IAES Inter national J our nal of Articial Intelligence (IJ-AI) V ol. 15, No. 2, April 2026, pp. 1982 ∼ 1998 ISSN: 2252-8938, DOI: 10.11591/ijai.v15.i2.pp1982-1998 ❒ 1982 De v elopment of r ough set based machine lear ning appr oach to scr een br east cancer Sangeetha Si v akumar 1 , Shak eela Sathish 2 , Debabrata Datta 3 1 Department of Mathematics, SRM Institute of Science and T echnology , Ramapuram, India 2 Department of Computing T echnologies, School of Computing, SRM Institute of Science and T echnology , Kattankulathur , India 3 Department of Information T echnology , Heritage Institute of T echnology , K olkata, India Article Inf o Article history: Recei v ed Jan 22, 2025 Re vised Jan 9, 2026 Accepted Feb 6, 2026 K eyw ords: AdaBoost Algorithm Breast cancer diagnosis Decision tree algorithm Logistic re gression Rough AdaBoost algorithm ABSTRA CT One of the major causes of death for w omen is breast cancer . A substantial number of w omen diagnosed with breast cancer die due to inaccuracies in diagnosis and delays in treatment. Cancer prediction must be accurate in order to impro v e treatment quality and patient survi v al rates. This study e v aluates logistic re gression (LR), decision tree algorithm (DT A), and adapti v e boosting (AdaBoost) (AB ensemble learning algorithm) in conjunction with rough set theory (RST) to enhance breast cancer classication using the W isconsin diagnosis breast cancer dat aset (WDBC). By emplo ying rough set approximations, including the upper and lo wer bounds of features, this study introduces a no v el rough AdaBoost (Rough AB) algorithm to impro v e classication accurac y . V arious perf ormance indices are compared across algorithms. The proposed Rough AB algorithm demonstrated superior performance, particularly in prediction accurac y for both benign and malignant cases. It incorporates roughness to determine the starting node of the decision stump, of fering a signicant impro v ement in ensemble learning techniques for medical diagnostics. It gi v es practical implications for clinical decision-making, potentially enabling more reliable and timely breast cancer diagnoses, which can signicantly impact patient outcomes. The proposed method le v erages rough set approximations to rene feature selection and impro v e prediction accurac y . Also, it positions RST as an e xplainable articial intelligence (XAI) technique, highlighting its interpretability , ethical transparenc y , and potential inte gration with deep learning for clinical deplo yment. This is an open access article under the CC BY -SA license . Corresponding A uthor: Shak eela Sathish Department of Computing T echnologies, School of Computing, SRM Institute of Science and T echnology Kattankulathur , T amil Nadu, India Email: shak eels1@srmist.edu.in 1. INTR ODUCTION Breast cancer remains one of the most pre v alent and deadly forms of cancer af fecting w omen w orldwide. Early detection is crucial for i mpro vi ng prognosis and survi v al rates. T raditional screening methods, such as mammograph y , while ef fecti v e, can sometimes yield f alse positi v es or ne g ati v es, leading to unnecessary anxiety or missed diagnoses. Recent adv ances in machine learning ha v e been used to enhance medical diagnostics by identifying patterns and making predictions by analyzing lar ge amounts of data. Cells in the human body gro w , di vide and die in an orderly manner . A person gets cancer when their cells di vide uncontrollably , according to the National Breast Cancer F oundation [1] and American Cancer Society [2]. J ournal homepage: http://ijai.iaescor e .com Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Artif Intell ISSN: 2252-8938 ❒ 1983 Spitale et al. [3] in 2009 found that among w omen in de v eloped countries, breast cancer accounts due to the uncontrolled gro wth of abnormal cells in the milk-producing glands of the breast. Subtypes of breast cancer v ary in terms of risk f actors, clinical presentation, histopathologic characteristics, outcome