EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS 2025, Vol. 18, Issue 2, Article Number 5934 ISSN 1307-5543 – ejpam.com Published by New York Business Global Enhancing Classification Performance Through Rough Set Theory Feature Selection: A Comparative Study Across Multiple Datasets T. Ashika1, G. Hannah Grace1,∗ 1 Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology Chennai, India Abstract. In Machine Learning (ML), handling high-dimensional data with redundant or irrel- evant features presents significant challenges. Effective feature selection is essential for enhancing model performance, reducing computational complexity, and improving interpretability. Rough Set Theory (RST) provides a powerful mathematical framework for managing uncertainty, mak- ing it a valuable tool for feature selection. This study applies RST-based feature selection to five diverse datasets, aiming to eliminate insignificant attributes. The performance of various ML models, including Logistic Regression (LR), K-Nearest Neighbor (KNN), Support Vector Ma- chine (SVM), Kernel SVM, Näıve Bayes (NB), Decision Tree (DT) and Random Forest (RF), on both the original and RST selected datasets was evaluated. Standard metrics such as accuracy, precision, recall, F1 score and Mean Absolute Error (MAE) are used for evaluation. Results demonstrate that RST effectively selects relevant features without significant information loss. Models trained on RST selected datasets exhibit comparable or improved performance. These findings highlight the potential of RST-based feature selection to enhance ML model perfor- mance while reducing computational complexity, making it a valuable approach for various ML applications. 2020 Mathematics Subject Classifications: 68T30, 68T37, 68U35 Key Words and Phrases: Quickreduct, machine learning, rough set theory, feature selection 1. Introduction A subfield of computer science and artificial intelligence (AI) called ”Machine Learn- ing” focuses on using data and algorithms to simulate human learning processes and progressively increase their accuracy. ML techniques have been used in many domains, such as email filtering, computer vision, speech recognition, agriculture, and health, where developing algorithms capable of carrying out the necessary functions would be costly. Although ML has made many revolutions in different fields, it also faces many ∗Corresponding author. DOI: https://doi.org/10.29020/nybg.ejpam.v18i2.5934 Email addresses: ashika.t2023@vitstudent.ac.in (T. Ashika), hannahgrace.g@vit.ac.in (G. H. Grace) https://www.ejpam.com 1 Copyright: © 2025 The Author(s). (CC BY-NC 4.0) T. Ashika, G. H. Grace / Eur. J. Pure Appl. Math, 18 (2) (2025), 5934 2 of 22 limitations such as lack of data, challenges in obtaining the data, bias in the data, and a vast amount of irrelevant attributes in the data. Pawlak [1] introduced RST, a technique used in mathematics that can be applied to problems involving imprecision and vagueness in intelligent data mining and analysis for handling huge data. RST provides several benefits, such as the ability to operate with- out needing prior or supplementary information about the data. It delivers meaningful analysis even when data is incomplete, supports the interpretation of both quantitative and qualitative data, and can model highly nonlinear or discontinuous relationships, of- fering intricate characterizations of the data. RST excels in uncovering hidden patterns and representing them as decision rules, all of which are grounded in facts supported by a set of examples. RST is a valuable tool for the ML community since it has signifi- cant potential in areas including dynamic learning, multi-label classification, imbalanced classification, and big data research [2]. In this paper, five datasets were sourced from Kaggle and the UCI ML repository. The study is organized into two phases. In the first phase, the data was pre-processed, followed by the application of various ML algorithms and an evaluation of their perfor- mance. The results of these models were analyzed to assess their classification effective- ness. In the second phase, RST feature selection was applied, involving similar steps of pre-processing and the application of ML algorithms. After evaluating the RST based models, a comparison was made between the results of the original ML models and those utilizing RST based feature selection. This comparative analysis highlights the impact of RST on improving classification performance in various models and provides insight into its potential to improve model accuracy and robustness. 1.1. Related Work Pawlak [1] was the one who first proposed the theory of uncertainty and RST, and later modified it. The cardiac-related dataset was classified and forecasted using a vari- ety of ML algorithms, such as NB, SVM, DT J48, JRip, Adaboost, KNN, and stochastic gradient descents (SGD), and several others by Mohan et al. [3]. Using RST, Mishra et al. [4] offered a set of guidelines for solving social science challenges. In order to obtain justice, employees frequently turn to legal authorities, which is harmful to both the employer and the employee. The paper addresses the need for employers in various organizations to provide proper justice. The key characteristics that contribute to this kind of situation in various establishments were identified using RST. Nayak et al. [5] created a model using RST for malaria symptom prediction. In order to identify the accurate symptoms of malaria, the study addresses the application of RST to extract hidden information from a set of imprecise data. Research has indicated that RST is marginally superior to other soft computing techniques and is a valuable tool for handling ambiguous data. Subhalaxmi Das et al. [6] has developed a technique for diagnosis of cardiac problem using RST and ML. The study proposes a model to diagnose cardiac disorders by utilizing ML techniques in conjunction with the stacking method. The study uses the Cleveland dataset to diagnose cardiac issues. RST was used T. Ashika, G. H. Grace / Eur. J. Pure