Soft Sets Research Articles

Insight into soft binary piecewise lambda operation: a new operation for soft sets

AbstractThe notion of soft set operations is one of the key concept for soft set theory as the theory has been progressing, both theoretically and practically, based on this notion. As proposing new soft set operations, deriving their algebraic properties, and studying the algebraic structure of soft sets from the perspective of soft set operations offer a comprehensive understanding of their applications as well as the appreciation of how soft set algebra can be applied to classical and nonclassical logic, in this study, a new soft set operation, called the “soft binary piecewise lambda operation" is proposed. Since one of the the main objective of abstract algebra is to analyze the properties of the operations defined on a set to classify the algebraic structures, the operation’s full properties and its distributions over other soft set operations are investigated to reveal which algebraic structures the operation forms individually, and together with other soft set operations in the collection of soft sets over the universe. It is showed that the operation forms a noncommutative semigroup and a right-left system, besides semi-rings and near-semi-rings together with certain types of soft set operations under certain conditions in the collection of soft sets over the universe. Since such in-depth analyses advance our knowledge of the applications of soft sets over a range of field, this novel operation may serve as an inspiration to create new perspectives for addressing issues related to parametric data, soft set-based cryptography, or decision-making techniques in practical settings, business, and technology.

A Short Note for Hypersoft Rough Graphs

Graph theory, a branch of mathematics, explores relationships among entities using vertices and edges. To address the uncertainties inherent in real-world networks, Uncertain Graph Theory has emerged as a significant extension within this field. Hypersoft Graphs advance traditional graphs further by incorporating multi-attribute nodes, allowing each node to represent multiple attribute values, thus capturing more complex, multi-dimensional relationships. The Soft Rough Set and Soft Rough Graph combine the principles of Soft Sets and Rough Sets to manage uncertainty in a more refined manner. In this paper, we introduce the Hypersoft Rough Graph and analyze its relationships with other graph classes.

Some Separation Axioms via Soft Somewhat Open Sets

It is commonly known that some topological spaces include structures that may be used to expand abstract notions. somewhat open sets and soft sets is such sort of structures. We obtain several properties and symmetry of the soft somewhat-R0 spaces and soft somewhat-R1 spaces obtained. Furthermore, we present new theorems and results and investigated relation between this concepts and the other structures.

A Synergistic Multi-Attribute Decision-Making Strategy for Selecting Sustainable Educational Institution Site Using Parameterized Single-Valued Neutrosophic Soft Sets

Selecting the ideal site for an educational institution is a challenging task that calls for a deep understanding of the available resources, the educational needs of society, and projected development patterns. To cope with such intricacies, this study proposes a novel mathematical context: A single-valued neutrosophic parameterized single-valued neutrosophic soft set ([Formula: see text]-set) that merges the versatility and adaptability of single-valued neutrosophic sets with parameterized single-valued neutrosophic soft settings. Using [Formula: see text]-set-based information, the study emphasizes the intrinsic uncertainty and inaccuracies in the decision-making process and enables a more thorough portrayal of the many criteria involved in site selection. In the first stage, the elementary notions of [Formula: see text]-set are explored with the description of understandable examples. In the second stage of the study, a decision-assistance mechanism is presented, and a strong algorithm is developed and evaluated using a case study prototype that focuses on choosing an appropriate location for an educational institution to be established. By guaranteeing that the chosen site satisfies the essential requirements for ideal placement, the algorithm proves its efficacy and improves the decision-making process.

Some Similarity Measures on Generalized Interval-Valued Intuitionistic Fuzzy Soft Expert Sets and Their Applications in Medical Diagnosis

In recent years, the application of fuzzy sets has gained significant attraction in various fields, including medical diagnosis, due to their ability to manage uncertainties and imprecise information. This paper focuses on the comparative analysis of similarity measures within the realm of Generalized Interval-Valued Intuitionistic Fuzzy Soft Expert Sets (GIVIFSESs) and explores their application in the domain of medical diagnosis. Most of the important topics in fuzzy set theory are the similarity measures between the generalizations of fuzzy set theory. Similarity measures are a crucial tool which was used in data science. In this process, we measure how much the data sets are related and comparable. Measures of similarity give a numerical value that reveals the strength of associations between sets or sets of variables. In this paper, we initiate a new concept of generalized interval-valued intuitionistic fuzzy soft expert sets and their fundamental operations. This new concept is more flexible than existing concepts based on their algebraic definition. Unlike fuzzy sets, the concept of generalized interval-valued intuitionistic fuzzy soft expert sets is characterized by a degree of membership and degree of non-membership along with fuzzy set theory. The proposed methodology is validated through an empirical application in medical diagnosis, where (GIV-IFSESs) are employed to model the uncertainty and imprecision inherent in expert assessments. The selected similarity measures are then applied to quantify the degree of resemblance between different medical cases, facilitating a more informed decision-making process. We introduce several types of similarity measures on generalized interval-valued intuitionistic fuzzy soft expert sets. We also discuss a similarity measure of Type-I, Type-II, and Type-III for two (GIVIFSESs) and its application in medical diagnosis problems.

