Soft Sets Research Articles

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.

A synergistic multi-attribute decision-making strategy for selecting sustainable educational institution site using parameterized of single-valued neutrosophic soft sets

A synergistic multi-attribute decision-making strategy for selecting sustainable educational institution site using parameterized of single-valued neutrosophic soft sets

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.

Covering rough set models, fuzzy rough set models and soft rough set models induced by covering similarity

In order to study the rule of quantity characteristics of rough set theory, a novel notion of covering similarity in a covering approximation space is introduced. Based on this new notion, novel covering rough set models, novel fuzzy rough set models and novel soft rough set models are defined. Further, the concept of similarity matrix is presented, and then the matrix calculation formulas of all the new concepts and new models are deduced. Moreover, aim to better solve the practical problems by comparing the similarity, a concept of similarity interval is introduced, then the covering classification is carried out and a partial order of all the classes is derived. Finally, a few practical examples are given to illustrate the simple applications of all the new concepts and models in this paper.

Time-series bidirectional adjustable N-soft expert MABAC method and its application for multi-attribute group decision-making

In hybrid models of soft expert sets, experts express only agreed or disagreed opinions about existing grades. This paper proposes a time-series bidirectional adjustable N-soft expert set model to address the shortcomings of existing models that cannot adjust existing grades to a more reasonable state or describe decision problems involving different times. Firstly, this model can explain the experts’ uncertain opinions and make positive or negative adjustments about existing grades. Secondly, the model contains information about time, describes dynamic multi-attribute group decision-making problems and explores objects’ changes and developments over time. And some related operations and propositions are derived. In addition, a new method called the bidirectional adjustable N-soft expert MABAC (multi-attributive border approximation area comparison) is proposed. On the one hand, the proposed method uses deviation maximizing and exponential decay methods to determine the time weights, ensuring the reliability of the time weights. On the other hand, it ranks objects based on their distances from an approximate boundary region, limiting the unconditional compensation among attribute values. Finally, this paper presents an example to verify its effectiveness and reliability by results analysis, sensitivity analysis, and comparison analysis.

Intuitionistic Fuzzy Binary Soft Sets and Its Properties

Objective : The objective of Intuitionistic fuzzy binary soft sets is to extend the existing frameworks of binary soft sets and Intuitionistic fuzzy sets to accommodate both uncertainty and ambiguity in decision-making processes. This extension aims to provide a more flexible, representation of real-world data and phenomena, allowing for analysis and reasoning. Specifically, the objective involves defining the fundamental structures of Intuitionistic fuzzy binary soft sets over two initial universal sets, U1 and U2. Method: Reviewing the existing literature on binary soft sets, Intuitionistic fuzzy sets, and their extensions. Defining the fundamental structures of Intuitionistic fuzzy binary soft sets over two initial universal sets, U1 and U2. The next step is to propose the operations on Intuitionistic fuzzy binary soft sets and analyze their characteristics. Findings: The extension of binary soft sets and Intuitionistic fuzzy sets to Intuitionistic fuzzy binary soft sets is feasible. Intuitionistic fuzzy binary soft sets possess distinct properties worthy of exploration. Operations such as union, intersection, difference, AND, Or of Intuitionistic fuzzy binary soft sets exhibit specific behaviors elucidated through our findings. Novelty: The development of operations on Intuitionistic fuzzy binary soft sets provides a comprehensive framework and analysis. Exploration of properties unique to Intuitionistic fuzzy binary soft sets is contributing to the advancement of soft computing and set theory. Mathematics Classification code: 03D45, 03F55, 03E72 Keywords: Fuzzy, Soft, Intuitionistic, Binary soft, Fuzzy binary soft

Nodecness of Soft Generalized Topological Spaces

In this work, we define a new class of soft generalized topological spaces, namely strongly soft nodec, with the use of strongly soft nowhere dense sets. Then, we study the basic properties of these spaces and show that if the product of two soft generalized topological spaces is a strongly soft nodec space, then each one is a strongly soft nodec space. Then, we extend these notions to T0-strongly soft nodec generalized topological spaces by using the soft quotient functions and discussing their main properties. We also show the inverse of a surjective soft quotient function preserves the soft closure and soft interior of a soft subset of a codomain soft set in soft generalized topological space. Further, we use soft quasi-homeomorphism and soft quotient functions to make comparisons and connections between these spaces with the support of appropriate counterexamples. Then, we successfully determine a condition under which the soft generalized topological space is a soft weak Baire space and hence a strongly soft second category.