Appl. Math, 18 (2) (2025), 5934 3 of 22 to determine the most significant disease among all cardiac-related disease. The model’s performance was assessed using F1 score, recall, accuracy, and precision. Additionally, error functions were computed to evaluate the performance of the models. Rani Nuraeni and Sugiyarto Surono [7] has proposed RST for dimension reduction on ML algorithm. The use of dimension reduction in ML to increase computational effi- ciency is covered in this paper. The authors convert high-dimensional data into much lower dimensions without appreciably losing the original characteristics and information of the data using RST. The authors make use of five UCI ML datasets and applied Core and Reduct. The performance of the reduced dataset is evaluated using popular ML techniques like SVM, LR, and KNN. According to the research, core and reduct can reduce computing time by up to 80% without compromising the value of each evaluation model. A prediction model for building energy consumption based on RST and Deep neural Network (DNN) has been developed by Lei Lei et al. [8]. RST is used to minimize unnecessary influencing factors and to identify the essential components of building en- ergy consumption. Next, a DNN receives these essential components. The output of the DNN is the amount of energy consumed by buildings. Initially, data was collected from 100 public buildings in the civil public buildings. Subsequently, DNNs were trained and tested using data gathered from a university lab in Dalian. The study examined both short- and medium-term energy consumption predictions for buildings. The outcomes of the fuzzy, Elman, and backpropagation neural networks were compared with those of the DNN. Compared to previous research works, the combination of RST and DNN turned out to be the most exact. Lukshmi R.A et al. [9] analyzed RST approach for attribute reduction. In order to create an efficient reduct set and formulate the core of the attribute set, the approach focuses on eliminating redundant attributes. Only a subset of the features that maintain the original feature’s accuracy are then chosen for further processing using ML models. Vamsidhar Talasila et al. [10] predicted diseases using RST with Recurrent Neural Net- work (RNN) in Big Data Analytics where RST technique was used to identify the most pertinent features for effective disease detection and medical data classification. The RNN method for disease prediction receives the chosen features as input. The experi- ments for the proposed method, also known as RST-RNN, are conducted on the UCI ML repository dataset with respect to accuracy, F-measure, sensitivity, and specificity. The outcomes demonstrated that the RST-RNN approach obtained accuracy of 98.57 % for the heart disease dataset. Touhid Mohammad Hossain et al. [11] had discussed a RST approach along with ML in Electrofacies Classification and Subsurface Lithology Interpretation. In order to classify electrofacies, the paper suggests a RST-based White box classification method that gen- erates decision rules. Additionally, the Extra Tree Classifier (ETC) was used to select significant well log features, from which they created five distinct electrofacies. Yılmaz Kayaa and Murat Uyar [12] proposed the use of a hybrid decision support system to identify hepatitis. RST and Extreme Learning Machine (ELM) algorithms form the foundation of the system. The proposed model was trained using the Indian Liver pa- T. Ashika, G. H. Grace / Eur. J. Pure Appl. Math, 18 (2) (2025), 5934 4 of 22 tient dataset, then evaluated the effectiveness of the suggested classification methods based on sensitivity and specificity to determine the model’s accuracy. A SVM classifier for breast cancer diagnosis using RST-based feature selection was pro- posed by Hui-Ling Chen et al. [13]. Using RST reducts, Asma Trabelsi et al.[14] created an ensemble classifier to handle data with evidential attributes. The objective is to use RS reduct to extract the best feature subsets for the ensemble classifier. The Diversity Reduct method (DR), the Accuracy-Diversity Assessment Function method (AD-AF), and the Ensemble Accuracy Assessment Function method (EA-AF) are the three strate- gies that have been suggested to choose the best reducts. The key differences between the previously mentioned methods have been compared using a statistical test in terms of reduct diversity, ensemble size, classification performance, and approach performance. The outcomes show that the EA-AF strategy generated the best effects. Ping-Feng Pai et al. [15] analysed foreign exchange rates by RST and directed acyclic graph SVM (DAGSVM). A new approach to foreign exchange rate analysis that com- bines DAGSVM and RST was proposed. They examined the US dollar’s exchange rates versus the euro and the Japanese yen using the suggested methodology. The outcome in- dicates that this method outperforms alternative strategies like Back Propagation Neural Network (BPNN) and Support Vector Regression (SVR). For real-valued classification problems, Essam Debie et al.[16] proposed an ensemble of learning classifier system based on reducts. An ensemble approach for RST-based learning classifier systems was pro- posed to construct ensemble learning systems. By using RST attribute reduction, the method creates a set of reducts. A variety of these reducts is then chosen and utilized for training of ensemble of base classifiers. According to the analysis, single learning classifier system models are outperformed by reduct-based ensemble systems in terms of classification accuracy. Georg Peters and Simon Poon [17] has discussed a Dominance based RS approach (DRSA) by analyzing IT business values. This paper examine how IT affects a partner- ship’s business value. A decision table with ordinal data can be used to generate rules using DRSA. An investigation into the IT management practices of Australian businesses was carried out by the Department of Communications, Information Technology, and the Arts in Australia, from which the authors have used ordinal data. The paper