Navigating Decision Making with Generalized Temporal Intuitionistic Fuzzy Sets and Soft Sets

The study addresses the challenges posed by evolving data within generalized intuitionistic fuzzy sets. Traditional methods often fall short in handling such complexity. To overcome this, we introduce the concept of a generalized temporal intuitionistic fuzzy set, extending the traditional framework to incorporate temporal dynamics. Additionally, we define a generalized temporal intuitionistic fuzzy soft set, integrating temporal aspects into the soft set framework. Recognizing the need for advanced operations like union and intersection to merge opinions across different periods, we propose practical solutions for decision-making in this dynamic context. Two novel multi-criteria decision-making methods are introduced, specifically designed to address decision-making problems within generalized temporal intuitionistic fuzzy soft sets. We develop Scilab codes for these methods, enabling the creation of a multiple-input single-output system. This system is applied to complex real-life examples, involving numerous parameters, time moments, and decision-makers. This comprehensive approach aims to provide robust tools and methodologies for decision-making processes amidst the intricate dynamics of temporal data within the framework of generalized temporal intuitionistic fuzzy sets.

Navigating Decision Making with Generalized Temporal Intuitionistic Fuzzy Sets and Soft Sets

The study addresses the challenges posed by evolving data within generalized intuitionistic fuzzy sets. Traditional methods often fall short in handling such complexity. To overcome this, we introduce the concept of a generalized temporal intuitionistic fuzzy set, extending the traditional framework to incorporate temporal dynamics. Additionally, we define a generalized temporal intuitionistic fuzzy soft set, integrating temporal aspects into the soft set framework. Recognizing the need for advanced operations like union and intersection to merge opinions across different periods, we propose practical solutions for decision-making in this dynamic context. Two novel multi-criteria decision-making methods are introduced, specifically designed to address decision-making problems within generalized temporal intuitionistic fuzzy soft sets. We develop Scilab codes for these methods, enabling the creation of a multiple-input single-output system. This system is applied to complex real-life examples, involving numerous parameters, time moments, and decision-makers. This comprehensive approach aims to provide robust tools and methodologies for decision-making processes amidst the intricate dynamics of temporal data within the framework of generalized temporal intuitionistic fuzzy sets.

On Fuzzy Soft α-open Sets, α-continuity, andα-compactness: Some Novel Results

In this paper, we defined the notions of fuzzy soft α-interior (α-closure) operators via fuzzy soft topologies based on the sense of Sostak and studied some topological properties of them. Also, the notion of r-fuzzy soft α-connected sets was introduced and investigated. Thereafter, we defined and characterized the notions of fuzzy soft weakly (almost) α-continuous mappings, which are weaker forms of fuzzy soft α-continuous mappings. Moreover, we established that fuzzy soft α-continuity → fuzzy soft almost α-continuity → fuzzy soft weakly α-continuity, but the converse may not be true. In addition, we investigated some properties of fuzzy soft α-continuity. It is also we showed that the composition is fuzzy soft almost α-continuous mapping if is fuzzy soft α-continuous mapping and is fuzzy soft almost continuous mapping. Finally, some novel types of fuzzy soft compactness via r-fuzzy soft α-open sets were introduced and the relationships between them were explored with the help of some examples.

Pythagorean Fuzzy Soft Somewhat Continuous Functions

In this work, we introduce the concept of Pythagorean fuzzy soft somewhat open sets utilizing the Pythagorean fuzzy soft interior operator, extending its application to Pythagorean fuzzy soft topological spaces. This study aims to enhance decision-making processes in future-assisted economies by addressing the limitations of existing fuzzy set theories. We investigate the distinctive properties of Pythagorean fuzzy soft somewhat open sets as a subclass of Pythagorean fuzzy soft somewhere dense sets. Additionally, we explore Pythagorean fuzzy soft somewhat metamorphism’s within the context of Pythagorean fuzzy soft somewhat continuous functions, offering new insights into their topological invariant. Through detailed analysis and examples, we demonstrate the applicability of these concepts in various scientific and engineering problems. This work provides a comprehensive framework for understanding and utilizing Pythagorean fuzzy soft sets in complex decision-making scenarios. Finally, we compare various relationships across some generalizations of Pythagorean fuzzy soft continuous functions.

