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Articles 31 - 60 of 956
Full-Text Articles in Mathematics
Module 1 Check Ups, Karon Klipple, Cheryl Hedden
Module 1 Check Ups, Karon Klipple, Cheryl Hedden
Module 1 Assessments
No abstract provided.
Module 2 Part A - Multiplication Is Repeated Addition, Karon Klipple, Cheryl Hedden
Module 2 Part A - Multiplication Is Repeated Addition, Karon Klipple, Cheryl Hedden
Module 2 Workbook
No abstract provided.
Module 2 - Student Workbook, Karon Klipple, Cheryl Hedden
Module 2 - Student Workbook, Karon Klipple, Cheryl Hedden
Module 2 Workbook
No abstract provided.
Activity Percentage Contexts Cards, Karon Klipple, Cheryl Hedden
Activity Percentage Contexts Cards, Karon Klipple, Cheryl Hedden
Module 1 Workbook
No abstract provided.
Module 2 Power Point Activity 2a.3, Karon Klipple, Cheryl Hedden
Module 2 Power Point Activity 2a.3, Karon Klipple, Cheryl Hedden
Module 2 Workbook
No abstract provided.
Module 2 Activity - 2b.4 Cards, Karon Klipple, Cheryl Hedden
Module 2 Activity - 2b.4 Cards, Karon Klipple, Cheryl Hedden
Module 2 Workbook
No abstract provided.
Module 2 - Warm Up 2c.5 Cards, Karon Klipple, Cheryl Hedden
Module 2 - Warm Up 2c.5 Cards, Karon Klipple, Cheryl Hedden
Module 2 Workbook
No abstract provided.
Module 2 Activity- 2b.3 Cards, Karon Klipple, Cheryl Hedden
Module 2 Activity- 2b.3 Cards, Karon Klipple, Cheryl Hedden
Module 2 Workbook
No abstract provided.
Mathematics In Everyday Life: Exploring Practical Applications And Real-World Impact, Priyant Banerjee, Arshad Bhat
Mathematics In Everyday Life: Exploring Practical Applications And Real-World Impact, Priyant Banerjee, Arshad Bhat
Himalayan Research Papers Archive
Mathematics is an essential part of daily life and influences decisions and problem-solving in various aspects of life. This study explores how mathematical concepts are embedded in daily activities such as financial management, cooking, travel planning, and technological interactions. We will show how arithmetic, algebra, geometry, and statistics are applied in real life to improve decision-making, efficiency, and productivity. Findings indicate that people with higher mathematical literacy solve problems more efficiently, especially in budgeting, as accurate calculations minimize financial mistakes and facilitate long-term financial planning. In cooking, proportional reasoning ensures the accuracy of recipes, thus providing consistent culinary results. Travel …
A Comparative Analysis Of Data-Driven And Model-Based Neutrosophication Methods: Advancing True Neutrosophic Logic In Medical Data Transformation, Maikel Yelandi Leyva Vázquez, Lorenzo Cevallos-Torres, Omar Mar Cornelio, Florentin Smarandache
A Comparative Analysis Of Data-Driven And Model-Based Neutrosophication Methods: Advancing True Neutrosophic Logic In Medical Data Transformation, Maikel Yelandi Leyva Vázquez, Lorenzo Cevallos-Torres, Omar Mar Cornelio, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
Neutrosophic logic extends fuzzy logic by explicitly modeling indeterminacy (I), offering a robust framework for uncertainty representation. The transformation of crisp data into neutrosophic triplets {T, I, F}—known as neutrosophication—is crucial for applying neutrosophic models in real-world analysis. However, comparative evaluations of existing neutrosophication methods remain limited. This study presents a systematic comparison of five approaches: three model-based methods (Parabolic, Threshold Distance, Fuzzy Membership), one density-based method (Kernel Density Estimation), and a proposed data-driven K-Means clustering method integrating sigmoid membership functions. Using a medical dataset of 299 patients and six continuous clinical variables, we assessed statistical behavior, consistency, and alignment …
A Critical Evaluation Of The Criticisms Against Neutrosophic Statistical Methods, Muhammad Aslam, Abdulrahman Alaita, Florentin Smarandache
A Critical Evaluation Of The Criticisms Against Neutrosophic Statistical Methods, Muhammad Aslam, Abdulrahman Alaita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