offers a thorough analysis of the underlying mechanisms that underpin IT beneficial effects on cooperatives business values. BrightBox is a RST-based technology designed by Andrzej Janusz et al. [18] for identify- ing errors in ML models. A new method for looking into errors in ML model operations is called BrightBox. The method relies on surrogate RST-based models that are in- ducted from data approximating the decisions made by the monitored Blackbox models. The neighborhoods of instances that go through the diagnostic process are computed using these approximators which consists of historical instances that were handled sim- ilarly by RST-based models. The analysis of mistakes reported in these neighborhoods serves as the foundation for the diagnostic procedure. The study also emphasizes how BrightBox technology can be applied to model and data-related problem identification and analysis as well as prediction model analysis. Experiments conducted on real-world T. Ashika, G. H. Grace / Eur. J. Pure Appl. Math, 18 (2) (2025), 5934 5 of 22 datasets verify that this type of analysis may provide us efficient and accurate insights into the reasons of ML model’s poor performance. Alessio Ferone [19] had proposed feature selection determined by the RST composition resulted by feature granulation. This research suggests a RST-based feature selection method that consists of two stages: Granulation and Roughinement. The suggested method reduces computation costs with respect to the Quickreduct (QR) algorithm. In recent years, several studies have advanced the application of RST in feature se- lection, addressing various challenges in dynamic and high-dimensional datasets. Zhao et al.[20] proposed a triple nested equivalence class (TNEC) approach for group incre- mental feature selection, which effectively reduces redundancy and enhances efficiency in processing ultra-high-dimensional datasets. Their experimental results demonstrated significant improvements in classification efficiency and selection accuracy across 18 dy- namic datasets. Similarly, Almania et al. [21] introduced a two-level feature selection approach that combines RST with Binary Particle Swarm Optimization (BPSO) to enhance accuracy and reduce computational overhead in Intrusion Detection Systems (IDS). Their method achieved a notable improvement in classification accuracy while streamlining the feature set. Furthermore, Alsabilah and Rawat [22] leveraged RST in conjunction with XGBoost to develop a robust network IDS , significantly outperforming existing methods in terms of accuracy and precision. Turaga and Chebrolu [23] addressed the inefficiencies of tradi- tional RST algorithms by proposing a novel attribute reduction algorithm designed for execution on Graphics Processing Units (GPUs), achieving high classification accuracies in reduced execution times. These studies collectively highlight the evolving landscape of RST applications and underscore the importance of integrating RST with modern computational techniques to enhance feature selection processes. The summary of the related work is provided in table 1. T. Ashika, G. H. Grace / Eur. J. Pure Appl. Math, 18 (2) (2025), 5934 6 of 22 Table 1: Comparison of RST-based and Non-RST Feature Selection Methods from Recent Literature Method References Approach Advantages Limitations RST [1, 5, 6] Rule-based reduction using core and reducts Handles uncertainty, generates human- understandable rules, supports imprecise data Needs discretization, can be computationally intensive for large feature sets RST vs Core + Reduct [7] Compared performance with and without RST-based dimensionality reduction Reduced computation time by up to 80% with minimal accuracy loss Focused on only a few ML models (SVM, LR, KNN) RST + DNN [8] RST for dimension reduction before Deep Learning (DL) Enhanced prediction accuracy by removing noisy/irrelevant features before DNN Requires tuning both RST reduct and DL model RST + RNN [10] Feature selection via RST, then fed to RNN Achieved 98.57% accuracy on heart disease dataset Limited to specific dataset; needs sequential data handling RST + ETC [11] RST to identify features for lithology; ETC to classify White-box interpretability with competitive classification performance Focused on geophys- ical/electrofacies domain Non-RST Feature Selection [3, 12] Used traditional ML or hybrid models (e.g., ELM, SVM) without RST Simpler implementation, fast training on structured datasets May not handle am- biguity/uncertainty well; lacks interpretability of RST rules RST Ensemble Feature Selection [14] DR, AD-AF, EA-AF for best reducts in ensemble classifiers EA-AF achieved highest classification performance using feature diversity metrics Needs statistical evaluation and multiple reduct generation RST + DRSA [17] Dominance relations used in ordinal decision tables Suitable for subjective/ordinal data (e.g., IT business values) More complex than standard RST; limited applicability RST + TNEC [20] Group incremental feature selection for high-dimensional dynamic data Reduces redundancy, improves classification accuracy on large-scale datasets Focused on dynamic datasets, complex implementation RST + BPSO [21] Two-level hybrid feature selection for IDS High accuracy and reduced overhead; robust for cybersecurity Tailored to IDS; parameter tuning required T. Ashika, G. H. Grace / Eur. J. Pure Appl. Math, 18 (2) (2025), 5934 7 of 22 1.2. Motivation and Novelty ML has revolutionized various fields by enabling systems to learn from data and make informed decisions. However, the presence of irrelevant or redundant features in datasets can hinder model performance, leading to overfitting, increased computational costs, and reduced interpretability. Traditional feature selection methods often rely on statistical measures or domain knowledge, which may not always be available or sufficient. This study is motivated by the need for an effective, data-driven approach to feature selection that can handle uncertainty and imprecision inherent in real-world datasets. This research introduces a novel application of RST for feature selection in ML workflows. The novelty lies in integrating RST-based feature selection with ML models across diverse domains, providing a comprehensive evaluation of its impact on model performance. 