NEW FORM OF SOFT SETS AND ITS PROPERTIES

Molodtsov introduced the concept of soft set theory as a general mathematical tool for dealing with uncertainty. Many researchers have studied this theory and developed several models to solve decision-making and medical diagnostic problems, but most of these models deal only one set of parameters. This causes problems for users, especially with those who use questionnaires in their work and studies. Also Alkhazaleh and Salleh, also introduced the concept of soft-expert sets. This structure can be considered as a generalization of soft-sets in which experts and their opinions have been added to make decision analysis easier to handle. In our model, is more generalization of soft- set and soft-expert set, the collection of more specific information about object sets using mappings. This concept is more powerful for information tables, since collection of the information is very particular to define by mapping and also this model is approaches to rough set theory and information system.

Indetermsoft-Set-Based D* Extra Lite Framework for Resource Provisioning in Cloud Computing

Cloud computing is an immensely complex, huge-scale, and highly diverse computing platform that allows the deployment of highly resource-constrained scientific and personal applications. Resource provisioning in cloud computing is difficult because of the uncertainty associated with it in terms of dynamic elasticity, rapid performance change, large-scale virtualization, loosely coupled applications, the elastic escalation of user demands, etc. Hence, there is a need to develop an intelligent framework that allows effective resource provisioning under uncertainties. The Indetermsoft set is a promising mathematical model that is an extension of the traditional soft set that is designed to handle uncertain forms of data. The D* extra lite algorithm is a dynamic heuristic algorithm that makes use of the history of knowledge from past search experience to arrive at decisions. In this paper, the D* extra lite algorithm is enabled with the Indetermsoft set to perform proficient resource provisioning under uncertainty. The experimental results show that the performance of the proposed algorithm is found to be promising in performance metrics such as power consumption, resource utilization, total execution time, and learning rate. The expected value analysis also validated the experimental results obtained.

Fuzzy Soft Sets and its Application to Decision Making: A Short Case Study Involving the Health Sector

The health sector faces uncertainty and complex decision-making scenarios, making traditional analytical tools insufficient. The fuzzy soft set theory has emerged as a powerful framework for modeling and reasoning with uncertain information, with promising applications in the health domain. This project explores the application of fuzzy soft sets in various decision-making processes in the health sector, including medical diagnosis, disease classification, treatment planning, risk assessment, patient stratification, and predictive modeling. The study reviews historical development of fuzzy set theory and its extension to soft sets, discussing challenges, limitations, and future research directions. The findings aim to contribute to the growing body of knowledge on the practical relevance and potential of fuzzy soft set theory in addressing healthcare decision-making needs.

Product ranking considering differences across online review platforms: a method based on intuitionistic fuzzy soft sets

Numerous online review platforms have become flooded with a large number of textual reviews, allowing consumers to compare and select products based on online reviews from multiple platforms. Existing studies have found that there may be certain differences in the content focus of online reviews from different platforms and that the evaluation indicators of different platforms may be different. Ranking products by considering differences in platforms and integrating online reviews from multiple platforms is of great significance in supporting consumer purchase decisions; however, relevant studies are relatively scarce. Therefore, this study proposes a product ranking method using intuitionistic fuzzy soft sets, considering the differences in platforms. First, online reviews were preprocessed to obtain product indicator parameters on different platforms. Second, a sentiment analysis algorithm was used to determine the sentiment strengths of the indicator parameters. Subsequently, an intuitionistic fuzzy soft set for each platform concerning the indicator parameters was constructed. Furthermore, a comprehensive intuitionistic fuzzy soft set was obtained by the AND operation, and the ranking of the products was determined. Finally, a case study was conducted to illustrate the use of the proposed method. Through a comparative analysis, the characteristics and advantages of the proposed method were further illustrated.

