Application Of Set Theory Research Articles

Fuzzy Soft Set Theory Applications in Medical Diagnosis: A Comprehensive Review and the Roadmap for Future Studies

This paper provides a literature review addressing the use of soft sets in medical diagnosis. Distinguishing itself from the existing literature, the study offers a comprehensive analysis of how fuzzy soft sets can be integrated into diagnostic processes, highlighting a novel fusion of fuzzy and soft sets in medical applications. Any soft set on a countably infinite universe can be regarded as a fuzzy set, recognizing the limitations of traditional diagnostic tools in dealing with vague and incomplete information, our research aims to utilize the flexibility and comprehensiveness of fuzzy soft sets to enhance decision-making accuracy in medical scenarios. The primary objective of this research is to present a thorough and critical analysis of fuzzy soft set theory in medical diagnosis, aiming to establish it as a fundamental approach in the field. By combining all of these results, we can generate a comprehensive picture of the connections between the many theories that account for fuzziness and imprecision, which helps to fill in the blanks left by recent surveys. The review will focus on identifying the main research trends in this field: the primary research topics that soft set theory addresses in medical applications, the community is currently facing and the major theoretical concepts used to study these topics. The primary objective of this review is to assist in the identifying of emerging research directions. Some of these trends are promising and will help shape a new role for soft set theory in the area of medical applications. The fusion of fuzzy and soft sets in medical applications represents a crucial and necessary stage in the research and diagnosis procedures. Key results include the study on development of algorithms and models that outperform traditional methods in accuracy and reliability.

Feature Imputation using Neutrosophic Set Theory in Machine Learning Regression Context

The prediction context of machine learning aims to discern the underlying patterns that dictate the characteristics to forecast the output. This prediction lacks precision when the input data is not accurate or precise. This study focuses on feature imputation through the application of the neutrosophic set theory. The primary concept involves substituting feature data, which may have accuracy and correctness issues, with neutrosophic variables considering the degrees of truth, indeterminacy, and falsity to produce more precise and resilient predictions. The proposed method was implemented in a specific case study, and the results are analyzed.

Binary relations applied to the fuzzy substructures of quantales under rough environment

Abstract Binary relations (BIRs) have many applications in computer science, graph theory, and rough set theory. This study discusses the combination of BIRs, fuzzy substructures of quantale, and rough fuzzy sets. Approximation of fuzzy subsets of quantale with the help of BIRs is introduced. In quantale, compatible and complete relations in terms of aftersets and foresets with the help of BIRs are defined. Furthermore, we use compatible and complete relations to approximate fuzzy substructures of quantale, and these approximations are interpreted by aftersets and foresets. This concept generalizes the concept of rough fuzzy quantale. Finally, using BIRs, quantale homomorphism is used to build a relationship between the approximations of fuzzy substructures of quantale and the approximations of their homomorphic images.

A systematic literature review of soft set theory

AbstractSoft set theory, initially introduced through the seminal article “Soft set theory—First results” in 1999, has gained considerable attention in the field of mathematical modeling and decision-making. Despite its growing prominence, a comprehensive survey of soft set theory, encompassing its foundational concepts, developments, and applications, is notably absent in the existing literature. We aim to bridge this gap. This survey delves into the basic elements of the theory, including the notion of a soft set, the operations on soft sets, and their semantic interpretations. It describes various generalizations and modifications of soft set theory, such as N-soft sets, fuzzy soft sets, and bipolar soft sets, highlighting their specific characteristics. Furthermore, this work outlines the fundamentals of various extensions of mathematical structures from the perspective of soft set theory. Particularly, we present basic results of soft topology and other algebraic structures such as soft algebras and $$\sigma$$ σ -algebras. This article examines a selection of notable applications of soft set theory in different fields, including medicine and economics, underscoring its versatile nature. The survey concludes with a discussion on the challenges and future directions in soft set theory, emphasizing the need for further research to enhance its theoretical foundations and broaden its practical applications. Overall, this survey of soft set theory serves as a valuable resource for practitioners, researchers, and students interested in understanding and utilizing this flexible mathematical framework for tackling uncertainty in decision-making processes.

