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Articles 1351 - 1380 of 10600
Full-Text Articles in Entire DC Network
Integrated Merec-Cocoso Approach Using Score Function Ofneutrosophic For Location Selection Of Special Economic Zone, Debashis Ghosh, Bahnishikha Roy Muhuri, G. S. Mahapatra, B. S. Mahapatra
Integrated Merec-Cocoso Approach Using Score Function Ofneutrosophic For Location Selection Of Special Economic Zone, Debashis Ghosh, Bahnishikha Roy Muhuri, G. S. Mahapatra, B. S. Mahapatra
Neutrosophic Sets and Systems
Special economic zones (SEZs) are essential if a developing country is to boost economic growth. The selection of an SEZ site might be viewed as a multi-criteria decision-making (MCDM) difficulty because of the many conflicting aspects connected to different locations. This work presents a flexible neutrosophic MCDM approach for optimal SEZ site search. The single-valued neutrosophic sets transform the qualitative evaluation of the criteria for SEZ alternatives into a quantitative evaluation. The method based on removal effect on criteria (MEREC) approach is improved in a neutrosophic environment to ascertain the relevance of every characteristic of SEZ alternatives. We suggested a …
Strategy Selection For Natural Resource Conservation Capturingvagueness Through Integrated Neutrosophic Critic-Maircaapproach, Bahnishikha Roy Muhuri, M. K. Mondal, Florentin Smarandache, G. S. Mahapatra, B. S. Mahapatra
Strategy Selection For Natural Resource Conservation Capturingvagueness Through Integrated Neutrosophic Critic-Maircaapproach, Bahnishikha Roy Muhuri, M. K. Mondal, Florentin Smarandache, G. S. Mahapatra, B. S. Mahapatra
Neutrosophic Sets and Systems
Conservation of natural resources like water, soil, and biodiversity is necessary for ecological balance and human survival. This article aims to identify potential ways to conserve natural resources while maintaining a balance between ecology and human survival. An integrated neutrosophic CRiteria Importance Through Intercriteria (CRITIC)-Multi-Atributive Ideal-Real Comparative Analysis (MAIRCA) approach is developed to handle uncertain and inconsistent information. The linguistic assessments of the criteria are quantified through single-valued neutrosophic sets (SVNSs). The CRITIC method evaluates the criteria weights to avoid subjective and biased assessments. The MAIRCA approach is improved in a neutrosophic context to identify the ranking of the alternatives. …
On The Basics Of Neutrosophic Homotopy Theory, S. Jafari, N. Rajesh, G. Nordo
On The Basics Of Neutrosophic Homotopy Theory, S. Jafari, N. Rajesh, G. Nordo
Neutrosophic Sets and Systems
In this paper, we introduce and study the concept of neutrosophic homotopic functions using topological properties. Also, we obtain some properties of neutrosophic homotopic functions and concept of neutrosophic homotopy.
Neutrosophic Rhotrices For Improved Diagnostic Accuracy Through Score Rhotrix Computation, Ananda Priya B, Gnanachandra P, Saeid Jafari, Florentin Smarandache
Neutrosophic Rhotrices For Improved Diagnostic Accuracy Through Score Rhotrix Computation, Ananda Priya B, Gnanachandra P, Saeid Jafari, Florentin Smarandache
Neutrosophic Sets and Systems
We introduce neutrosophic rhotrices, which serve as a novel extension of neutrosophic matrices. The primary objective is to establish the foundational structure for neutrosophic rhotrices and to define crucial operations that can be performed on them. We explore the concept of neutrosophic rhotrices in depth, outlining the fundamental operations necessary for their effective manipulation. Furthermore, we investigate the essential properties of neutrosophic rhotrices utilizing these newly established operations. In addition, we provide an algorithm designed to enhance decision-making processes in medical diagnostics, supported by an illustrative example to clarify its application.