Novel Picture of Topological Spaces in the Frame of Fuzzy Soft Sequential Sets

Novel Picture of Topological Spaces in the Frame of Fuzzy Soft Sequential Sets

Climate Change Prediction Model using MCDM Technique based on Neutrosophic Soft Functions with Aggregate Operators

The increasing impact of climate change necessitates innovative approaches in modeling and prediction to mitigate its adverse effects. This paper introduces a novel methodology integrating Neutrosophic Soft Functions (NSFs) into climate change prediction frameworks. NSFs, a hybrid of Neutrosophic Set Theory and Soft Set Theory, provide a flexible framework for handling uncertain and imprecise information inherent in climate data. This study explores the application of NSFs in capturing the complex interplay of various climatic variables, including temperature, precipitation, humidity, and atmospheric pressure, thereby enhancing the accuracy and reliability of climate change predictions. By incorporating NSFs into existing predictive models, such as neural networks and fuzzy systems, this research demonstrates significant improvements in forecast precision, particularly in scenarios with limited or noisy data. Additionally, the paper discusses the integration of NSFs with advanced machine learning algorithms for climate pattern recognition and anomaly detection, enabling timely identification of climate change indicators and facilitating proactive measures for adaptation and mitigation. Through empirical validation using real-world climate datasets, this study underscores the efficacy of NSFs in enhancing the predictive capabilities of climate change models, thereby contributing to more informed decision-making in climate-related policies and strategies.

An Innovative Algorithm Based on Octahedron Sets via Multi-Criteria Decision Making

Octahedron sets, which extend beyond the previously defined fuzzy set and soft set concepts to address uncertainty, represent a hybrid set theory that incorporates three distinct systems: interval-valued fuzzy sets, intuitionistic fuzzy sets, and traditional fuzzy set components. This comprehensive set theory is designed to express all information provided by decision makers as interval-valued intuitionistic fuzzy decision matrices, addressing a broader range of demands than conventional fuzzy decision-making methods. Multi-criteria decision-making (MCDM) methods are essential tools for analyzing and evaluating alternatives across multiple dimensions, enabling informed decision making aligned with strategic objectives. In this study, we applied MCDM methods to octahedron sets for the first time, optimizing decision results by considering various constraints and preferences. By employing an MCDM algorithm, this study demonstrated how the integration of MCDM into octahedron sets can significantly enhance decision-making processes. The algorithm allowed for the systematic evaluation of alternatives, showcasing the practical utility and effectiveness of octahedron sets in real-world scenarios. This approach was validated through influential examples, underscoring the value of algorithms in leveraging the full potential of octahedron sets. Furthermore, the application of MCDM to octahedron sets revealed that this hybrid structure could handle a wider range of decision-making problems more effectively than traditional fuzzy set approaches. This study not only highlights the theoretical advancements brought by octahedron sets but also provides practical evidence of their application, proving their importance and usefulness in complex decision-making environments. Overall, the integration of octahedron sets and MCDM methods marks a significant step forward in decision science, offering a robust framework for addressing uncertainty and optimizing decision outcomes. This research paves the way for future studies to explore the full capabilities of octahedron sets, potentially transforming decision-making practices across various fields.

Understanding normal and restricted normal products in soft directed graphs

This paper extends the framework of soft set theory to directed graphs by introducing and analyzing the concepts of the normal product and restricted normal product of soft directed graphs. Building on Molodtsov’s foundational work in developing soft set theory to address uncertainty in data, this study presents new methods for modeling and understanding complex systems where uncertainty plays a significant role. Soft directed graphs, which enhance traditional graph models by incorporating parameters and uncertain relationships, serve as the foundation for this investigation. The normal product, defined as a combination of two soft directed graphs based on their respective parameter sets, and the restricted normal product, which combines soft directed graphs only where their parameter sets intersect, provide a comprehensive framework for these new operations. This paper also establishes the structural properties of these products, ensuring they are well-defined and retain the key features of soft directed graphs. Furthermore, we derive combinatorial identities related to vertex and arc counts, as well as degree sums, offering deeper insights into the composition and behavior of these graph products.

Distance and similarity measures on belief and plausibility under q-rung orthopair fuzzy sets with applications

Belief and plausibility functions based on evidence theory (ET) have been widely used in managing uncertainty. Various generalizations of ET to fuzzy sets (FSs) have been reported in the literature, but no generalization of ET to q-rung orthopair fuzzy sets (q-ROFSs) has been made yet. Therefore, this paper proposes a novel, simple, and intuitive approach to distance and similarity measures for q-ROFSs based on belief and plausibility functions within the framework of ET. This research addresses a significant research gap by introducing a comprehensive framework for handling uncertainty in q-ROFSs using ET. Furthermore, it acknowledges the limitations inherent in the current state of research, notably the absence of generalizations of ET to q-ROFSs and the challenges in extending belief and plausibility measures to certain aggregation operators and other generalizations including Hesitant fuzzy sets, Bipolar fuzzy sets, Fuzzy soft sets etc. Our contribution lies in the proposal of a novel approach to distance and similarity measures for q-ROFSs under ET, utilizing Orthopairian belief and plausibility intervals (OBPIs). We establish new similarity measures within the generalized ET framework and demonstrate the reasonability of our method through useful numerical examples. Additionally, we construct Orthopairian belief and plausibility GRA (OBP-GRA) for managing daily life complex issues, particularly in multicriteria decision-making scenarios. Numerical simulations and results confirm the usability and practical applicability of our proposed method in the framework of ET.