1.3. Contribution The contribution of this study is provided below (i) Application of RST-based feature selection to five diverse datasets, encompassing domains such as Seed, Heart Attack, Obesity, Online Delivery, and Breast Cancer. This extensive evaluation provides insights into the applicability and effectiveness of RST across various contexts. (ii) Comparative analysis of ML models trained on datasets with and without RST- based feature selection is conducted. The results indicate that RST either enhances or maintains model performance, highlighting its potential as a valuable tool in ML workflows. (iii) The findings suggest that integrating RST into feature selection processes can lead to more efficient and accurate ML models, with potential applications in various fields. By addressing the limitations of traditional feature selection methods and demonstrating the efficacy of RST, this work contributes to the advancement of ML techniques and their practical applications. The structure of the paper is as follows: Section 2 presents the materials and methods. The Research findings of the suggested model are covered in Section 3. Section 4 discusses the paper and Section 5 concludes the suggested work. 2. Materials and Methods This section outlines the materials and methods utilized in this study, including the proposed methodology, description of the datasets, the data preprocessing steps, the application of RST for feature selection, the ML models employed, and the evaluation metrics used to assess model performance. T. Ashika, G. H. Grace / Eur. J. Pure Appl. Math, 18 (2) (2025), 5934 8 of 22 2.1. Proposed work The paper proposes two process which includes classification without RST and classi- fication with RST. Five different datasets with varying number of attributes and variables are chosen. Firstly, these datasets were preprocessed and evaluated using various ML classifiers like LR, KNN, SVM, Kernel SVM, NB, DT and RF. The model’s performance is then assessed using evaluation metrics, which include MAE, accuracy, precision, re- call, F1 score, and confusion matrix. Secondly, the insignificant features of these five datasets are reduced using RST reduct and core. These reduced dataset are evaluated using the ML techniques like LR, KNN, SVM, Kernel SVM, NB, DT and RF and the performance of these models is evaluated and compared with the original dataset to analyse whether the RST selected features improve performance compared to the origi- nal dataset. Suitable ML algorithms for each dataset were also identified based on the comparative analysis. The architecture of the suggested work is shown in figure 1. Figure 1: Overall Architecture of the suggested work 2.2. Dataset Description The study utilized five datasets sourced from Kaggle and the UCI ML Repository, a widely recognized platform for its diverse and comprehensive data. This selection pro- vides a robust foundation for evaluating the effectiveness of classification models both with and without RST based feature selection. The selected datasets include Seeds [24], online food delivery [25], Heart attack [26], Obesity [27] and Breast cancer [28]. The Seeds dataset features 7 conditional attributes and 1 decision attribute to clas- T. Ashika, G. H. Grace / Eur. J. Pure Appl. Math, 18 (2) (2025), 5934 9 of 22 sify wheat types. The Online Food Delivery dataset, focusing on the Bangalore region, includes 54 conditional attributes and 1 decision attribute, examining the growth in de- mand for food delivery. The Heart Attack dataset, with 54 conditional attributes and 1 decision attribute, identifies predictors of heart disease and classifies outcomes as posi- tive (disease present) or negative (absent). The Obesity dataset contains 6 conditional attributes and 1 decision attribute, categorizing individuals into weight classifications such as Overweight, Underweight, Normal, or Obese. For Breast Cancer, the Wisconsin dataset includes 8 conditional attributes and 1 decision attribute to classify tumors as benign or malignant. Together, these datasets provide a diverse and structured basis for classification and prediction in the study. Table 2 presents a list of datasets, detailing the number of attributes and instances for each dataset. Table 2: List of Dataset along with the number of features and instances S. No Datasets Number Conditional Decision Number of features Attribute attribute of Instances 1 Seeds 8 7 1 211 2 Online Food Delivery 55 54 1 387 3 Heart attack 9 8 1 1319 4 Obesity 7 6 1 108 5 Breast Cancer 9 8 1 699 2.3. Data preprocessing The dataset might include insufficient data, missing data or categorical data. In order to convert this raw dataset into a clean dataset, data preprocessing is performed. Data preprocessing techniques include: handling missing data, splitting the dataset, feature scaling, and encoding categorical data. Missing values were imputed by replacing them with the column average to mitigate potential errors. Categorical features were converted into numerical format using one-hot encoding to create binary vectors for each category. In addition, standardization was applied to scale all features uniformly, typically adjusting values to a range between -3 and +3. Finally, each dataset was divided into training and testing sets using an 80:20 split, ensuring a consistent evaluation framework across the diverse datasets. 