Innovative Approach to Android Malware Detection: Prioritizing Critical Features Using Rough Set Theory

The widespread integration of smartphones into modern society has profoundly impacted various aspects of our lives, revolutionizing communication, work, entertainment, and access to information. Among the diverse range of smartphones available, those operating on the Android platform dominate the market as the most widely adopted type. With a commanding 70% share in the global mobile operating systems market, the Android OS has played a pivotal role in the surge of malware attacks targeting the Android ecosystem in recent years. This underscores the pressing need for innovative methods to detect Android malware. In this context, our study pioneers the application of rough set theory in Android malware detection. Adopting rough set theory offers distinct advantages, including its ability to effectively select attributes and handle qualitative and quantitative features. We utilize permissions, API calls, system commands, and opcodes in conjunction with rough set theory concepts to facilitate the identification of Android malware. By leveraging a Discernibility Matrix, we assign ranks to these diverse features and subsequently calculate their reducts–streamlined subsets of attributes that enhance overall detection effectiveness while minimizing complexity. Our approach encompasses deploying various Machine Learning (ML) algorithms, such as Support Vector Machines (SVM), K-Nearest Neighbor, Random Forest, and Logistic Regression, for malware detection. The results of our experiments demonstrate an impressive overall accuracy of 97%, surpassing numerous state-of-the-art detection techniques proposed in existing literature.

Valued-inverse dombi fuzzy graphs

Fuzzy graphs as labeled graphs (fuzzy vertex labeling and fuzzy edge labeling) have many applications in real life such as complex networks, coding theory, medical sciences, communication networks, and management sciences. Also, triangular norms as a special class of functions, have many applications in fuzzy set theory, probability and statistics, and other areas. This paper considers the notations of an inverse fuzzy graph and triangular norms to introduce the new type of graphs as valued-inverse Dombi fuzzy graphs. The valued-inverse Dombi fuzzy graphs are a generalization of inverse fuzzy graphs and are dual to Dombi fuzzy graphs. For any given greater than or equal to one real number, we construct a type of Dombi inverse fuzzy graph and investigate some conditions such that the product and union of Dombi inverse fuzzy graphs be a Dombi inverse fuzzy graph.

Multi-objective non-linear programming problem with rough interval parameters: an application in municipal solid waste management

In dealing with the real-world optimization problems, a decision-maker has to frequently face the ambiguity and hesitancy due to various uncontrollable circumstances. Rough set theory has emerged as an indispensable tool for representing this ambiguity because of its characteristic of incorporating agreement and understanding of all the involved specialists and producing more realistic conclusions. This paper studies an application of the rough set theory for a multi-objective non-linear programming problem that originates for the management of solid wastes. Municipal solid waste management is a global problem that affects every country. Because of the poor waste management system in many nations, the bulk of municipal solid waste is disposed of in open landfills with no recovery mechanism. Hence, an effective and long term waste management strategy is the demand of the day. This research offers an incinerating, composting, recycling, and disposing system for the long-term management of the municipal solid waste. A model for the municipal solid waste management with the goal of minimizing the cost of waste transportation, cost of waste treatment and maximizing the revenue generated from various treatment facilities is developed under rough interval environment. To tackle the conflicting nature of different objectives, an approach is proposed that gives the optimistic and pessimistic views of the decision-maker for optimizing the proposed model. Also, the biasness/preference of the decision-maker for a specific objective is handled by establishing the respective non-linear membership and non-membership functions instead of the linear ones. Finally, to demonstrates the practicality of the proposed methodology, a case study is solved and the obtained Pareto-optimal solution has been compared to those obtained by the existing approaches.

An application of rough set theory to predict telecom customer churn

An application of rough set theory to predict telecom customer churn

Extension of topological structures using lattices and rough sets

<abstract><p>This paper explores the application of rough set theory in analyzing ambiguous data within complete information systems. The study extends topological structures using equivalence relations, establishing an extension of topological lattice within lattices. Various relations on topological spaces generate different forms of exact and rough lattices. Building on Zhou's work, the research investigates rough sets within the extension topological lattice and explores the isomorphism between topology and its extension. Additionally, the paper investigates the integration of lattices and rough sets, essential mathematical tools widely used in problem-solving. Focusing on computer science's prominent lattices and Pawlak's rough sets, the study introduces extension lattices, emphasizing lower and upper extension approximations' adaptability for practical applications. These approximations enhance pattern recognition and model uncertain data with finer granularity. While acknowledging the benefits, the paper stresses the importance of empirical validations for domain-specific efficacy. It also highlights the isomorphism between topology and its extension, revealing implications for data representation, decision-making, and computational efficiency. This isomorphism facilitates accurate data representations and streamlines computations, contributing to improved efficiency. The study enhances the understanding of integrating lattices and rough sets, offering potential applications in data analysis, decision support systems, and computational modeling.</p></abstract>

An application of rough set theory to predict telecom customer churn

An application of rough set theory to predict telecom customer churn

Application of Soft Set Theory in Choice Selection and Purchase

We study the fundamentals of soft set theory which includes soft set operations, soft set relations and functions with applications in purchase and decision making. Selection from different varieties of phones is considered in this paper.