Multi-Attribute Three-Way Decision Approach Based on Ideal Solutions under Interval-Valued Fuzzy Soft Environment

The interval-valued fuzzy soft set (IVFSS) model, which combines the benefits of the soft set model with the interval-valued fuzzy set (IVFS) model, is a growing and effective mathematical tool for processing hazy data. In detail, this model is characterized by symmetry, which has the lower and upper membership degree. The study of decision-making based on IVFSS has picked up more steam recently. However, existing multi-attribute decision-making (MADM) methods can only sort alternative schemes, but are not able to classify them, which is detrimental to decision-makers’ efficient decision-making. In this paper, we propose a multi-attribute three-way decision-making (MATWDM) algorithm based on ideal solutions for IVFSS. MATWDM is extended to the IVFSS environment by incorporating the concept of the ideal solution, offering a more adaptable and comprehensive approach for addressing uncertain MADM issues. The method not only obtains the ranking results of the alternatives, but also divides them into acceptance domain, rejection domain, and delayed-decision domain, which makes the decision results more reasonable and effective, facilitating decision-makers to make better decisions. We apply the proposed three-way decision algorithm to two practical cases as diverse as mine emergency decision and Homestay selection decision. Additionally, the effectiveness and viability of the suggested method are confirmed by experimental findings.

Innovative Soft Cryptosystem for Encrypting and Decrypting Messages with IDEA

This paper introduces an advanced cryptosystem for message encryption and decryption, integrating the International Data Encryption Algorithm (IDEA) with soft set and soft matrix principles. Soft sets, conceptualized by Molodtsov, are adept at managing uncertainty, making them ideal for cryptographic frameworks. Our approach utilizes inverse and characteristic products of soft sets and matrices, combined with the robust IDEA algorithm, to significantly enhance security. The IDEA algorithm operates on 64 -bit data blocks with a 128 -bit key, ensuring strong encryption. Additionally, we incorporate the symmetric to introduce complex permutations, further strengthening the cryptographic process by ensuring unique encryptions for identical plaintexts. This layered approach drastically improves resilience against unauthorized decryption. Practical applications demonstrate the system's efficacy, highlighting its superior security and reliability for data transmission in environments with high uncertainty. This innovative cryptosystem provides a formidable solution for contemporary encryption challenges.

Holistic Methodology of Hypersoft in Tandem with Uncertainty-based Triangular Neutrosophic for Wave Energy Converter Optimization

Global warming, environmental degradation, and climate change have recently emerged as compelling arguments against the combustion of fossil fuels. As well Eliminating and forgoing the intake of fossil fuels is also encouraged by the Sustainable Development Agenda's goals. The healthy substitute for fossil fuels, renewable energy is one of the main devoid power sources found in our natural surroundings. An effective proposition for harnessing wave energy with an emphasis on increasing energy and efficiency are wave energy converters, or WEnCos. It contributes to producing a clean, limitless energy source that might drastically lessen our need for fossil fuels. Generally speaking, the selecting of the appropriate converter is an important endeavor that this study takes on. The process of selecting the optimal converter has been conducted based on effective benchmarks or criteria and its attributes. Multiple Criteria Decision Making (MCDM) techniques seem to be effective tools when it comes to handling the complex issue of benchmarking WEnCos. These approaches consider a variety of criteria, allowing for a comprehensive and nuanced examination. Each utilized technique plays vital role in our decision problem. Hence, CRiteria Importance Through Inter-criteria Correlation (CRITIC) method—which determines the weights of criteria and its attributes in decision making problems. These weights are utilized in Weighted Sum Product (WISP) method. Totally, these techniques are implemented under uncertainty theory of Neutrosophic which combined with soft sets notion to generate Triangular Neutrosophic HyperSoft (TrNSHSS). Totally, all these techniques are contributed to constructing soft decision-making model for analyzing and recommending optimal WEnCo.

Soft set-based MSER end-to-end system for occluded scene text detection, recognition and prediction

The presence of unpredictable occlusions on natural scene text is a significant challenge, exacerbating the difficulties already posed on text detection and recognition by the variability of such images. Addressing the need for a robust, consistently performing approach that can effectively address the above challenges, this paper presents a new Soft Set-based end-to-end system for text detection, recognition and prediction in occluded natural scene images. This is the first approach to integrate text detection, recognition and prediction, unlike existing systems developed for end-to-end text spotting (text detection and recognition) only. For candidate text components detection, the proposed combination of Soft Sets with Maximally Stable Extremal Regions (SS-MSER) improves text detection and spotting in natural scene images, irrespectively of the presence of arbitrarily orientated and shaped text, complex backgrounds and occlusion. Furthermore, a Graph Recurrent Neural Network is proposed for grouping candidate text components into text lines and for fitting accurate bounding boxes to each word. Finally, a Convolutional Recurrent Neural Network (CRNN) is proposed for the recognition of text and for predicting missing characters due to occlusion. Experimental results on a new occluded scene text dataset (OSTD) and on the most relevant benchmark natural scene text datasets demonstrate that the proposed system outperforms the state-of-the-art in text detection, recognition and prediction. The code and dataset are available at https://github.com/alloydas/Softset-MSER-Based-Occluded-Scene-Text-Spotting/blob/master/Soft_set_MSER.ipynb