2.4. Rough set theory A mathematical tool called RST is used to deal with uncertain and inconsistent data. It was first proposed by Pawlak [1] at the beginning of the 1980’s. RST expresses un- certainty and imprecision through a set’s boundary region rather than through partial membership function as Fuzzy Set Theory does. RST consists of lower and upper ap- proximations, a boundary region, and the concepts of indiscernibility, which lead to the identification of reducts and cores. RST allows for a crisp set to be formally approxi- mated using the lower and upper approximations of the original set. To enable effective classification, the most pertinent features are selected using the RST technique. Let T. Ashika, G. H. Grace / Eur. J. Pure Appl. Math, 18 (2) (2025), 5934 10 of 22 I = (U, A) represent an information system, where U denotes a nonempty set of finite objects that is the universe of discourse. A is non-empty. An associated set of values (Va) exists for each attribute a ∈ A. For a subset, X ⊆ U , X can be approximated using only information contained within P by constructing the P -lower approximation given as P∗X, is the set of all elements of U , which can be certainly classified as elements of X based on the attribute set P . The P - upper approximation of X, denoted as P ∗X, which can be possibly classified as elements of X based on the attribute set P . The lower and upper approximation can be defined as shown in equations (1) and (2), P∗(X) = {x ∈ U : P (x) ⊆ X} (1) P ∗(X) = {x ∈ U : P (x) ∩X ̸= ∅} (2) The difference of the upper P ∗X and the lower approximation P∗X yields the boundary region PN(X) as shown in equation (3). PN(X) = P ∗(X)− P∗(X) (3) The accuracy of approximation αP (X) is shown in equation (4) where the resultant values lies in the range of 0 ≤ αP (X) ≤ 1. αP (X) = |(P∗X)| |(P ∗(X))| (4) Dependency between the decision attribute D and the condition attribute C, where D depends on C in a degree k(0 ≤ k ≤ 1), denoted C ⇒k D, if k = γ(C, D) are represented as given in equation (5) and (6). γ(C, D) = |(POSC(D))| |U | (5) POSC(D) = ∪P∗(X) (6) where, the set of all elements of U that can be specifically assigned to blocks of the partition U/D by means of C is known as POSC(D) also known as the positive region of the partition U D with respect to C. Definition of the indiscernibility relation IND(P ) is shown in equation (7). IND(P ) = {(x, y) ∈ U2|∀a ∈ P, a(x) = a(y)} (7) The minimum subset of attributes known as a reduct that permits the same classification of universe’s elements as the entire set of attributes is known as a reduct where if I(P ) = I(P −{a}), then ’a’ is dispensable in P ; otherwise, ’a’ is indispensable in P . Set P is independent if all its attributes are indispensable. Subset P ′ of P is a reduct of P if P ′ is independent and I(P ′) = I(P ). Assume P is a subset of A. The combination of all the vital attributes that make up P is its core. Core is the intersection of all reducts as shown in equation (8). Core(P ) = ∩Red(P ) (8) Red(P ) denotes the set of all reduct of P . Numerous applications of RST have shown it to be effective, including data reduction, identifying hidden trends in data, assessing the significance of data, and creating sets of decision rules based on data. T. Ashika, G. H. Grace / Eur. J. Pure Appl. Math, 18 (2) (2025), 5934 11 of 22 2.4.1. RST QR Algorithm QR algorithm [29] constructs a reduct by sequentially adding those attributes that most significantly enhance the dependency degree, halting the process when no further im- provement is observed. Because it is computationally impractical to evaluate all possible feature combinations, QR adopts a greedy strategy by selecting one attribute at a time for inclusion. Algorithm 1 provides the implementation of the QR approach. Algorithm 1: QR Algorithm Input: C : Set of all Conditional attributes D : Set of Decision attribute Output: A : Minimal Subset of C that retains the same classification power as the full set of attributes C w. r. t. D Step 1: Start with empty set A A← ∅ Step 2: Iterate until the discernibility measure of A equals to C Step 3: Repeat until γA(D) = γC(D) Step 3.1: Assign T = A Step 3.2: For each x ∈ C −A: Compute, γR(A∪{x})(D) Step 3.3: If γR(A∪{x})(D) > γT (D), Update, T ← A ∪ {x} Step 3.4: Set A← T Step 4: Return A where, γA(D)→ Discernibility of A w. r. t. D γC(D)→ Discernibility of C w. r. t. D A→ Set of selected attributes T → Temporary set to evaluate attribute addition 2.5. Models of ML For the study, several well-established ML classifiers are employed to evaluate the diverse datasets. LR [30] was chosen for its simplicity in modeling binary outcomes using a logistic function, while KNN [31] offers a non-parametric approach based on eu- clidean distance to classify data points. SVM [32] was included for its robust ability to find optimal decision boundaries, and its extension, Kernel SVM [33], enables non-linear classification by mapping inputs into high-dimensional feature spaces. Additionally, NB [31] was utilized for its probabilistic framework based on Bayes’ Theorem and the as- sumption of predictor independence, and DT [31] was selected for its clear, interpretable structure driven by entropy measures. To further enhance prediction accuracy and ad- dress complex patterns, ensemble methods such as RF[34]. These classifiers were chosen for their complementary strengths and proven effectiveness in tackling varied classifica- tion challenges. 2.6. Evaluation metrics Evaluation metrics like accuracy, precision, recall, F1-score, and MAE rate are used to assess the effectiveness of the suggested approach. The percentage of all subjects T. Ashika, G. H. Grace / Eur. J. Pure Appl. Math, 18 (2) (2025), 5934 12 of 22 correctly classified is known as accuracy. The percentage of subjects correctly classified as positive out of all positive subjects is known as precision. The recall evaluates the model’s ability to recognize positive samples. A harmonic mean of recall and precision is the F1-Score. A measure of errors between paired observations expressing the same phenomenon is called MAE. The Formula of the evaluation metrics and error rate is shown in table 3. Table 3: Formulae of Evaluation metrics and error function S. No. Evaluation metrics Formulae 1 Accuracy (TP + TN) (TP + TN + FP + FN) 2 Precision (TP ) (TP + FP ) 3 Recall (TP ) (TP + FN) 4 F1 score 2×Recall × Precision Recall + Precision 5 MAE 1 n ∑n i=1 |yi − xi| 3. Experimental results The study results include the following steps: feature selection using RST with the QR algorithm, classification with ML algorithms using the original features, classification using features selected by RST, and a comparison of the results before and after feature selection. 