Fuzzy Optimization, Rough Set Theory, Intuitionistic Fuzzy Sets.
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Scopus Publications
Scopus Publications
Development of rough set based machine learning approach to screen breast cancer Sangeetha Sivakumar, Shakeela Sathish, Debabrata Datta Iaes International Journal of Artificial Intelligence, 2026 One of the major causes of death for women is breast cancer. A substantial number of women diagnosed with breast cancer die due to inaccuracies in diagnosis and delays in treatment. Cancer prediction must be accurate in order to improve treatment quality and patient survival rates. This study evaluates logistic regression (LR), decision tree algorithm (DTA), and adaptive boosting (AdaBoost) (AB ensemble learning algorithm) in conjunction with rough set theory (RST) to enhance breast cancer classification using the Wisconsin diagnosis breast cancer dataset (WDBC). By employing rough set approximations, including the upper and lower bounds of features, this study introduces a novel rough AdaBoost (Rough AB) algorithm to improve classification accuracy. Various performance indices are compared across algorithms. The proposed Rough AB algorithm demonstrated superior performance, particularly in prediction accuracy for both benign and malignant cases. It incorporates roughness to determine the starting node of the decision stump, offering a significant improvement in ensemble learning techniques for medical diagnostics. It gives practical implications for clinical decision-making, potentially enabling more reliable and timely breast cancer diagnoses, which can significantly impact patient outcomes. The proposed method leverages rough set approximations to refine feature selection and improve prediction accuracy. Also, it positions RST as an explainable artificial intelligence (XAI) technique, highlighting its interpretability, ethical transparency, and potential integration with deep learning for clinical deployment.
Rough Injective G-Modules S. Sangeetha, Shakeela Sathish, B. Muthu Deepika, B. Srirekha Mathematics and Statistics, 2025 The concept of a G-module serves as a fundamental link between group theory and module theory, offering a powerful algebraic framework for analyzing group actions on modules. In this paper, we extend the classical theory of G-modules by incorporating the mathematical foundation of rough set theory, which is well-suited for modeling uncertainty, vagueness, and indiscernibility. To this end, we introduce and formalize the notion of rough G-modules—algebraic structures where the module operations and group actions are subject to approximation, based on lower and upper bounds. Also, we define and investigate rough injective G-modules, which generalize the classical concept of injectivity under rough approximations. We examine their structural properties, provide characterizations, and explore their behavior under homomorphisms and extensions. The paper establishes key embedding theorems and extension criteria, ensuring the compatibility of injectivity with rough approximation operators. The practical relevance of these theoretical developments through an application to data access control systems is provided where user permissions and role hierarchies naturally exhibit rough and uncertain relationships. Our results offer a novel algebraic framework for reasoning about access privileges in the presence of partial or uncertain information, thus highlighting the potential of rough G-module theory in real-world computational settings.
A New Approach towards Rough Lattice Using Rough Relation with a Condition B. Srirekha, Shakeela Sathish Mathematics and Statistics, 2025 The concept of rough relations plays a significant role in rough set theory, introduced by Zdzisław Pawlak in 1981. This study employs the rough membership function as a key tool to represent and analyze rough relations over a universe of discourse. A specific condition is applied to these relations and examined through ordered pairs, allowing systematic evaluation of approximations and their behavior. The work investigates the algebraic properties of rough relations within a lattice-theoretic framework, particularly on distributive lattices equipped with a complementary operation. This structure provides a clear interpretation of the approximation process and the relationship between elements. The existence and behavior of upper approximations are illustrated through examples, with emphasis on how granularity refines approximation boundaries and improves the classification of indiscernible objects. Key theoretical results demonstrate that in a rough lattice, if two elements are ordered, then their meet and join operations preserve non-negativity under the rough membership function, reflecting algebraic consistency. This property extends to complementary elements, ensuring that their mutual relationships also maintain non-negative rough membership values. Additionally, when comparing two rough lattices over the same universe, inclusion between their approximation sets leads to a monotonic increase in rough membership values, indicating order preservation. In distributive lattices, specific inequalities involving elements and their complements reinforce internal consistency between the algebraic and rough structures. Within the upper approximation space, element ordering is symmetrically reflected through complementation, supporting the duality principle. The study also confirms the transitivity of the rough membership function: if one element is roughly related to a second, and that second to a third, then the first is also roughly related to the third—highlighting logical coherence. Overall, these findings advance the theoretical understanding of rough lattice structures and underscore their importance in modeling uncertain and incomplete information, with applications in logic programming, data mining, and formal concept analysis.