Neutrosophic statistical analysis has gained attention for incorporating the degree of indeterminacy when analyzing imprecise and interval data under uncertainty—an aspect often overlooked by classical statistics, fuzzy statistical analysis, and interval statistics. Recently, critical discussions have emerged regarding the use and applications of neutrosophic statistics, with some questioning its usefulness and validity. In this paper, we present a critical assessment of the existing literature, focusing on areas where misunderstandings and misinterpretations of neutrosophic statistical methods have occurred. We also examine flawed comparisons made between the results of neutrosophic statistics and interval statistics. Furthermore, substantial issues have been identified in the …
Some Types Of Hyperneutrosophic Set (6): Multineutrosophic Set And Refined Neutrosophic Set, Takaaki Fujita, Florentin Smarandache
Some Types Of Hyperneutrosophic Set (6): Multineutrosophic Set And Refined Neutrosophic Set, Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
This paper builds on the foundational advancements introduced in [22, 29–32]. The Neutrosophic Set pro-vides a flexible mathematical framework for managing uncertainty by utilizing three membership functions: truth, indeterminacy, and falsity. Recent extensions, such as the HyperNeutrosophic Set and the SuperHy-perNeutrosophic Set, have been developed to address increasingly complex and multidimensional challenges. Comprehensive formal definitions of these concepts are provided in [26]. In this paper, we further extend various specialized classes of Neutrosophic Sets. Specifically, we explore extensions of the MultiNeutrosophic Set and the Refined Neutrosophic Set using HyperNeutrosophic Sets and 𝑛-SuperHyperNeutrosophic Sets, providing detailed analysis and examples.
Superhypergraph Neural Networks And Plithogenic Graph Neural Networks: Theoretical Foundations, Takaaki Fujita, Florentin Smarandache
Superhypergraph Neural Networks And Plithogenic Graph Neural Networks: Theoretical Foundations, Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
Hypergraphs extend traditional graphs by allowing edges to connect multiple nodes, while superhypergraphs further generalize this concept to represent even more complex relationships. Neural networks, inspired by biological systems, are widely used for tasks such as pattern recognition, data classification, and prediction. Graph Neural Networks (GNNs), a well-established framework, have recently been extended to Hypergraph Neural Networks (HGNNs), with their properties and applications being actively studied. The Plithogenic Graph framework enhances graph representations by integrating multi-valued attributes, as well as membership and contradiction functions, enabling the detailed modeling of complex relationships. In the context of handling uncertainty, concepts such as …
Significado Neutrosófico: Partes Comunes De Cosas Poco Comunes Y Partes Poco Comunes De Cosas Comunes, Florentin Smarandache
Significado Neutrosófico: Partes Comunes De Cosas Poco Comunes Y Partes Poco Comunes De Cosas Comunes, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
Esta investigación explora la Neutrosofía, un enfoque filosófico que se centra en la identificación de elementos comunes entre conceptos opuestos y en el análisis de las diferencias entre conceptos semejantes. En este contexto, se estudian las Partes Comunes a Cosas No Comunes, que se manifiestan cuando elementos como y < antiA > comparten aspectos en su intersección, y las Partes No Comunes a Cosas Comunes, donde conceptos iguales como y difieren al exhibir elementos únicos. Este análisis permite comprender mejor la neutralidad e indeterminación representada por < neutA > y < neutB >, situados entre sus respectivos opuestos. La investigación abarca diversas áreas como la Dialéctica, el Yin …
Some Types Of Hyperneutrosophic Set (1): Bipolar, Pythagorean, Double-Valued, Interval-Valued Set, Takaaki Fujita, Florentin Smarandache
Some Types Of Hyperneutrosophic Set (1): Bipolar, Pythagorean, Double-Valued, Interval-Valued Set, Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
The Neutrosophic Set is a mathematical framework designed to manage uncertainty, characterized by three membership functions: truth (T), indeterminacy (I), and falsity (F). In recent years, extensions such as the Hyperneutrosophic Set and SuperHyperneutrosophic Set have been introduced to address more complex scenarios. This paper proposes new concepts by extending Bipolar Neutrosophic Sets, Interval-Valued Neutrosophic Sets, Pythagorean Neutrosophic Sets, and Double-Valued Neutrosophic Sets using the frameworks of Hyperneutrosophic and SuperHyperneutrosophic Sets. Additionally, a brief analysis of these extended concepts is presented.