On ((Τ ) ̃^*-N)^η-Fuzzy Soft Quasi Normal Operators

The concept of fuzzy soft sets is considered more versatile and widely applicable than traditional soft set theory, as the latter struggles to handle the fuzziness of problem parameters effectively. In this study, we introduce and describe the fuzzy soft quasinormal operator in a more concise manner. This operator is defined on a fuzzy soft Hilbert space, based on the notion of a fuzzy soft vector space, which has been adapted to an FS-inner product space in this work. We present various characterizations and results related to the fuzzy soft quasinormal operator, demonstrating that it serves as an appropriate example of FS-Hilbert spaces, alongside other related examples. Furthermore, we explore the relationships between these categories. Finally, we provide some fundamental guidelines on this topic.

Soft Sets Extensions: Innovating Healthcare Claims Analysis

In the dynamic arena of healthcare research, where the complexities of data often rival the intricacies of biological systems, the ability to model and analyze such multifaceted datasets is crucial. This comprehensive review delves into the evolution and application of soft sets and their extensions, including HyperSoft Sets, SuperHyperSoft Sets, IndetermSoft Sets, IndetermHyperSoft Sets, and TreeSoft Sets, in healthcare claims data analysis. These extensions address intricate challenges in data analysis, offering versatile frameworks for managing the uncertainty and indeterminacy inherent in healthcare claims data. By exploring their definitions and applications, this review elucidates how these mathematical tools have evolved and their significance in advancing healthcare research and enhancing data analysis methodologies. Real-world examples underscore the implications of these tools, emphasizing their pivotal role in facilitating informed decision-making and knowledge discovery in healthcare. The review systematically examines various case studies and research findings to illustrate the practical utility of soft set extensions. Detailed analyses of real-world scenarios highlight advancements in processing complex healthcare data. The conclusions drawn from this analysis indicate that the adoption of soft sets and their extensions can significantly improve the accuracy and efficiency of healthcare data analysis, ultimately contributing to better healthcare outcomes and more informed policy-making. Future research directions are also discussed, suggesting further potential applications and developments in this field.

Assessing anthropogenic influences on the water quality of Gomati River using an innovative weighted fuzzy soft set based water pollution rating system

The increasing pollution of river systems poses a significant challenge to water quality management and public health. This study was conducted to evaluate the water quality of the Gomati River in India, focusing on the impact of anthropogenic activities on pollution levels across different seasons. The primary objective was to develop a comprehensive assessment model using an effective weighted fuzzy soft expert system (WFSES) to derive a weighted water pollution score (WWP-score) for rating water pollution levels based on various water quality parameters. To achieve this, we employed a fuzzy soft set (FSS) methodology integrated with a weighted fuzzy soft set (WFSS) model to analyze water quality indices at six sampling stations along the Gomati River, the largest river in Tripura, India. Originating from the Raima and Sarma streams, the river flows westward through key regions, providing 249.39 million cubic meters of water annually, essential for drinking, agriculture, fishing, and transportation. The study utilized crisp data summaries of key water quality parameters, including pH, total dissolved solids, total suspended solids, electrical conductivity, biochemical oxygen demand, dissolved oxygen, total hardness, chloride, total alkalinity, and total coliform, across the pre-monsoon, monsoon, and post-monsoon seasons from May 2022 to April 2023, guided by the distribution of waste discharge points. Fuzzy membership functions were defined for these parameters, and the root mean square (RMSQR) operation was used to combine multiple FSSs. The results revealed that the WWP-scores, a measure of water quality, ranged from 0.744 to 0.872 across the sampling stations, with Srimantapur exhibiting the highest level of pollution and Udaipur showing comparatively better quality. These scores indicate that water quality at all sites falls into the poor category, with Srimantapur experiencing the most severe contamination due to high levels of coliform bacteria and organic pollutants. The analysis highlights the impact of domestic wastewater and agricultural runoff on the river's health. This research offers a novel application of FSS and WFSS theory in environmental management, providing a robust framework for evaluating and ranking water quality across multiple parameters. The findings are valuable to the scientific community as they offer detailed insights into the pollution dynamics of the Gomati River and propose a methodological approach for assessing water quality in other river systems facing similar challenges. The study's results underscore the need for targeted pollution control measures and continuous monitoring to safeguard water resources and public health.