3.1. Experimental Setup The experiments were conducted using R programming, specifically utilizing the RoughSets package for feature selection. Model training was performed in Google Colab, a cloud-based Jupyter notebook environment, utilizing PyTorch for ML implementation. The system used for training was equipped with a 12th Gen Intel Core i3-1215U processor (1.20 GHz) and 8 GB RAM, ensuring efficient data processing and optimal performance across the five different datasets. 3.2. Feature selection In this study, the QR algorithm of RST is utilized to determine the reducts, enabling the selection of the most relevant features while discarding irrelevant ones. The seeds dataset was reduced from 7 attributes to 2 attributes. The online food delivery dataset was reduced from 54 attributes to 4 attributes. The Heart attack dataset was reduced from 8 attributes to 2 attributes. The Obesity dataset was reduced from 6 attributes to 5 attributes. The Breast cancer dataset was reduced from 8 attributes to 4 attributes. The dataset before reduction and after reduction is shown in table 4. T. Ashika, G. H. Grace / Eur. J. Pure Appl. Math, 18 (2) (2025), 5934 13 of 22 Table 4: List of Dataset along with attribute list before and after reduction S. No Datasets No. of attributes before No. of attributes after reduction reduction 1 Seeds 7 2 2 Online Food Delivery 54 4 3 Heart attack 8 2 4 Obesity 6 5 5 Breast Cancer 8 4 3.3. Classification with ML Algorithms Using Original Features The original dataset is pre-processed and then evaluated using various ML classifiers like LR, KNN, SVM, Kernel SVM, NB, DT, and RF. The model’s performance is assessed using evaluation metrics. Figure 2 shows that certain algorithms perform best across different datasets: SVM works well for Seeds, while DT and RF are effective for Heart Attack and Obesity. In Online Food Delivery, LR, SVM, Kernel SVM, NB, and RF shows similar performance, and NB yields the best results in Breast Cancer. Figure 2: ML Algorithm Performance with Original Features across Datasets T. Ashika, G. H. Grace / Eur. J. Pure Appl. Math, 18 (2) (2025), 5934 14 of 22 3.4. Classification with ML Algorithms Using Features selected by RST This section discusses the performance evaluation after applying RST feature selec- tion, focusing on the performance of selected features. From figure 3, it is evident that after applying RST-selected features, LR, SVM, and Kernel SVM perform well for the Seeds dataset; RF achieves the best performance for Heart Attack; DT is most effective for Obesity; KNN, Kernel SVM, and DT perform well for Online Food Delivery; and KNN yields the best results for Breast Cancer. Figure 3: ML Algorithm Performance with RST-Selected Features across different Datasets 3.5. Comparison of Results Before and After Feature Selection using RST This section discusses the performance changes after applying RST feature selection. By comparing the results before and after feature selection, The study evaluate how RST affects classification accuracy, precision, recall, and other metrics across various ML algorithms. This analysis showcases how reducing the feature set to the most relevant attributes can improve model performance and efficiency. T. Ashika, G. H. Grace / Eur. J. Pure Appl. Math, 18 (2) (2025), 5934 15 of 22 3.5.1. Seeds Dataset Table 5, shows that applying RST for feature selection for the Seeds dataset results enhances model performance across metrics, with substantial gains observed in models such as LR, SVM, and Kernel SVM, where accuracy, precision, recall, and F1 scores all increase significantly. While RF shows only a slight improvement, most other mod- els benefit notably from the refined feature set, confirming the effectiveness of RST in boosting classification metrics. Table 5: Different ML algorithms on Seeds dataset ML model Accuracy Precision Recall F1 score MAE Before RST After RST Before RST After RST Before RST After RST Before RST After RST Before RST After RST LR 0.9245 0.9623 0.9265 0.9649 0.9328 0.968 0.9266 0.9648 0.0943 0.0377 KNN 0.8868 0.9056 0.8844 0.9025 0.8936 0.9094 0.8870 0.9043 0.1509 0.1321 SVM 0.9434 0.9623 0.9421 0.9649 0.9486 0.9683 0.9440 0.9648 0.0755 0.0377 Kernel SVM 0.9245 0.9623 0.9233 0.9649 0.9290 0.9683 0.9256 0.9648 0.0943 0.0377 NB 0.8868 0.9057 0.9010 0.9158 0.9010 0.9106 0.8947 0.9101 0.1132 0.1132 DT 0.9245 0.9434 0.9216 0.95 0.9290 0.9524 0.9233 0.9473 0.1132 0.0566 RF 0.9245 0.9245 0.925 0.9365 0.9264 0.9365 0.9241 0.9298 0.1132 0.0755 3.5.2. Heart attack dataset Table 6 shows that applying RST feature selection for the Heart Attack dataset signifi- cantly enhances classification performance for several models. LR improving from 0.7424 to 0.8101, and Kernel SVM, DT, and RF achieving high metrics across the board, high- lighting the effectiveness of RST in enhancing model precision and accuracy. Table 6: Different ML algorithms on Heart Attack dataset ML model Accuracy Precision Recall F1 score MAE Before RST After RST Before RST After RST Before RST After RST Before RST After RST Before RST After RST LR 0.7424 0.8101 0.7471 0.8864 0.8355 0.7697 0.7888 0.8239 0.2576 0.1894 KNN 0.625 0.9811 0.67096 0.9868 0.6842 0.9803 0.6775 0.9835 0.375 0.0189 SVM 0.7841 0.7803 0.8025 1 0.8289 0.6184 0.8155 0.7642 0.2159 0.2197 Kernel SVM 0.6856 0.8106 0.6885 1 0.8289 0.6711 0.7522 0.8031 0.3144 0.1894 NB 0.6894 0.7121 0.9861 1 0.4671 0.5 0.6339 0.6667 0.3106 0.2879 DT 0.9962 0.9886 0.9935 0.9806 1 1 0.9967 0.9902 0.0038 0.0114 RF 0.9924 0.9962 1 0.9935 0.9868 1 0.9934 0.967 0.0076 0.0038 T. Ashika, G. H. Grace / Eur. J. Pure Appl. Math, 18 (2) (2025), 5934 16 of 22 3.5.3. Obesity dataset RST feature selection maintains high classification performance for DT with perfect metrics across all evaluation measures, while RF experiences a slight decline in accuracy from 1 to 0.9091, showcasing the robustness of DT and RF even after feature selection. Table 