Decision-making in diagnosing heart failure problems using basic rough sets

<p>This manuscript introduces novel rough approximation operators inspired by topological structures, which offer a more flexible approach than existing methods by extending the scope of applications through a reliance on a general binary relation without constraints. Initially, four distinct types of neighborhoods, termed basic-minimal neighborhoods, are generated from any binary relation. The relationships between these neighborhoods and their properties are elucidated. Subsequently, new rough set models are constructed from these neighborhoods, outlining the main characteristics of their lower and upper approximations. These approximations are applied to classify the subset regions and to compute the accuracy measures. The primary advantages of this approach include its ability to achieve the highest accuracy values compared to all approaches in the published literature and to maintain the monotonicity property of the accuracy and roughness measures. Furthermore, the efficacy of the proposed technique is demonstrated through the analysis of heart failure diagnosis data, showcasing a 100% accuracy rate compared to previous methods, thus highlighting its clinical significance. Additionally, the topological properties of the proposed approaches and the topologies generated from the suggested neighborhoods are discussed, positioning these methods as a bridge to more topological applications in the rough set theory. Finally, an algorithm and flowchart are developed to illustrate the determination and utilization of basic-minimal exact sets in decision-making problems.</p>

Curriculum System Design and Teaching Mode Innovation for Specialized College English Platforms

Abstract This study addresses the application of rough set theory in English hierarchical teaching and explores how to optimize the teaching mode and improve the teaching quality and learning effect through this theory. This paper adopts a literature analysis and questionnaire survey method to study rough set theory’s knowledge expression and systematic decision-making mechanism. It applies it to the design of the curriculum system and the innovation of the teaching mode in the English platform of special-purpose universities. The optimized English hierarchical teaching mode using rough set theory significantly improved students’ learning interest and learning effect, in which 87.53% of the students believed it could improve their mastery of knowledge. The average score of 90.3 was 23.4 points higher than that of the control group, which was statistically significant (P<0.05). This study also found that the level of teacher specialization, students’ study habits, and school policies are key factors that influence the implementation of the teaching model. The introduction of rough set theory in this study provides new perspectives and methods for English teaching, promoting innovation in teaching methods and improving students’ learning ability.

Modelling of similarity characteristics of polycyclic aromatic hydrocarbons (PAHs) in Sungai Perak, Malaysia via rough set theory and principal component analysis (PCA)

This paper presents application of rough set theory and PCA for modelling of similarity characteristics of PAHs from Perak River: Tanjung Belanja Bridge (TBB, l1), Water Treatment Plant Parit (WTPP, l2), Parit Town Discharge (PTD, l3), Water Treatment Plant Senin (WTPS, l4), and Water Treatment Plant Kepayang (WTPK, l5). The clustering involved PAHs as attributes and sampling stations as objects. The l1 and l3 were clustered in Simdegx,y≥0.8. The Simdegx,y≥0.7 was observed in all attributes (except l5) forming two sets of clusters. PCA showed that low molecular weight (LMW) PAHs were prominent with variances of 68.47% (naphthalene, Nap) and 27.63% (carbazole).

Applications of Soft Set Theory to the Subalgebras of CI-Algebras

In this paper, the applicability of soft set theory to subalgebras of CI-algebras is investigated. CI-algebras are utilized in algebraic logic and computer science. Soft set theory is a framework for dealing with ambiguous or imprecise information. We employ soft sets to investigate the intersection and union of subalgebras, among other properties of subalgebras of CI-algebras. We demonstrate that soft set theory is a valuable tool for analyzing subalgebras of CI-algebras and developing new results in this domain. This paper contributes to the comprehension of soft set theory and its applications in CI algebras with the findings presented herein.

Automatic Exercise Generation for Exploring Connections between Mathematics and Music

Abstract Mathematics and Music are closely connected and their multifaceted relationship has been explored since ancient times. Pythagoras was one of the first who discovered and formalized one of those connections by studying the arithmetic of musical intervals, expressing them by numerical ratios and relating ratios to consonance/dissonance notions, being the Pythagorean tuning and scale based on arithmetic principles. Another interesting link between Mathematics and Music is the geometric approach to musical composition. Geometric patterns are present in different musical style compositions and some composing techniques, such as the 12-tone technique, use geometric transformations, involving also applications of modular arithmetic and set theory to Music. The aim of this work is to present existing relations between Mathematics and Music and to propose automatic exercise generation for exploring and studying those relations. The exercises are generated using the system MVGEN and the LaTeX package MusiXTeX. The generation process and the automatically generated exercises can be used for creating learning and assessment materials for education in Mathematics and Music, linking Science and Art.