Neutrosophic Sets And Systems {Special Issue: Mediterranean Conference On Three Decades Of Neutrosophic And Plithogenic Theories And Applications (Meconet 2024)}, Vol. 73, 2024, Florentin Smarandache, Mohamed Abdel-Basset, Giorgio Nordo, Maikel Y. Leyva-Vázquez
Neutrosophic Sets And Systems {Special Issue: Mediterranean Conference On Three Decades Of Neutrosophic And Plithogenic Theories And Applications (Meconet 2024)}, Vol. 73, 2024, Florentin Smarandache, Mohamed Abdel-Basset, Giorgio Nordo, Maikel Y. Leyva-Vázquez
Neutrosophic Sets and Systems
the whole volume
Three Decades Of Neutrosophic And Plithogenic Theories With Their Applications (1995 - 2024), Florentin Smarandache
Three Decades Of Neutrosophic And Plithogenic Theories With Their Applications (1995 - 2024), Florentin Smarandache
Neutrosophic Sets and Systems
No abstract provided.
Methods For Efficient Computation Of Neutron Multiplicity Distributions And Snm Sample Characterization, Jawad Ribhi Moussa
Methods For Efficient Computation Of Neutron Multiplicity Distributions And Snm Sample Characterization, Jawad Ribhi Moussa
Nuclear Engineering ETDs
This dissertation advances neutron multiplicity counting (NMC) by developing a hierarchy of computational methods that combine deterministic and stochastic techniques with modern machine learning for improved special nuclear material (SNM) characterization. A system state-updating Monte Carlo method is introduced in addition to a dynamic point kinetic model based on a backward Master equation (BME) formulation. These models, along with newly developed distribution reconstruction methods, enable more efficient computation of neutron count distributions in a fixed detector time-gate. NMC limitations associated with finite-size and neutron phase effects are also addressed by extending the BME model to account for time-gated neutron count …
On Extension Of Metricspace To Neutro Hypermetricspace, Kianoosh Polvan
On Extension Of Metricspace To Neutro Hypermetricspace, Kianoosh Polvan
Neutrosophic Sets and Systems
Polvan introduced the impression of strong neutro metricspaces. He demonstrtated this impression depending on the neutro precepts from the neutro function one of the impressions of Smarandache. In this study, we introduce an extension of neutro metricspaces as neutro hypermetricspaces and investigated their qualities. We show that neutro hypermetricspaces are an extension of metricspaces and analyzed the relations between metricspaces and neutro hypermetricspaces. The basic impressions such as open positive-ball subsets and open negative-ball subsets are defined and are presented by some finite and finite neutro hypermetricspaces. Based on the open positive-ball subsets and open negative-ball subsets, we demonstrate the …
Neutrosophic Sets And Systems, Vol. 72,2024, Florentin Smarandache, Mohamed Abdel-Basset, Said Broumi
Neutrosophic Sets And Systems, Vol. 72,2024, Florentin Smarandache, Mohamed Abdel-Basset, Said Broumi
Neutrosophic Sets and Systems
the whole volume
The Extended Study Of 2-Refined Neutrosophic Numbers, Yaser Ahmad Alhasan, Florentin Smarandache, Abuobida Alfahal, Raja Abdullah Abdulfatah
The Extended Study Of 2-Refined Neutrosophic Numbers, Yaser Ahmad Alhasan, Florentin Smarandache, Abuobida Alfahal, Raja Abdullah Abdulfatah
Neutrosophic Sets and Systems
Numerical roots play a crucial role in real or complex equations, as well as in various mathematical models involving differentiation, integration, and other mathematical relationships. In the realm of mathematics, there is a growing trend of utilizing new formulas that incorporate non classical numbers, such as neutrosophic and refined neutrosophic numbers. The objective of this research is to establish precise and comprehensive mathematical procedures for dealing with refined neutrosophic roots within mathematical formulas, be it equations or other mathematical constructs. This paper presents an extensive study on 2-refined neutrosophic numbers, focusing on the square root of a 2-refined neutrosophic real …
Unveiling Uncertainty: Neutrosophic Set-Based Algorithms For Robust Decision-Making, A. A. Salama, Huda E. Khalid, Ahmed G. Mabrouk
Unveiling Uncertainty: Neutrosophic Set-Based Algorithms For Robust Decision-Making, A. A. Salama, Huda E. Khalid, Ahmed G. Mabrouk
Neutrosophic Sets and Systems
Traditional decision-making methods often struggle with inherent uncertainty and imprecision in data. Neutrosophic set-based algorithms offer a novel approach by incorporating degrees of truth, indeterminacy, and falsity. This paper explores the structure and implementation of these algorithms, highlighting their potential to handle real-world complexities. The application of neutrosophic sets in medical diagnosis is presented as a case study, demonstrating how the algorithm aids in evaluating probabilities for various diagnoses under uncertain conditions. The paper concludes by discussing limitations and potential applications in diverse fields.