Some Types Of Hyperneutrosophic Set (7): Type-M, Nonstationary, Subset-Valued, And Complex Refined, Takaaki Fujita, Florentin Smarandache
Some Types Of Hyperneutrosophic Set (7): Type-M, Nonstationary, Subset-Valued, And Complex Refined, Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
This paper builds upon the foundational advancements introduced in [26,39–43]. TheNeutrosophic Set provides a versatile mathematical framework for addressing uncertainty through its three membership functions: truth, indeterminacy, and falsity [84]. Extensions such as the Hyperneutrosophic Set and the SuperHyperneutrosophic Set have been recently proposed to address increasingly complex and multidimensional problems. Detailed formal definitions of these concepts can be found in [33]. In this paper, we extend the Type-𝑚, Nonstationary, Subset-Valued, and Complex Refined Neutrosophic Sets using the Hyperneutrosophic Set and the SuperHyperneutrosophic Set frameworks.
Some Types Of Hyperneutrosophic Set (5): Support, Paraconsistent, Faillibilist, And Others, Takaaki Fujita, Florentin Smarandache
Some Types Of Hyperneutrosophic Set (5): Support, Paraconsistent, Faillibilist, And Others, Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
This paper builds upon the foundational advancements introduced in [14, 25–27]. The Neutrosophic Set offers a versatile mathematical framework for addressing uncertainty through its three membership functions: truth, indeterminacy, and falsity. Extensions such as the Hyperneutrosophic Set and the SuperHyperneutrosophic Set have been recently proposed to tackle increasingly sophisticated and multidimensional problems. Detailed formal definitions of these concepts can be found in [20]. In this paper, we extend various specialized classes of Neutrosophic Sets—namely, the Support Neutrosophic Set, Neutrosophic Intuitionistic Set (distinct from the Intuitionistic Fuzzy Set), Neutrosophic Paraconsistent Set, Neutrosophic Faillibilist Set, Neutrosophic Paradoxist Set, Neutrosophic Pseudo-Paradoxist Set, Neutrosophic …
Forestfuzzy, Forestneutrosophic, Forestplithogenic, And Forestrough Set, Takaaki Fujita, Florentin Smarandache
Forestfuzzy, Forestneutrosophic, Forestplithogenic, And Forestrough Set, Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
Concepts such as Fuzzy Sets [30, 72], Neutrosophic Sets [53, 55], Rough Sets [37], and Plithogenic Sets [59] have been extensively studied to address uncertainty, with diverse applications across various fields. Recently, TreeFuzzy, TreeNeutrosophic, TreePlithogenic, and TreeRough Sets have been defined [15]. This work examines their extensions: ForestFuzzy, ForestNeutrosophic, ForestPlithogenic, and ForestRough Sets.
A Family Of Neutrosophic Estimators For Estimating Mean: An Application To Real Data, Bavita Singh, Abhishek Singh, Florentin Smarandache
A Family Of Neutrosophic Estimators For Estimating Mean: An Application To Real Data, Bavita Singh, Abhishek Singh, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
In the realm of sample survey research, the classical statistics approach primarily deals with precise and definitive types of data to estimate population parameters when additional information is available. However, this approach fails when faced with data indeterminacies. To address such ambiguities, neutrosophic statistics emerges as an extension of both fuzzy and classical statistics. Thus, in light of the challenges posed by indeterminacy in sampling, we have introduced a proficient neutrosophic class of estimators, with and without Searls technique (optimization tool) for estimating the mean utilizing additional (ancillary) information under neutrosophic simple random sampling (NeSRS). The expression for the Bias …
Hyperplithogenic Cubic Set And Superhyperplithogenic Cubic Set, Florentin Smarandache
Hyperplithogenic Cubic Set And Superhyperplithogenic Cubic Set, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
Concepts such as Fuzzy Sets [23, 47], Neutrosophic Sets [32, 33], and Plithogenic Sets [35] have been extensively studied for addressing uncertainty, with diverse applications across numerous fields. Building on the Plithogenic Set, the HyperPlithogenic Set and SuperHyperPlithogenic Set have also gained recognition [15]. A Plithogenic Cubic Set integrates interval-valued and single-valued fuzzy memberships, augmented by multiattribute aggregation using plithogenic structures. This paper defines the HyperPlithogenic Cubic Set and SuperHyperPlithogenic Cubic Set and explores related concepts such as the HyperPlithogenic Fuzzy Cubic Set, HyperPlithogenic Intuitionistic Fuzzy Cubic Set, and HyperPlithogenic Neutrosophic Cubic Set.