Design and Application of Vague Set Theory and Adaptive Grid Particle Swarm Optimization Algorithm in Resource Scheduling Optimization.

The purpose of resource scheduling is to deal with all kinds of unexpected events that may occur in life, such as fire, traffic jam, earthquake and other emergencies, and the scheduling algorithm is one of the key factors affecting the intelligent scheduling system. In the traditional resource scheduling system, because of the slow decision-making, it is difficult to meet the needs of the actual situation, especially in the face of emergencies, the traditional resource scheduling methods have great disadvantages. In order to solve the above problems, this paper takes emergency resource scheduling, a prominent scheduling problem, as an example. Based on Vague set theory and adaptive grid particle swarm optimization algorithm, a multi-objective emergency resource scheduling model is constructed under different conditions. This model can not only integrate the advantages of Vague set theory in dealing with uncertain problems, but also retain the advantages of adaptive grid particle swarm optimization that can solve multi-objective optimization problems and can quickly converge. The research results show that compared with the traditional resource scheduling optimization algorithm, the emergency resource scheduling model has higher resolution accuracy, more reasonable resource allocation, higher efficiency and faster speed in dealing with emergency events than the traditional resource scheduling model. Compared with the conventional fuzzy theory emergency resource scheduling model, its handling speed has increased by more than 3.82 times.

Application of Rough Set Theory and Bow-Tie Analysis to Maritime Safety Analysis Management: A Case Study of Taiwan Ship Collision Incidents

The surrounding waters of Taiwan are evaluated as a moderate risk environment by Casualty Return, Lloyd’s Registry of Shipping. Among all types of maritime accidents, ship collisions occur most often, which has severe consequences, including ship damage, sinking and death of crews, and destruction of marine environments. It is, therefore, imperative to mitigate the risk of ship collision by exploring the risk factors and then providing preventive measures. This study invited domain experts to form a decision-making group, which helped with the risk assessment. The initial set of risk factors was selected from the literature. The expert group then identified seven representative risk factors using rough set theory (RST). The researchers worked with the experts to delineate the diagram of a bow-tie analysis (BTA), which provided the causes, consequences, and preventive and mitigation measures for ship collision incidents. The results show an integrated research framework for the risk assessment of ship collision that can effectively identify key factors and associated managerial strategies to improve navigation safety, leading to a sound marine environment.

Modeling adoption of genetically modified foods: Application of Rough Set Theory and Flow Network Graph

IntroductionThe main purpose of this study is to extract the rules and patterns governing the behavioral intention of consumers towards the adoption of genetically modified foods (GMFs).MethodThe proposed method is a combination of Rough Set Theory (RST) and Flow Network Graph (FNG). Data was collected from 386 consumers to extract rough rules. 13 rules have been chosen from 289 original rules that were divided into three groups: low, medium, and high intention to use GMFs. They were chosen because of the support values and other indexes that were used in the RST. Eventually, to interpret the performance of the generated rules, FNG were illustrated for each decision-making class, and seven patterns were extracted.ResultsThe findings confirm that corporate social responsibilities, consumer concerns, occupational status, and consumer autonomy are more important than other observed dimensions in consumers' decision-making. Moreover, the findings illustrate that combining Rough Set Theory and Flow Network Graph could predict customers' intentions and provide valuable information for policy-makers in related active industries.DiscussionBased on the analysis outcomes, the most significant factors that affect consumers' intention to use GMFs are: “consumer perception of CSR”; “consumer concerns”; “occupational status”; and “consumer autonomy”. Thus, managers and policymakers must pay more attention to these concepts when they survey consumer intention behavior.

Application of rough set theory to identify priorities in project management

The purpose of this paper is to demonstrate the use of Rough Set Theory to identify information that can be used in project management, namely the knowledge about the appropriate prioritization of activities and the use of resources directed towards the adopted project objectives. Rough Set Theory operates on large data sets and permits the reduction of irrelevant data and the induction of decision rules that discover recursion and relationships in the data. The discovered rules can prove valuable for decision-making project managers. All the rules found in course of the proposed rule-finding process have been considered interesting and are discussed in the paper. The paper also provides an example of the application of Rough Set Theory in the field mentioned above.