The 2-Refined Neutrosophic Fraction Function And Its Integrals, Yaser Ahmad Alhasan, Suliman Sheen, Qusay Ahassan
The 2-Refined Neutrosophic Fraction Function And Its Integrals, Yaser Ahmad Alhasan, Suliman Sheen, Qusay Ahassan
Neutrosophic Sets and Systems
The goal of this article is to study the 2-refined neutrosophic fraction function and its integrals. We were defining the 2-refined neutrosophic fraction function and discussing Algorithm for finding the integral of the 2-refined neutrosophic proper rational function and introduce the integral of the 2-refined neutrosophic improper rational functions. Where each case was explained by given specific examples
A Novel And An Efficient Codas Technique To Solve Real-Life Magdm Problems In Fermatean Neutrosophic Environment, S. Bhuvaneshwari, C. Antony Crispin Sweety, Akanksha Singh, Said Broumi, Mohamed Talea, Prasanta Kumar Raut
A Novel And An Efficient Codas Technique To Solve Real-Life Magdm Problems In Fermatean Neutrosophic Environment, S. Bhuvaneshwari, C. Antony Crispin Sweety, Akanksha Singh, Said Broumi, Mohamed Talea, Prasanta Kumar Raut
Neutrosophic Sets and Systems
As a generalization of fuzzy sets and intuitionistic fuzzy sets, neutrosophic sets, and their combinations have been developed to represent uncertain, imprecise, incomplete, and inconsistent information existing in the real world. A neutrosophic set has the potential to be a general framework for uncertainty analysis in various spectra. On the other hand, the idea of Fermatean neutrosophic sets (FNSs) is the hybrid model of Fermatean fuzzy sets and neutrosophic sets, developed to enable the analytical management of ambiguous data from relatively typical real world decision-making scenarios. In this work, we develop an algorithm to compare the Fermatean neutrosophic set and …
The Cubic Bipolar Neutrosophic Sets Theory And Uncertainty Management In Environmental Data Analysis, A. A. Salama, Huda E. Khalid, Ahmed G. Mabrouk
The Cubic Bipolar Neutrosophic Sets Theory And Uncertainty Management In Environmental Data Analysis, A. A. Salama, Huda E. Khalid, Ahmed G. Mabrouk
Neutrosophic Sets and Systems
Environmental data analysis often faces uncertainties in measurements. Cubic Bipolar Neutrosophic Sets (CBN Sets) provide a powerful framework to address this challenge. This paper explores the mathematical foundations of CBN Sets and highlights their practical applications through illustrative examples. We demonstrate how CBN Sets effectively capture varying degrees of certainty, possibility, and impermanence in environmental parameters. The concept of inclusion relations facilitates comparisons and information fusion. Fundamental set operations (intersection, union, complement) are explored for manipulating and analyzing uncertain environmental data. We present the application of CBN Sets in water quality assessment, highlighting their ability to analyze parameters while accounting …
The Structure Of The Binary Two Fold Algebra Based On Intuitionistic Fuzzy Groups, Ramazan Yasar, Ahmed Hatip
The Structure Of The Binary Two Fold Algebra Based On Intuitionistic Fuzzy Groups, Ramazan Yasar, Ahmed Hatip
Neutrosophic Sets and Systems
In this paper, we study the binary two-fold algebra built over intuitionistic fuzzy groups, where the two-fold binary operations and some related substructures such as binary two-fold sub-algebras of intuitionistic fuzzy groups two-fold algebras, binary two-fold centers, binary normality, binary two-fold group products. On the other hand, we illustrate many examples to explain the validity of our discussion
Unveiling Big Data Insights: A Neutrosophic Classification Approach For Enhanced Prediction With Machine Learning, Ahmed Z.M. Elsherif, A. A. Salama, O. M. Khaled, Mostafa Herajy, E. I. Elsedimy, Huda E. Khalid, Ahmed K. Essa
Unveiling Big Data Insights: A Neutrosophic Classification Approach For Enhanced Prediction With Machine Learning, Ahmed Z.M. Elsherif, A. A. Salama, O. M. Khaled, Mostafa Herajy, E. I. Elsedimy, Huda E. Khalid, Ahmed K. Essa
Neutrosophic Sets and Systems