Heart Failure Prediction Improvement Using Fuzzy Logic Pre-processing and Random Forest Classifier S. Parthasarathy, Shakeela Sathish, M. Logeshwari New Mathematics and Natural Computation, 2025 Heart Failure (HF) is a critical condition that necessitates precise prediction for effective intervention. Traditional machine learning approaches have shown promise in predicting heart failure, yet their performance can be hindered by noisy and imprecise data. This study explores the integration of fuzzy logic pre-processing with a Random Forest classifier to enhance the prediction accuracy of heart failure outcomes. The objective of this work is to determine how well a Random Forest classifier predicts heart failure when pre-processed with fuzzy logic. Could fuzzy logic pre-processing improve machine learning models’ ability to predict medical prediction. This is the research subject that is being tackled. In order to convert raw input characteristics into more informative fuzzy features, fuzzy logic pre-processing is applied in the methodology. The classification accuracy of the Random Forest model is then compared with and without this pre-processing. Crucial results indicate that adding fuzzy logic pre-processing led to a marginal increase in accuracy, from 76.67% to 77.78%. The primary finding indicates that pre-processing with fuzzy logic has a beneficial effect on model performance, indicating that it may improve medical predictions. Fuzzy logic, with its capability to handle uncertainty and imprecision, can preprocess the data, making it more suitable for subsequent classification tasks. Furthermore, we provided key performance metrics such as accuracy, precision, recall, and F1-score for the models tested (Gaussian Kernel and Bayesian Inference before and after balancing). We present a case study demonstrating the effectiveness of this hybrid approach.
Roughness in S|U|-Submodules Sangeetha Sivakumar, Shakeela Sathish Mathematical Modelling of Engineering Problems, 2024 A rough set theory (RST) was developed by Zdzislaw Pawlak to handle vagueness and uncertainty in data analysis.An approximation of a vague concept consists of two precise concepts a lower and an upper approximation.These approximations are two basic operations in rough set theory.An upper approximation contains all objects that may possibly belong to a concept, and a lower approximation contains all objects that certainly belong.The boundary region is the difference between the upper and lower approximations.Thus, rough set theory expresses vagueness by using a boundary region of a set rather than by using membership.By using the pair of sets, rough set theory extends traditional set theory by defining a subset of a universe.The properties of any set can be clearly understood if an algebraic structure is developed.This paper considers an approximation space with a finite universe and introduces a rough action by a symmetric group S|U| acting on all rough sets in this space.Also, we proved that the number of orbits of the symmetric group S|U| in rough sets is one.We then introduced the S|U|-submodule and proved that the kernel of rough homomorphism is a rough || submodule.An example of how rough action can be used to find missing values in sample cancer data has also been provided.
Enhanced Characterization of Rough Semigroup Ideals: Extension and Analysis Sangeetha Sivakumar, Shakeela Sathish Mathematical Modelling of Engineering Problems, 2024 Rough set theory (RST) is a formal theory derived from logical properties of information systems.Rough set theory extends traditional set theory by defining a subset of a universe through the use of a pair of sets referred to as the lower and upper approximations.It is a mathematical approach for dealing with ambiguities and imprecisions in a variety of situation.Since its introduction by Zdislaw Pawlak in the late eighties of the previous century, it has evolved into pure and applied directions from mathematical, logical, and computational perspectives.The area of rough set theory in computational mathematics is rapidly developing.As far as vagueness and imprecision are concerned, rough set theory is basically a mathematical approach.An equivalence relation is a key concept in rough set models.Approximations at the lower and upper levels are constructed based on equivalence classes.There is wide application of algebraic systems in sequential machines, formal languages, arithmetic codes, and error-correction algorithms.The study of any set will be effective if an algebraic structure is developed for it.In the context of semigroups research, rough set theory can be used to analyse and understand the properties and relationships within semigroups.Semigroups and related algebraic structures and their properties can be explored more deeply when rough set theory is applied.The aim of this paper is to extend the concept of rough semigroup ideals.It has already been shown that some properties of rough (left, right) ideals in semigroups can be obtained by extending the notion of a left (right) ideal in a semigroup.As a result of considering h-ideals in semigroups, rough upper hideals (left & right) have been introduced here along with their properties.Also, the results related to rough semi-lattices and rough quotient semigroups are given.These concepts are explained with suitable examples.