Plithogenic Superhypersoft Set And Plithogenic Forest Superhypersoft Set, Takaaki Fujita, Florentin Smarandache
Plithogenic Superhypersoft Set And Plithogenic Forest Superhypersoft Set, Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
No abstract provided.
Quantified Neutrosophic Set (Qtns)-Based Mcdm Algorithms For Sustainable Material Selection For Anti-Microbial Bio-Fabricated Textile Manufacturing, Muhammad Saeed, Neha Andaleeb Khalid, Florentin Smarandache
Quantified Neutrosophic Set (Qtns)-Based Mcdm Algorithms For Sustainable Material Selection For Anti-Microbial Bio-Fabricated Textile Manufacturing, Muhammad Saeed, Neha Andaleeb Khalid, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
This paper proposes a modified structure for the neutrosophic set called the Quantified Neutrosophic Set (QtNS) with a parameterized setting. Unlike conventional approaches, the QtNS provides a quantified environment for the indeterminacy by its dependence on truthness and falsity components. This innovative approach quantifies the uncertainty and improves the assessment process via expert-guided opinions, customising it according to the specific situations in real-world decision-making scenarios. Some QtNS operations along with useful characteristics are addressed. Furthermore, two algorithms, QtNSUI and QtNSAO, are developed for the proposed operations of union, intersection, AND, and OR based on QtNS. In the world of sustainable …
Artificial Intelligence, Society 5.0 And Smart City Adaptation Initiatives For Businesses: An Integrated Approach, Inês A.M. Gil, Fernando A.F. Ferreira, Neuza C.M.Q.F. Ferreira, Florentin Smarandache, Momtaj Khanam, Tugrul Daim
Artificial Intelligence, Society 5.0 And Smart City Adaptation Initiatives For Businesses: An Integrated Approach, Inês A.M. Gil, Fernando A.F. Ferreira, Neuza C.M.Q.F. Ferreira, Florentin Smarandache, Momtaj Khanam, Tugrul Daim
Branch Mathematics and Statistics Faculty and Staff Publications
The unprecedented migration of populations to urban areas has created major challenges for municipalities and service providers. To address these issues, decision-makers must embrace smart city and Society 5.0 paradigms, both of which focus on adaptability and sustainable development. Artificial intelligence (AI) plays a pivotal role by expanding service capacity, enabling automation, and processing vast data to align urban development with the UN’s Sustainable Development Goals (SDGs). This paper develops a multi-criteria analysis system designed to support decision-making in complex socio-technological contexts. Using cognitive mapping and the Decision-Making Trial and Evaluation Laboratory (DEMATEL) technique within a neutrosophic environment, the study …
A Neutrosophic Approach To Social Phenomena, Florentin Smarandache
A Neutrosophic Approach To Social Phenomena, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
Sociology has long sought to understand human societies and the social behaviors within them. It explores the organization, structure, dynamics, and transformations of society over time. However, traditional sociological methods face significant challenges in addressing the complexity and indeterminacy inherent in social data—data that is often ambiguous, incomplete, and contradictory. The Neutrosociology offers a novel approach to studying and modeling social phenomena by employing mathematical and philosophical tools that can accommodate uncertainty.