and response to systemic treatments. Breast cancer must therefore be class ied accurately and early . Earlier diagnosis and treatment ha v e been made poss ible by impro v ements in pre v ention and diagnosis. The medical databases contain a great deal of information about patients with their medical conditions. Among the most serious medical conditions is breast cancer . It has become increasingly dif cult for humans to analyze lar ge amounts of data and databases that are a v ailable. One of the most challenging tasks in the medical en vironment is analyzing these databases. Extraction of kno wledge from databases is therefore both necessary and possible. Breast cancer outcomes can be classied and predicted using a v ariety of algorithms. Rough set theory (RST) of fers a lot to the machine learning community in terms of data analysis and kno wledge disco v ery . Both RST and machine learning emphasize remo ving irrele v ant/redundant attrib utes. P a wlak [4] introduced the concept of rough sets as an e xtension of set theory in 1982. Unlik e other methods that require additional information about data distrib ution or membership functions, RST relies s o l ely on the data itself, making it particularly suitable for medical applications where data may be incomplete or imprecise. By inte grating RST with machine learning, we can de v elop rob ust models that impro v e accurac y also reliability of breast cancer screening. Concepts are approximated under uncertainty using this approach. By reducing the precision of the data presented by Su and Hsu [5] in 2006, the rough set approach enables pattern disco v ery in imperfect data. Data mining, machine learning and medical diagnoses are some of the areas where the theory has been used e xtensi v ely , including attrib ute selection, data reduction, rule disco v ery and genetics. In 2010, Busse [6] presented a rough set approach to mining numerical data. Ja w aorski [7] g a v e a rule induction method that combined rough set with statistical approaches in 2008. Medical classication has been addressed by a number of published a lgorithms recently . According to La vra ˇ c [8], neural netw orks, Bayesian class ications, genetic algorithms, decision trees (DT), and fuzzy theory are some of the most commonly used algorithms in medical elds. Indiscernibility and information systems are the tw o components of RST . In light of its dependence on an information system, it can s erv e as a training set for both unsupervised and supervised learning models, enabling a close connection between data-dri v en disco v ery and learning. Indiscernibility results in granulation of the information system. An e xtended RST method for constructing similarity relations w as introduced by Filberto et al. [9] in 2010. In 2004, Busse [10] proposed characteris tic relations based on indiscernibility . In 2007, Zhu [11] proposed generalized rough sets based on relations and topological approaches in co v ering rough sets. A composite rough set for dynamic data mining w as described by Zhang et al. [12] in 2014. Zhang et al. [13] presented a parallel method f o r computing rough set approximations in 2013. In 2012, Zhang et al. [14] dened neighborhood rough sets for dynamic data mining. Greco et al. [15] presented a parameterized rough set model using rough membership and Bayes ian conrmation measures in 2008. In 1988, P a wlak et al. [16] discussed the probabilistic and deterministic approaches. Slezak and Ziark o [17] introduced decision-theoretic rough set models in 2005. A probabilistic rough set as well as tw o Bayesian approaches to rough sets ha v e been proposed in [18], [19]. Model of v ariable precision rough set w a s presented by Y ao and Zhou [20] in 2016. Ziarco [21] proposed machi ne learning techniques in 1993 for diagnosing breast cancer based on image processing nuclear features. Feature selection in pattern recognition w as applied using the rough set method by Swiniarski and Sk o wron [22] in 2003. Ghasemi et