. The results demonstrate that simply reducing does not consistently improve model accuracy. This may occur because excessively small values filter out critical information that is beneficial for classification. Similarly, blindly increasing does not guarantee better performance, as it may introduce excessive noise that interferes with decision-making. Additionally, as increases, the model’s computational time increases accordingly. Therefore, in practical applications, the value of should be carefully selected on the basis of specific data characteristics to achieve an optimal balance between accuracy and efficiency.

4.2.4. Experimental summary.

This section validates the generalizability and effectiveness of the proposed NCR-EBRB model via four public datasets (Iris, Banknote, Ecoli, and Newthyroid). The experimental results demonstrate that the NCR-EBRB significantly outperforms benchmark models in terms of accuracy, precision, and recall across all datasets, further confirming its superior performance in classification tasks.

Furthermore, the analysis of the impact of the hyperparameter on model performance reveals significant variations in the optimal values across different datasets. For example, Iris, Ecoli, and Newthyroid achieve peak performance at values across different datasets. Banknote achieve peak performance at . This phenomenon highlights the sensitivity of the NCR-EBRB model to the rule fusion threshold: excessively low values may filter out critical information, whereas excessively high values may introduce redundant noise, degrading classification decisions. Therefore, in practical applications, should be carefully configured on the basis of specific data characteristics. Future research could explore adaptive adjustment mechanisms to enhance the model’s generalization ability across diverse scenarios.

In summary, the NCR-EBRB method exhibits excellent classification performance and robustness in most experimental settings, effectively validating the feasibility and practicality of the neighborhood coverage reduction strategy and parameter optimization method.