The ever-growing volume and complexity of Big Data pose challenges for traditional classification tasks. This paper explores the potential of Neutrosophic Sets (NS), a powerful framework for handling uncertainty, in building robust classification models for Big Data prediction using Machine Learning (ML) techniques. We provide a detailed background on NS and discuss its advantages over Fuzzy Sets. We then propose a methodology that integrates NS with relevant ML algorithms for classification. We evaluate the performance of our Neutrosophic-based model on a Big Data source. The results are analyzed to assess the effectiveness of the Neutrosophic approach for Big Data prediction. …
Introduction To Neutrosophic Soft Ideal Topological Spaces, Aysegul Caksu Guler
Introduction To Neutrosophic Soft Ideal Topological Spaces, Aysegul Caksu Guler
Neutrosophic Sets and Systems
In this paper, we give the definition of neutrosophic soft Cl∗ -closure, which is more general than neutrosophic soft closure of neutrosophic soft set, with the help of neutrosophic soft ideal and neutrosophic soft point. Then we investigate some basic properties of this new concept. Moreover, we define the notion of τ ∗ and give the concept of neutrosophic soft-I−compactness. Besides, we examine the relationship between these concepts and give the relations with previously given concepts
, Circular Economy Strategies To Promote Sustainable Development Using T-Neutrosophic Fuzzy Graph, M. Kaviyarasu, Hossein Rashmanlou, Saeed Kosari, Said Broumi, R. Venitha, M. Rajeshwari, Farshid Mofidnakhaei
, Circular Economy Strategies To Promote Sustainable Development Using T-Neutrosophic Fuzzy Graph, M. Kaviyarasu, Hossein Rashmanlou, Saeed Kosari, Said Broumi, R. Venitha, M. Rajeshwari, Farshid Mofidnakhaei
Neutrosophic Sets and Systems
This study discusses the use of t-neutrosophic graphs to express and understand complex interactions. It also shows how these graphs might manage intricate relationships with a wide range of variables or scenario elements. Additionally, it offers fundamental t-neutrosophic graph operations and talks about concepts in these graphs such as homomorphism and isomorphism. Additionally, the study addresses how this approach may be applied in practical contexts to address circular economies and sustainability growth. Through the use of t-neutrosophic graphs, various components, and their connections, the research demonstrates that managing the several circular dimensions is feasible. financial system. This example shows how …
The Principles Of (Partial Locality, Partial Indeterminacy, Partial Nonlocality) And (Multi Locality, Multi Indeterminacy, Multi Nonlocality), Florentin Smarandache
The Principles Of (Partial Locality, Partial Indeterminacy, Partial Nonlocality) And (Multi Locality, Multi Indeterminacy, Multi Nonlocality), Florentin Smarandache
Neutrosophic Sets and Systems
This article introduces new neutrosophic principles aiming to extend and generalize the concepts of locality and nonlocality by addressing scenarios involving indeterminacy, together with partiality and multitude, in physics, mechanics, cosmology, biology, medicine, chemistry, economics, ecology, sociology. Locality refers to interactions or processes confined within a limited region of space or time. But there may be a Total (100%) Locality, or a Partial Locality (less than 100% and greater than 0%). The effects are constrained to the immediate environment. Contrariwise, NonLocality refers to interactions or connections between entities separated by space or time. The changes in one location have instantaneous …
Implementation Of Circle-Breaking Algorithm On Fermatean Neutrosophic Graph To Discover Shortest Path, S. Krishna Prabha, Said Broumi, Souhail Dhouib, Mohamed Talea
Implementation Of Circle-Breaking Algorithm On Fermatean Neutrosophic Graph To Discover Shortest Path, S. Krishna Prabha, Said Broumi, Souhail Dhouib, Mohamed Talea
Neutrosophic Sets and Systems
In many scientific domains, there is a growing interest in the shortest path problem. Traffic routes that can be precisely defined become arbitrary due to the damage that natural catastrophes inflict on roads and bridges. The truth membership, indeterminacy membership, and falsity membership of the component elements make up a neutrosophic set. Their axis of symmetry is indeterminacy membership, and it has a symmetric form. The neutrosophic number is a better way to express the edge distance in uncertain circumstances. With an edge distance stated using Fermatean neutrosophic numbers (FrNN), the study aims to solve the shortest path problem of …
Exploring Neutrosophic Over Supra Exterior Modal Topological Structure: Theory And Application In Healthcare Decision-Making, R.Narmada Devi, Yamini Parthibanm