al. [23] conducted a systematic scoping re vie w on the application of e xplainable articial intelligence (XAI) in breast cancer detection and risk predic tion. A systematic re vie w on e xplainable machine learning for breast cancer diagnosis from mammograph y and ultrasound im ages is gi v en in [24]. A federated learning frame w ork for breast cancer prediction demonstrated that deep neural netw ork models can achie v e high diagnostic performance while preserving patient pri v ac y through col laborati v e learning across healthcare institutions, with a reported accurac y of 97.54% and an F1-score of 97% [25]. T ransfer learning has been ef fecti v ely emplo yed for deep neural netw ork-based classication of bre ast cancer X-ray images, which pro v es that this technique is able to produce better diagnostic accurac y with limited labeled data [26]. While the application of machine learning in the diagnosis of breast cancer has seen considerable progress, there should be further e xploration on ho w it can best be combined with RST in impro ving diagnostic performance using cl assication algorithms. This study compares the ef fecti v eness of logistic re gression (LR), DT , and the ensemble algorithm AdaBoost (AB), focusing on their accurac y . sensiti vity , specicity , and precision. By inte grating RST into the analysis, this paper aims to pro vide ne w perspecti v es on enhancing data-dri v en diagnostic methodologies. Recent results in AI ha v e accelerated the use De velopment of r ough set based mac hine learning appr oac h to scr een br east cancer (Sang eetha Sivakumar) Evaluation Warning : The document was created with Spire.PDF for Python.
1984 ❒ ISSN: 2252-8938 of machine learning for medical diagnostics. Ho we v er , man y high-performing models, such as deep neural netw orks, are often vie wed as black box es, limiting their trust and adoption in clinical settings. Therefore, there is a gro wing need for interpretable and transparent AI models that balance accurac y with e xplainability . In this study , LR, decision tree algorithm (DT A) and AB (ensemble learning algorithm) are e xamined for the purpose of implementing rough set concepts in the diagnosis of breast cancer using W isconsin diagnosis breast cancer dataset (WDBC). W e emplo y RST , which is a mathematical frame w ork for handling uncertainty and v agueness in data, in order to reduce attrib utes by identifying the minimal subset of attrib utes (reduct) necessary for retaining the same classication po wer as the original dataset. By reducing redundanc y and enhancing computational ef cienc y , only the most signicant fea tures are used for classication. A dataset containing data fr o m v e patients w as used to v alidate the approach. W e successfully classied patients using the Rough AB algorithm after e xtracting reducts using RST and demonstrating the method’ s reliability . A comparison of RST with other classication algorithms consistently produced superior results. It is e vident from these ndings that RST holds up when f aced with uncertainty or incomplete information when it comes to identifying patterns and relationships in data. The no v elty of this research is the inte gration of roughness measures in the AB frame w ork to form the proposed Rough AB algorithm. Unlik e typical rough ensemble methods, the proposed model initializes weak learners by weighting attrib utes with information about roughness, whi ch impro v es ef cienc y in both learning and interpretability . Additionally , this w ork more clearly positions RST as a basis of XAI in healthcare, which lls the g ap between accurac y-dri v en ensemble models and rule-based transparenc y . Extensi v e performance e v aluation on the WDBC dataset and a ne wly introduced cli n i cal dashboard m ock-up demonstrate the method’ s diagnostic ef fecti v eness and deplo yment potential. In this paper , an analysis of data of breast cancer patients using rough sets is presented. An information system with 569 objects (patients) described