An Innovative Method for Attribute Reduction: Weighted Attribute Concepts for Probabilistic Analysis of Decision Attributes Srirekha Baskaran, Shakeela Sathish Mathematical Modelling of Engineering Problems, 2023 Attribute reduction, a seminal aspect of data analysis, primarily hinges on the indiscernibility matrix.Previous studies have explored the weight of an attribute via various methods, yet achieving optimal reduction remains elusive.This study proposes a novel approach to optimal reduction, leveraging the concept of weighted attributes based on the probability values of core and non-core elements.This approach scrutinizes the accuracy of both core and non-core attributes, thereby enhancing our comprehension of the object's attributes.The weighted attribute concept is derived in light of entropy information and the indiscernibility matrix.A discernibility matrix aids in ascertaining the reduct, whereas entropy information facilitates the analysis of the weight of uncertain data.By deploying decision attributes, we derive the core and its corresponding probabilistic value, establishing an algebraic structure as an ordered pair of objects with associated weight concepts.This structure further enables the investigation of the consistency set and the join (meet) irreducible set employing weighted attribute concepts.Ultimately, optimal reduction is determined by the weight of non-core elements, allowing a comprehensive analysis of the information system and procurement of its essential attributes for decision-making.The proposed concept of weighted attributes is elucidated using a biological dataset.
Aspects of Algebraic Structure of Rough Sets S. Sangeetha, Shakeela Sathish Mathematics and Statistics, 2023 Rough sets are extensions of classical sets characterized by vagueness and imprecision. The main idea of rough set theory is to use incomplete information to approximate the concept of imprecision or uncertainty, or to treat ambiguous phenomena and problems based on observation and measurement. In Pawlak rough set model, equivalence relations are a key concept, and equivalence classes are the foundations for lower and upper approximations. Developing an algebraic structure for rough sets will allow us to study set theoretic properties in detail. Several researchers studied rough sets from an algebraic perspective and a number of structures have been developed in recent years, including rough semigroups, rough groups, rough rings, rough modules, and rough vector spaces. The purpose of this study is to demonstrate the usefulness of rough set theory in group theory. There have been several papers investigating the roughness in algebraic structures by substituting an algebraic structure for the universe set. In this paper, rough groups are defined using upper and lower approximations of rough sets from a finite universe instead of considering the whole universe. Here we have considered a finite universe <img src=image/13433180_01.gif> along with a relation <img src=image/13433180_02.gif> which classifies the universe into equivalence classes. We have identified all rough sets with respect to this relation. The upper and lower approximated sets have been taken separately and these form a rough group equivalence relation (<img src=image/13433180_03.gif>) and it partitions the group (<img src=image/13433180_04.gif>) into equivalence classes. In this paper, the rough group approximation space (<img src=image/13433180_05.gif>) has been defined along with upper and lower approximations and properties of subsets of <img src=image/13433180_06.gif> with respect to rough group equivalence relations have been illustrated.
Attributes Reduction on SE-ISI Concept Lattice for an Incomplete Context Using Object Ranking B. Srirekha, Shakeela Sathish, R. Narmada Devi, Miroslav Mahdal, Robert Cep, K. Elavarasan Mathematics, 2023 The formal concept of lattice plays a vital role in knowledge discovery. Reduction of the attribute has many applications in machine learning technology and data mining fields. In this paper, we introduce an object ranking concept to define a consistency set and the reduction of the attributes by structural features. An incomplete information system works on the three-way concepts using the SE-ISI Context. The granular was emphasized with join (meet) irreducible sets using the object ranking concepts. A dual operator is defined based on the object ranking concepts and its properties and conditions are verified. Hence, this elaborates on the four kinds of reduction of the attributes. The ordered pairs give the knowledge of the attributes that deal with the interval set of both the approximation of rough set theory concerning the objects. Therefore, the relationship between four kinds of reduction of the attribute was appropriate to access the consistency set using the object ranking concepts by some of the theorems and examples.
Generalized Intuitionistic Fuzzy Flow Shop Scheduling Problem with Setup Time and Single Transport Facility T. Yogashanthi, Shakeela Sathish, K. Ganesan International Journal of Fuzzy Logic and Intelligent Systems, 2023 Setup time is the amount of time required for a machine to adjust its settings or the preparation of a device at each stage to process and deliver a completed job.A novel approach for the n-job 2-machine generalized intuitionistic fuzzy flow shop scheduling problem, subject to the setup time, was proposed.When the machines are kept in different places, the transporting and return times of transport play a significant role in the production.Generalized triangular intuitionistic fuzzy numbers were considered to represent the processing, setup, transportation, and return times.This study aims to minimize the intuitionistic fuzzy total production time with less vagueness.