Exploring Neutrosophic Over Supra Exterior Modal Topological Structure: Theory And Application In Healthcare Decision-Making, R.Narmada Devi, Yamini Parthibanm
Neutrosophic Sets and Systems
Neutrosophic environments have gained significant relevance across diverse disciplines. Neutro sophic Over Supra Exterior Modal Topological Structure is introduced, demonstrating the generation of two distinct structures through traditional Neutrosophic Over supra topological operations, denoted as ⊞ (closure) and ⊡ (interior), along with novel Neutrosophic Over Supra Exterior Modal Operations, expressed as ✖ (modal closure) and ⊙ (modal interior). This exploration delves into the essential properties and characteristics of these structures, illuminating their behavior and implications. To illustrate the practical relevance, a numerical example is presented, demonstrating the identification of disease types using a score function. The study conclusively shows that …
Evaluating The Nuclear Power Plant Safety System Under Neutrosophic Environment, Debapriya Mondal, Totan Garai, Gopal Chandra Roy, Shariful Alam
Evaluating The Nuclear Power Plant Safety System Under Neutrosophic Environment, Debapriya Mondal, Totan Garai, Gopal Chandra Roy, Shariful Alam
Neutrosophic Sets and Systems
The safety system of nuclear power plants is very crucial for protecting the environment and the living world. In this article, we have addressed the nuclear power plant safety system in a neutrosophic environment. Here, we have mathematically presented a nuclear power plant safety system in terms of neutrosophic differential equations. We have thoroughly examined and discussed both analytically and numerically the solution of the nuclear power plant safety model considering the underlying model parameter as single-valued triangular neutrosophic number. We have focused to find out probability of the nuclear power plant’s safety system working normally and shutdown in safe …
Neutrosophic Quadruple Hv-Modules And Their Fundamental Module, Madeleine Al Tahan, Saba Al-Kaseasbeh, Bijan Davvaz
Neutrosophic Quadruple Hv-Modules And Their Fundamental Module, Madeleine Al Tahan, Saba Al-Kaseasbeh, Bijan Davvaz
Neutrosophic Sets and Systems
This article aims to explore the deeper connections between neutrosophy and hyperstructures. Specifically, we introduce the concept of neutrosophic quadruple Hv-modules over neutrosophic quadruple Hv rings, examine their properties, and identify their fundamental module.
Deneutrosophication Of Neutrosophic Bézier Surface Approximation Model, Siti Nur Idara Rosli, Mohammad Izat Emir Zulkifly
Deneutrosophication Of Neutrosophic Bézier Surface Approximation Model, Siti Nur Idara Rosli, Mohammad Izat Emir Zulkifly
Neutrosophic Sets and Systems
The deneutrosophication process is a process transforming from neutrosophic values to crisp output values. It is the final step for the operations within a neutrosophic set and system. Neutrosophic set theories are a generalization of intuitionistic fuzzy and fuzzy set theories, focusing on truth, indeterminacy, and falsity memberships independently. However, it isn't easy to generate a geometrical model such as a Bézier surface by using neutrosophic set theory through the deneutrosophication process. Therefore, this paper used an average of triangular footprint method in the deneutrosophication process to construct the neutrosophic Bézier surface (NBS) models by using approximation methods. Before generating …
Product Operations On Pythagorean Co-Neutrosophic Graphs And Its Application, G. Vetrivel, M. Mullai, G. Rajchakit
Product Operations On Pythagorean Co-Neutrosophic Graphs And Its Application, G. Vetrivel, M. Mullai, G. Rajchakit
Neutrosophic Sets and Systems
Pythagorean Co-Neutrosophic Graphs (PyCNGs) have newly emerged after the foundation of Pythagorean fuzzy graph and Co-neutrosophic graphs, where the membership of indeterminacy(uncertain) is independent and membership of truth(existence) & false(non-existence) are dependent. This paper has a wide discussion of different product operations carried out in PyCNGs. Some properties like strong, complete with consideration of a vertex’s degree in the graph are explored with examples. Also, an application related to the product on PyCNGs is demonstrated with brain network analysis and its function.