by attrib utes w as dened for the analysis of patients. It is important to correctly identify benign and malignant cases to a v oid deciding benign patients to be malignant, causing them mental distress, or malignant patients to be classied as benign, resulting in their health deteriorating. In this chapter we present three dif ferent algorithms (LR, DT A, and AB) based on rough sets for classifying breast cancer data. Specically , we emphasize the role of reducts and their approximations in feature selection. The roughness of each attrib ute has been considered to deci de the starting node of the decision stump under the Rough AB algorithm. 2. D A T A AND METHOD 2.1. Dataset W e used data from WDBC for this study . A dataset repository at Uni v ersity of California, Irvine (UCI) w as used to obtain this dataset [1]. A total of 569 records are included in the dataset. Benign breast changes account for 357 cases (62.7%) and malignant breast cancer accounts for 212 cases (37.3%). Each record contains an ID, diagnosis (‘B’indicates benign, ‘M’ indicates malignant) and 30 features (rad mean ( r m ), t e x mean ( t m ), peri mean ( p m ), ar mean ( a m ), smooth mean ( s m ), compact mean ( c m ), conca v mean ( co m ), conca v e points mean ( cp m ), symm mean ( sy m ), frac dimension mean( f r m ), rad se ( r e ), te x se ( t e ), peri se ( p e ), ar se ( a e ), smooth se ( s e ), compact se ( c e ), conca v se ( co e ), conca v points se( cp e ), symm se( sy e ), frac dim se ( f r e ), rad w orst ( r w ), te x w orst ( t w ), peri w orst ( p w ), ar w orst ( a w ), smooth w orst ( sy w ), compact w orst ( c w ), conca v w orst ( co w ), conca v points w orst ( cp w ), symm w orst ( sy w ), frac dime w orst ( f r w )) assigned a real-v alue. An image of a ne needle aspirate of a breast mass is digitized for the m easurement of these 30 real-v alued features. Cell nuclei in the image are represented by these characteristics. There are ten features that are estimated for each nucleus of each cell, including radi us, te xture, perimeter , area, smoothness, compactness, conca vity , conca v e points, symmetry , and fractal dimension. This resulted in a database of 30 real-v alued input attrib utes for 569 images, which consisted of the a v erage v alue, the mean of the three w orst measurements, and the standard error . The dataset does not contain an y missing v alues. 2.2. Data pr epr ocessing As data science de v elops rapidly and b uilding operational data becomes more readily a v ai lable, opportunities for de v eloping data dri v en b uilding ener gy manage ment systems ha v e increased. V alid data analysis requires preprocessing of data. There is no missing v alue in the data, as ranges for all features are dif ferent. During data preparation, we used normalization, which is scaling technique used in machine learning. Int J Artif Intell, V ol. 15, No. 2, April 2026: 1982–1998 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Artif Intell ISSN: 2252-8938 ❒ 1985 3. ALGORITHMS FOR MA THEMA TICAL CLASSIFICA TION This study used LR, DT A, and AB algorithm the ensemble learning algorithm on rough sets fore predicting breast cancer . 3.1. Logistic r egr ession The use of this approach in machine learning is widespread. In this approach, dif ferent input feat ures are compared by the LR algorithm to establish a decision boundary . A cost function is then computed to map the inputs to outputs. The sigmoid (logistic) function, is gi v en by (1). h ( x ) = g ( θ T x ) where g ( θ T x ) = 1 1 + e − θ T x (1) Here g ( θ T x ) is sigmoid functi on, θ T are model parameters and x is the input feature. Gradient descent is used to optimize the results from the cost function after the sigmoid function has been computed [27]. 