7: Different ML algorithms on Obesity dataset ML model Accuracy Precision Recall F1 score MAE Before RST After RST Before RST After RST Before RST After RST Before RST After RST Before RST After RST LR 0.7727 0.7727 0.7917 0.7917 0.7917 0.7917 0.6881 0.6881 0.3182 0.3182 KNN 0.7727 0.7727 0.7875 0.7875 0.7708 0.7708 0.7261 0.7261 0.4545 0.4545 SVM 0.8636 0.8636 0.8542 0.8542 0.8889 0.875 0.8496 0.83095 0.2727 0.2272 Kernel SVM 0.6818 0.6818 0.5063 0.5063 0.6875 0.6875 0.5761 0.5761 0.6364 0.6364 NB 0.7727 0.7727 0.8438 0.8438 0.7917 0.7917 0.7078 0.7078 0.2273 0.2273 DT 1 1 1 1 1 1 1 1 0 0 RF 1 0.9091 1 0.9167 1 0.9167 1 0.9 0 0.1818 Table 7 shows that the DT classifier achieved perfect scores both before and after RST-based feature reduction for the Obesity dataset. Given the small dataset size, such uniform performance strongly indicates overfitting, where the model memorizes patterns including noise rather than generalizing effectively. In contrast, the RF model, which also achieved 1.0 before RST, dropped slightly to 0.9091 after RST, reflecting its ensemble robustness and sensitivity to the removal of marginally informative features. Compared to SVM (0.8636) and LR (0.7727), RF maintains stronger generalization, making it a more reliable choice for small datasets under feature reduction. 3.5.4. Online food delivery dataset RST feature selection leads to improved performance in classifiers like KNN, Kernel SVM, and DT, especially enhancing recall and F1 scores across these models. Table 8 describes the online food delivery dataset, where some algorithms show improvement, while others yield comparable results. T. Ashika, G. H. Grace / Eur. J. Pure Appl. Math, 18 (2) (2025), 5934 17 of 22 Table 8: Different ML algorithms on Online food Delivery dataset ML model Accuracy Precision Recall F1 score MAE Before RST After RST Before RST After RST Before RST After RST Before RST After RST Before RST After RST LR 0.7526 0.7308 0.7526 0.8305 1 0.8167 0.8588 0.8235 0.2474 0.2692 KNN 0.7216 0.7564 0.7614 0.7971 0.917 0.9167 0.8323 0.8527 0.2784 0.2436 SVM 0.7526 0.7308 0.7526 0.8305 1 0.8167 0.8588 0.8235 0.2474 0.2692 Kernel SVM 0.7526 0.7564 0.7526 0.7971 1 0.9167 0.8588 0.8527 0.2474 0.2436 NB 0.7526 0.7308 0.7526 0.8305 1 0.8167 0.8588 0.8235 0.2474 0.2692 DT 0.7423 0.7564 0.75 0.7971 0.9863 0.9167 0.8521 0.8527 0.2577 0.2436 RF 0.7526 0.7308 0.7526 0.8305 1 0.8167 0.8588 0.8235 0.2474 0.2692 3.5.5. Breast cancer dataset RST feature selection results in consistent performance for most classifiers, with KNN showing a slight reduction in precision but maintaining high recall and F1 scores, while RF and NB demonstrate stable accuracy, highlighting the utility of RST in retaining essential classification performance. Table 9 describes the breast cancer dataset, where RST yields comparable results. Table 9: Different ML algorithms on Breast cancer dataset ML Model Accuracy Precision Recall F1 score MAE Before RST After RST Before RST After RST Before RST After RST Before RST After RST Before RST After RST LR 0.9571 0.9429 0.9551 0.9467 0.9551 0.9337 0.9551 0.9393 0.0857 0.1143 KNN 0.9643 0.95 0.9640 0.94896 0.96096 0.94598 0.9624 0.9474 0.0714 0.1 SVM 0.9572 0.9357 0.9551 0.9339 0.9551 0.9310 0.9551 0.9324 0.0857 0.1286 Kernel SVM 0.9571 0.9429 0.9551 0.9401 0.9551 0.9401 0.9551 0.9401 0.0857 0.1143 NB 0.9643 0.9429 0.9594 0.9401 0.9674 0.9401 0.9629 0.9401 0.0714 0.1143 DT 0.9357 0.9286 0.9461 0.9356 0.9214 0.9155 0.9309 0.9235 0.1286 0.1429 RF 0.9286 0.9429 0.9313 0.9467 0.9187 0.9337 0.9241 0.9393 0.1429 0.1143 In conclusion, the comparison of results before and after applying RST feature se- lection highlights its significant impact on enhancing classification performance across various datasets. RST consistently improves or maintains high performance for multiple ML models. While some models, such as LR and Kernel SVM, show considerable im- provements, others like RF exhibit slight variations in performance, yet still retain their robustness. Overall, RST proves to be an effective method for reducing dimensionality while preserving or enhancing essential classification capabilities, thus improving model efficiency and performance across diverse datasets. T. Ashika, G. H. Grace / Eur. J. Pure Appl. Math, 18 (2) (2025), 5934 18 of 22 3.6. Statistical validation In this study, the impact of RST based feature selection on the performance of classi- fication models across five datasets was evaluated. To statistically validate the observed improvements, paired t-tests on performance metrics was conducted, comparing model results before and after RST-based feature selection. The p-values for each performance metric across the five datasets are summarized in table 10. Table 10: P-values from Paired t-Tests Comparing Performance Metrics Before and After RST-Based Feature Selection Metric Seeds Heart Attack Obesity Online Food Delivery Breast Cancer Accuracy 0.1536 0.3559 0.5902 0.0524 0.00468 Precision 0.0455 0.3559 0.0001 0.0632 0.00122 Recall 0.8392 0.2814 0.0042 0.0489 0.00254 F1 Score 0.2754 0.2743 0.0827 0.0522 0.00248 Based on the results presented in table 10, the paired t-tests confirm that precision and recall show statistically significant improvements in several datasets, particularly obesity, online food delivery, and breast cancer. This indicates that RST-based fea- ture selection enhances the model’s ability to accurately identify and classify positive instances. While accuracy did not significantly improve in most cases, marginal gains were observed in the online food delivery and breast cancer datasets. Similarly, F1-score showed borderline significance in some scenarios, suggesting a balanced enhancement in both precision and recall. By evaluating a range of performance metrics, comprehensive assessment of model behaviour is ensured. Notably, improvements in precision and recall are especially critical in medical and sensitive applications, where minimizing false posi- tives and false negatives is essential. The inclusion of statistical validation addresses the credibility of the findings. These results support the conclusion that RST-based feature selection is an effective and valuable technique for enhancing classification performance across diverse datasets, reinforcing its potential for broader application in ML tasks. 