Modified Non-Linear Triangular Neutrosophic Numbers: Theory And Applications In Integral Equation, A. Mohammed Shapique, E. Mathivadhana
Modified Non-Linear Triangular Neutrosophic Numbers: Theory And Applications In Integral Equation, A. Mohammed Shapique, E. Mathivadhana
Neutrosophic Sets and Systems
Existing methods for handling uncertainty and imprecision often fall short in addressing complex real-world problems. To overcome these limitations, this paper introduces a novel Generalized Non-Linear Triangular Neutrosophic Number (GNLTNN) that effectively captures uncertainty, indeterminacy, and falsity. By analysing GNLTNN through (α, β, γ)-cuts and defining arithmetic operations using the max-min principle, we provide a robust framework for handling neutrosophic information. The proposed neutrosophic Laplace transform method enables efficient solutions to integral equations involving non-linear neutrosophic numbers. The efficacy of our approach is demonstrated through graphical representations
A Novel Medical Image Segmentation Using Neutrosophic Sets With Slope Variation, Sangeeta K Siri, S Pramod Kumar, Mrityunjaya V. Latte
A Novel Medical Image Segmentation Using Neutrosophic Sets With Slope Variation, Sangeeta K Siri, S Pramod Kumar, Mrityunjaya V. Latte
Neutrosophic Sets and Systems
Computer-Aided Diagnostic methods demand the precise segmentation of medical images. The important stage in diagnosis is the extraction of the Region of Interest (ROI). Illustration of the image in a more meaningful way is the aim of segmentation. Segmentation finds extensive use in computer vision, object recognition, image recovery based on the content, etc. In the proposed model, Slope Variation Scatter (SVS) plot of image is obtained to compute vertices of Neutrosophic Gaussian Function (NGF). The SVS describes global variation rate of image histogram. In this, the crests represent local mean of pixels/ certainty mean and valleys represents uncertainty mean. …
Neutrosophic Log-Gamma Distribution And Its Applications To Industrial Growth, Fuad S. Al-Duais
Neutrosophic Log-Gamma Distribution And Its Applications To Industrial Growth, Fuad S. Al-Duais
Neutrosophic Sets and Systems
This study suggests a novel statistical distribution known as the neutrosophic log gamma distribution (NLGD) for analyzing the interval value data. The proposed distribution is derived from the transformation method, utilizing the approach of neutrosophic logic. The statistical characteristics of the proposed are studied within a neutrosophic framework. Basic statistical properties such as moments of origin, mode, mean deviation, and other related functions that are commonly employed in statistical applications are derived. In addition to the basic properties of the model, the estimation approach of maximum likelihood is also studied. The derived estimators of the proposed model are further assessed …
Hybrid Neutrosophic Deep Learning Model For Enhanced Arabic Handwriting Recognition, Mohamed G. Mahdi, Ahmed Sleem, Ibrahim M. Elhenawy, Soha Safwat
Hybrid Neutrosophic Deep Learning Model For Enhanced Arabic Handwriting Recognition, Mohamed G. Mahdi, Ahmed Sleem, Ibrahim M. Elhenawy, Soha Safwat
Neutrosophic Sets and Systems
Recognizing handwritten Arabic characters poses a significant challenge due to the complexities of the cursive script and the visual similarities between characters. While deep learning techniques have shown substantial promise, advancements in model architectures are essential to further enhance performance. Neutrosophic Sets (NS) have demonstrated their potential in improving classification models by effectively handling indeterminate and inconsistent data. This paper introduces a novel approach that integrates Neutrosophic Sets with a hybrid deep learning model, combining Convolutional Neural Networks (CNNs) with Bidirectional Recurrent Neural Networks (Bi-LSTM and Bi-GRU). This integration allows for the extraction of spatial features and modeling of temporal …
Soft Sets Extensions: Innovating Healthcare Claims Analysis, Daniela Gifu, Florentin Smarandache
Soft Sets Extensions: Innovating Healthcare Claims Analysis, Daniela Gifu, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
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.