3.2. Decision tr ee algorithm There are man y classi cation problems that can be solv ed using the DT A. By pruning datasets, DT identify hidden patterns in data and are highly accurate. Nodes that do not pro vide meaningful insight into the classication process can be pruned from the DT . The iterati v e Dichotomi ser 3 (ID3) algorithm is one method of implementing a DT . An ID3 algorithm determines its output label based on information g ain and entrop y . The y are gi v en by (2) and (3). H ( s ) = Σ − P ( C ) l og 2 P ( C ) ( E ntr opy ) (2) Where s is input data and c is output class. I G ( A, S ) = H ( S ) − Σ P ( t ) H ( t ) ( I nf or mation G ain ) (3) Where H ( t ) ⊆ H ( s ) and P ( t ) is the number of elements after split t [27]. 3.3. AdaBoost Ensemble learning is a method to train a group of indi vidual classiers and combine their pre dictions before clas sifying ne w e xamples. As an inducti v e learning technique, ensemble learning has recent ly g ained great attention in the machine learning and data mining communities . An illustration of the basic frame w ork for ensemble learning can be found in Figure 1. Figure 1. AB algorithm AB algorithm, is one of the ensemble algorithm. It is also called adapti v e boosting, which can be applied for both the classication (binary and multiclass). A threshold or weighting v alue is assigned to each classier in this boosting algorithm. An indi vidual classier’ s weighted v ote determines the nal output class. De velopment of r ough set based mac hine learning appr oac h to scr een br east cancer (Sang eetha Sivakumar) Evaluation Warning : The document was created with Spire.PDF for Python.
1986 ❒ ISSN: 2252-8938 A weak classier is con v erted into a strong one by adding e xtra weights. Using the (4), we determine the weights for each classier . α i = 1 2 l n ( 1 − ϵ i ϵ i ) , H ( s ) = Σ α i h i ( s ) (4) Where α i and ϵ i are weight and weighted error of each sample i respecti v ely [27]. The nal output prediction is gi v en by H ( s ) 4. EV ALU A TION METRICS F ollo wing are v arious parameters that inuence the performance of the three algorithms disussed in section 3. A confusion matrix represents the performance of the algorithms. It is possible to calculate accurac y ( a r ), precision ( p r ), recall ( r c ), F1 measure ( f 1 m ), sensiti vity ( ss t ), and specicity ( s p t ) based on true positi v e ( T P ), true ne g ati v e ( T N ), f alse positi v e ( F P ), and f alse ne g ati v e ( F N ) v alues. The sample accurac y is calculated using the formula a r = T P + T N T P + T N + F P + F N . In precision, we measure ho w man y of the positi v e samples are correctly anticipated gi v en by p r = T P T P + F P . The recall indicates ho w man y positi v e samples the model correctly predicted. Recall r c = T P T P + F N is essential in medical situations since positi v e cases may go undetected. A model’ s reliability w ould be determined by its precision and recall. f 1 m is a harmonic mean of r c and p r , pro viding an o v ervie w of these tw o f actors f 1 m = 2 T P 2 T P + F P + F N . Basically , sensiti vity refers to a test’ s abilit y to properly classify a sample as malignant or positi v e. In contrast, specicity refers to ho w well a test can determine whether a sample is ne g ati v e or benign. 5. R OUGH SETS RST pro vides a mathematically transparent approach to reasoning under uncertainty . Its ability to generate decision rules directly from data mak es it highly suitable for e xplainable medical diagnostics, where model interpretability is critical. i) Denition 1: the approximation space consists of a set with nite elements Ω , called uni v erse, and an equi v alence relation R on Ω , which is represented by K = (Ω , R ) . ii) Denition 2: classication of f amily of subsets F = C 1 , C 2 , C 3 ...C n on Ω is − C 1 ∪ C 2 ∪ ..... ∪ C n = Ω & C i ∩ C j = ϕ, f or i ̸ = j iii) Denition 3: let A ⊆ Ω } − Ω A = { a i | [ a i ] R ∩ A ̸ = ϕ } , Ω A = { a i | [ a i ] R ⊆ A } and B N A = Ω A − Ω A − P O S ( A ) = Ω A , N E G ( A ) = Ω − B N A . The y describe the upper , lo wer , boundary , positi v e, and ne g ati v e re gions of A respecti v ely and A is rough if B N A is not empty . i v) Denition 4: The approximation accurac y , also re ferred to as the accurac y of roughness, measures ho w well a subset X ⊆ U is approximated with respect to an equi v alence relation gi v en by α R ( X ) = | R ( X ) | | R ( X ) | , where R ( X ) and R ( X ) are lo wer and upper approximation of X respecti v ely . 