4. Discussion Although RST may result in marginally lower classification metrics in certain cases, its value extends beyond predictive accuracy. As a feature selection method, RST excels in enhancing model interpretability, reducing computational complexity, and minimiz- ing overfitting. These advantages are particularly important in fields like healthcare, where both transparency and efficiency are crucial. The results of this study indicate that RST-based feature selection consistently preserves or improves classification per- formance across various datasets. For instance, in the high-dimensional Online Food Delivery dataset (54 features), RST reduced the feature set to just 4 attributes, improv- ing KNN accuracy from 0.7216 to 0.7564. In the low-dimensional Seeds dataset, RST T. Ashika, G. H. Grace / Eur. J. Pure Appl. Math, 18 (2) (2025), 5934 19 of 22 reduced the features from 7 to 2, increasing SVM accuracy from 0.9421 to 0.9649. Larger datasets, such as the Breast Cancer dataset (699 instances), also showed im- provements (e.g., RF accuracy increased from 0.9286 to 0.9429), demonstrating that RST scales effectively with dataset size. Model-specific analysis revealed that algo- rithms sensitive to feature space, such as LR and SVM, benefitted the most from RST, as seen in the Seeds dataset, where LR improved from 0.9245 to 0.9623. On the other hand, ensemble models like RF, which are robust to redundant features, showed smaller improvements or slight performance degradation, such as in the Obesity dataset (RF ac- curacy dropped from 1.0 to 0.9091). RST’s impact also varied depending on the dataset characteristics. In balanced datasets like Seeds, improvements were consistent across classifiers, while in imbalanced datasets like Heart Attack, the effects were more varied. For example, KNN in Heart Attack improved significantly from 0.625 to 0.9811, likely due to RST’s focus on features associated with the majority class. Despite these benefits, RST has limitations, including the need for discretization of continuous attributes, which can introduce quantization bias or reduce information pre- cision. Additionally, RST can be sensitive to noisy or overlapping data. The QR al- gorithm, while computationally efficient, may not always identify the globally optimal reduct. Future research could address these issues by integrating advanced discretization techniques, noise handling methods, and metaheuristic-based feature selection strategies to enhance RST’s robustness and scalability. 5. Conclusion The study presents a two-phase evaluation framework to assess the impact of RST on classification performance. In the first phase, standard ML models are applied to raw datasets. In the second phase, RST-based feature selection was implemented using the QR algorithm, and classifier performance was re-evaluated on the reduced feature sets. Overall, RST generally enhanced or maintained classification performance across the five datasets examined. Notable improvements were observed for models such as LR, SVM, and KNN, particularly in datasets where redundant or noisy features were effectively eliminated. However, slight performance declines occurred in certain cases, for exam- ple, RF on the Obesity dataset (accuracy declined from 1.0 to 0.9091) and SVM on the Breast Cancer dataset (from 0.9572 to 0.9357). These declines may be attributed to the removal of minor yet informative features during the reduction process. Such outcomes underscore that while RST enhances model interpretability and computational efficiency, its effectiveness can vary depending on dataset-specific factors such as sample size, class balance, and feature dependencies. To address the limitations of the QR algorithm and improve generalizability, future re- search could explore hybrid approaches. Integrating RST with metaheuristic optimiza- tion techniques such as Genetic Algorithms may enhance reduct selection by evolving multiple candidate subsets in parallel potentially identifying more discriminative fea- ture sets for complex, high-dimensional datasets. Additionally, combining RST with DL could capitalize on RST’s interpretability and DL’s representational power. For in- T. Ashika, G. H. Grace / Eur. J. Pure Appl. Math, 18 (2) (2025), 5934 20 of 22 stance, RST-reduced features could be used as inputs to feedforward or convolutional neural networks, reducing training time and mitigating overfitting by focusing on the most relevant predictors. References [1] Zdzis law Pawlak. Rough sets. International journal of computer & information sciences, 11:341–356, 1982. [2] Rafael Bello and Rafael Falcon. Rough sets in machine learning: a review. 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Machine learning, 45:5–32, 2001. https://www.kaggle.com/datasets/benroshan/online-food-delivery-preferencesbangalore-region/code https://www.kaggle.com/datasets/benroshan/online-food-delivery-preferencesbangalore-region/code https://www.kaggle.com/datasets/benroshan/online-food-delivery-preferencesbangalore-region/data https://www.kaggle.com/datasets/benroshan/online-food-delivery-preferencesbangalore-region/data https://archive.ics.uci.edu/dataset/15/breast+cancer+wisconsin+original https://archive.ics.uci.edu/dataset/15/breast+cancer+wisconsin+original Introduction Related Work Motivation and Novelty Contribution Materials and Methods Proposed work Dataset Description Data preprocessing Rough set theory RST QR Algorithm Models of ML Evaluation metrics Experimental results Experimental Setup Feature selection Classification with ML Algorithms Using Original Features Classification with ML Algorithms Using Features selected by RST Comparison of Results Before and After Feature Selection using RST Seeds Dataset Heart attack dataset Obesity dataset Online food delivery dataset Breast cancer dataset Statistical validation Discussion Conclusion