6. PR OPOSED SCHEME There are tw o fundamental stages to our proposed approach. T o handle v agueness and uncertainty in data, RST is applied to the rst stage. Using this, we determine the reduct to retain the same classication po wer as the original dataset during this stage. In this step, the most signicant features are used for classication, reducing redundanc y and impro ving computational ef cienc y . The second stage of the process in v olv es classication using well-established algorithms. The accurac y of classication is then determined by comparing these algorithms. Compared to other classication algorithms, RST consistently outperformed them. RST is ef fecti v e at identifying patterns and relationships in data despite uncertainty or incomplete information. Additionally , we v alidated our proposed approach using data from v e patients. W e emplo yed the Rough AB algorithm for classication after applying RST to e xtract reducts. A Rough AB classication w as successful in classifying the patients, demonstrating its reliability . The accurac y le v els of RST were also superior to those of other classication algorithms. An illustration of the Int J Artif Intell, V ol. 15, No. 2, April 2026: 1982–1998 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Artif Intell ISSN: 2252-8938 ❒ 1987 proposed approach is pro vided in Figure 2, sho wing the sequential steps from attrib ute reduct ion using RST to the nal classication and accurac y comparison across dif ferent algorithms. Figure 2. Proposed scheme 7. FEA TURE APPR O XIMA TION AND REDUCTION The tw o k e y issues in RST are approximation and reduction. An approximation approximates a subset of the uni v erse based on a gi v en set of features which preserv e the same discriminati v e po wer as whole features. A ner approximation results in a ner reduction. Approximation accurac y meas ure α is an uncertainty measure that identies rough approximations’ imprecision. An approximation with greater accurac y has greater characterizing po wer . Performed by means of the R programming softw are. Algorithm 1 pro vides accurac y approximation. De velopment of r ough set based mac hine learning appr oac h to scr een br east cancer (Sang eetha Sivakumar) Evaluation Warning : The document was created with Spire.PDF for Python.
1988 ❒ ISSN: 2252-8938 Algorithm 1 Accurac y approximation Requir e: T = ( U , A, D , f ) : An information system Requir e: U = { X 1 , X 2 , . . . , X m } : set of objects (ro ws) and A = { a 1 , a 2 , . . . , a n } : set of attrib utes (columns) Requir e: D = { h 1 , h 2 , . . . , h q } : set of decision v alues, f : U × A → A : attrib ute function 1: f or each object x i ∈ U do 2: Group objects into equi v alence classes based on A { Compute I N D ( A ) , the indiscernibility relation. } 3: f or each equi v alence class [ X ] ∈ I N D ( A ) do 4: if the class contains redundant objects then 5: Remo v e redundant objects from the equi v alence class 6: Compute the lo wer approximation 7: f or each equi v alence class [ X ] do 8: Find lo wer approximation X 9: if x i ∈ X then 10: Insert the rule into rules 11: Compute the upper approximation 12: f or each equi v alence class [ X ] do 13: Find upper approximation X 14: if x i ∈ X then 15: Insert the rule into Rules 16: Calculate Accurac y: Accurac y = | X | | X | 17: r etur n Accurac y =0 7.1. Reduction of attrib utes T o determine whether a set of attrib utes is dependent, a decision table is constructed using RST and indiscernible sets. This section presents reducts of attrib utes necessary to describe these classes. The quick reduct algorithm has been used to achie v e reduction as gi v en in Algorithm 2. Using indiscernibility relation, we obtained the reduct using quick reduction algorithm performed using R softw are. R 1 = { t m , a m , s m , cp m , sy m , f r m , t e , t w , p w , sy w , c w , co w } . Classication w as performed using pro v en algorithms—namely LR, DT A, and the AB algorithm—which were compared with RST . Algorithm 2 Reduct Requir e: C n , D n ( C n conditional and D n ar e decision attrib utes) and R (A minimal subset of attrib utes) 1: R d ← {} 2: r epeat 3: T d ← R d 4: f or γ ∈ ( C n − R d ) do 5: if dep R d ∪{ γ } ( D ) > dep T d ( D n ) then 6: T d ← R d ∪ { γ } 7: R ed ← T d 8: until dep R ( D ) = dep C ( D ) 9: r etur n R ed =0 7.2. Accuracy comparison of algorithms T able 1 sho ws the accurac y le v els achie v ed by LR, DT , AB, and RST . An illustration of t he accurac y of four algorithms can be found in Figure 3, which pro vides an o v ervie w of ho w each algorithm performs relati v e to the others. The com parison sho ws that RST is an ef fecti v e method for handling uncertainty and approximation, making it a competiti v e alternati v e. Int J Artif Intell, V ol. 15, No. 2, April 2026: 1982–1998 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Artif Intell ISSN: 2252-8938 ❒ 1989 T able 1. Accurac y comparison of algorithms Algorithm Accurac y (%) LR 96 DT 90 AB 93 RST 100 Figure 3. Accurac y and F1-score comparison across dif ferent algorithms 8. CLASSIFICA TION B ASED ON FEA TURE SUBSETS W e ha v e found that the Benign and Malignant classes are rough in terms of the indiscernibil ity relation R for feature subsets X 1 to X 13 , and the y are gi v en as follo ws: X 1 = { c m , s m , a m , r m , t m , p m , co m , , sy m , f r m , cp m , r e , t e , p e , a e , s e , c e , co e , cp e , sy e , f r e , r w , t w , p w , a w } X 2 = { c m , s m , a m , r m , t m , p m , co m , , sy m , f r m , cp m , r e , t e , p e , a e , s e , c e , co e , cp e , sy e , f r e , r w , t w , p w } X 3 = { c m , s m , a m , r m , t m , p m , co m , , sy m , f r m , cp m , r e , t e , p e , a e , s e , c e , co e , cp e , sy e , f r e , r w , t w } X 4 = { c m , s m , a m , r m , t m , p m , co m , , sy m , f r m , cp m , r e , t e , p e , a e , s e , c e , co e , cp e , sy e , f r e , r w } X 5 = { c m , s m , a m , r m , t m , p m , co m , , sy m , f r m , cp m , r e , t e , p e , a e , s e , c e , co e , cp e , sy e , f r e } X 6 = { c m , s m , a m , r m , t m , p m , co m , , sy m , f r m , cp m , r e , t e , p e , a e , s e , c e , co e , cp e , sy e } X 7 = { c m , s m , a m , r m , t m , p m , co m , , sy m , f r m , cp m , r e , t e , p e , a e , s e , c e , co e , cp e } X 8 = { c m , s m , a m , r m , t m , p m , co m , , sy m , f r m , cp m , r e , t e , p e , a e , s e , c e , co e } X 9 = { r m , t m , p m , a m , s m , c m , co m , cp m , sy m , f r m , r e , t e , p e , a e , s e , c e } X 10 = { c m , s m , a m , r m , t m , p m , co m , , sy m , f r m , cp m , r e , t e , p e , a e , s e } X 11 = { r m , t m , p m , a m , s m , c m , co m , cp m , sy m , f r m , r e , t e , p e , a e } X 12 = { r m , t m , p m , a m , s m , c m , co m , cp m , sy m , f r m , r e , t e , p e } X 13 = { c m , s m , a m , r m , t m , p m , co m , , sy m , f r m , cp m , r e , t e } The accuracies for benign and malignant classes using RST are sho wn in T able 2 of feature s ubsets also compared with other algorithms. Comparison of DT A, AB, LR, and rough set algorithms are gi v en in Figure 4. From T able 2, we can conclude that for the feature subsets X 1 to X 13 , the RST pro vided higher accurac y than the DT A, LR and AB for each class. De velopment of r ough set based mac hine learning appr oac h to scr een br east cancer (Sang eetha Sivakumar) Evaluation Warning : The document was created with Spire.PDF for Python.
1990 ❒ ISSN: 2252-8938 T able 2. Accuracies using RST , LR, DT A, and AB Sets Class | X | | X | a r (RST) a r (AB) a r (LR) a r (DT A) X 1 M 211 213 0.99 0.94 0.76 0.90 B 356 358 0.99 X 2 M 211 213 0.99 0.94 0.75 0.91 B 356 358 0.99 X 3 M 211 213 0.99 0.94 0.75 0.91 B 356 358 0.99 X 4 M 206 214 0.96 0.93 0.75 0.91 B 355 359 0.99 X 5 M 206 214 0.96 0.95 0.70 0.91 B 355 359 0.99 X 6 M 206 214 0.96 0.94 0.71 0.91 B 355 359 0.99 X 7 M 206 214 0.96 0.94 0.71 0.91 B 355 359 0.99 X 8 M 206 214 0.96 0.94 0.72 0.91 B 355 359 0.99 X 9 M 196 214 0.92 0.93 0.70 0.91 B 355 359 0.99 X 10 M 207 220 0.94 0.94 0.72 0.91 B 355 362 0.98 X 11 M 204 220 0.93 0.94 0.71 0.91 B 364 365 0.99 X 12 M 189 221 0.86 0.93 0.68 0.91 B 348 365 0.95 X 13 M 203 222 0.91 0.93 0.66 0.91 B 346 366 0.95 Figure 4. Accurac y comparison of algorithms across dif ferent sets 9. R OUGH AB ALGORITHM Algorithm 3 formalizes the proposed Rough AB procedure. It dif fers from classical AB in that each weak learner is guided by RST through a roughness-based attrib ute e v aluation. A set of attrib utes with a lo w roughness measure is selected at e v ery iteration, highlighting those whose positi v e re gions most accurately reect decision classes. The inte gration of data granularity and boundary-re gion uncertainty impro v es interpretability without reducing accurac y . In the Rough AB algorithm, the roughness measure ρ ( a j ) Int J Artif Intell, V ol. 15, No. 2, April 2026: 1982–1998 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Artif Intell ISSN: 2252-8938 ❒ 1991 is incorporate d into t he weak l earner selection process. In the decision space, attrib utes with lo wer roughness v alues are associated with more certain re gions, thereby minimizing classication ambiguity . Algorithm 3 Rough AB Requir e: T raining dataset D = { ( x i , y i ) } N i =1 where y i ∈ {− 1 , +1 } and number of weak classiers T Ensur e: Final strong classier H ( x ) based on Rough Set-guided boosting 1: Step 1: Initialization 2: Compute the initial uni v erse U = { x 1 , x 2 , . . . , x N } & Determine the indiscernibility relation I N D ( B ) using the full attrib ute set B 3: Initialize sample weights w (1) i = 1 N for all i 4: Step 2: F eatur e Reduction using RST 5: Compute lo wer and upper approximations for each decision class 6: Ev aluate the signicance of each attrib ute a j using the dependenc y de gree: γ ( a j ) = | POS B ( D ) | | U | 7: Select a reduct R ⊆ B containing only the most signicant attrib utes 8: Step 3: Iterati v e Boosting 9: f or t = 1 to T do 10: (a) Roughness-guided weak lear ner selection 11: f or each candidate attrib ute a j ∈ R do 12: Compute roughness measure: ρ ( a j ) = 1 − | POS { a j } ( D ) | | U | 13: Select attrib ute a ∗ = arg min a j ∈ R ρ ( a j ) 14: T rain a decision stump h t ( x ) using a ∗ 15: (b) W eighted err or and classier weight 16: Compute weighted error: ϵ t = P i w ( t ) i I [ h t ( x i ) ̸ = y i ] 17: Compute classier weight: α t = 1 2 ln 1 − ϵ t ϵ t 18: (c) Update sample weights 19: Update weights: w ( t +1) i = w ( t ) i exp( − α t y i h t ( x i )) 20: Normalize weights so that P i w ( t +1) i = 1 21: Step 4: Final classier 22: Combine weak classiers: H ( x ) = sign   T X t =1 α t h t ( x ) ! 23: r etur n H ( x ) =0 A rough estimate of the computational com p l e xity is O ( T × n × m ) , where T corresponds to the number of steps, n , sample attrib utes, and m , the number of att rib utes. The algorithm in Figure 5 be gins with rough set based feature reduction to identify reduct attrib utes, follo wed by roughness-guided boosting iterations. Combined, RST and AB of fer high predicti v e accurac y and transparent, rule-based interpretation suitable for clinical AI applications. 9.1. P erf ormance e v aluation T o ensure rob ust and unbiased performance estimates, all classiers were e v aluated using strat ied 10-fold cross-v alidation. F or each fold we computed precision, recall, F 1 -score, and the area under the recei v er operating characteristic (R OC) curv e (A UC). T able 3 reports the mean ± standard de viation across the folds; Figure 6 sho ws the mean R OC curv es. De velopment of r ough set based mac hine learning appr oac h to scr een br east cancer (Sang eetha Sivakumar) Evaluation Warning : The document was created with Spire.PDF for Python.