A Neutrosophic Exploration Of Creative Ideational Dynamics, Florentin Smarandache
A Neutrosophic Exploration Of Creative Ideational Dynamics, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
Philosophy has always tried to illuminate the complexity of existence, but often faced its own paradoxes. The emergence of philosophical schools and concepts, along with their arguments, reflect the dynamic interaction of ideas. This short note explores some nuanced principles governing philosophical thought, summarized in the proposed “philosophical formulas.” These formulas are intended to mathematically and conceptually express the tensions, complementarities, and movements intrinsec in a given philosophical system.
Approches Neutrosophiques Et Plithogéniques En Science Des Données Et Analyse Multivariée : Contributions De La Ixe Réunion Ibéro-Américaine De Biométrie, Florentin Smarandache, Maikel Y. Leyva Vázquez, Mohamed Abdel-Basset
Approches Neutrosophiques Et Plithogéniques En Science Des Données Et Analyse Multivariée : Contributions De La Ixe Réunion Ibéro-Américaine De Biométrie, Florentin Smarandache, Maikel Y. Leyva Vázquez, Mohamed Abdel-Basset
Branch Mathematics and Statistics Faculty and Staff Publications
Ce numéro spécial de "Neutrosophic Sets and Systems" rassemble une sélection de travaux remarquables présentés lors de la IXe Réunion Ibéro-américaine de Biométrie, qui a eu lieu les 8 et 9 juillet 2025 à Quito, en Équateur. Sous la direction d'une équipe éditoriale de prestige, ce volume explore l'application des approches neutrosophiques et plithogéniques dans divers domaines tels que la biométrie, la bioinformatique, la santé publique, l'éducation et l'économie. Les articles mettent en lumière la convergence entre les statistiques classiques et l'intelligence artificielle, illustrant comment les méthodes neutrosophiques offrent des outils puissants pour modéliser l'incertitude et la complexité des données …
A Position Indicator With Applications In The Field Of Designing Forms With Artificial Intelligence, Ovidiu Ilie Șandru, Florentin Smarandache, Alexandra Șandru
A Position Indicator With Applications In The Field Of Designing Forms With Artificial Intelligence, Ovidiu Ilie Șandru, Florentin Smarandache, Alexandra Șandru
Branch Mathematics and Statistics Faculty and Staff Publications
The indicators used so far within the Theory of Extension can be synthetically expressed by the notion of “position indicators”. More exactly, these indicators can be grouped in two main sub-categories: point-set position indicators and point-two sets position indicators. The secondary goal of this paper is to define these classifications, while the primary goal is that to extend the two notions to the most general notion of set-set position indicator.
A Plausible Formal Correspondence Between Tetrahedral Condensates/Tsc And Pt-Symmetric Crystals Model Of Cmns (Aka. Low-Energy Nuclear Reactions), Victor Christianto, Florentin Smarandache
A Plausible Formal Correspondence Between Tetrahedral Condensates/Tsc And Pt-Symmetric Crystals Model Of Cmns (Aka. Low-Energy Nuclear Reactions), Victor Christianto, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
Akito Takahashi's Tetrahedral Symmetric Condensate (TSC) model, detailed in several of his earlier works1 proposes a mechanism for condensed matter nuclear science (CMNS) aka. low-energy nuclear reactions (LENR) within palladium lattices. The model centres on the formation of a tetrahedral cluster of deuterons, enhancing the probability of nuclear fusion. Here, we explore the possibility of extending this framework by considering the TSC within a more general crystalline solid with tetrahedral symmetry, and by approximating the screening potential experienced by the deuterons using PT-symmetric potentials.
Competition Super-Hypergraphs: Revealing Hierarchical Competition In Real-World Networks, Takaaki Fujita, Florentin Smarandache
Competition Super-Hypergraphs: Revealing Hierarchical Competition In Real-World Networks, Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
Graph theory provides a powerful language for modeling pairwise connections through vertices and edges [9, 20]. Hypergraphs generalize this idea by permitting hyperedges that join any number of vertices simultaneously [7], while super-hypergraphs iterate the Power-set operation to capture multi-level, hierarchical relationships among hyperedges [40, 22]. A competition hypergraph associates each prey species with a hyperedge containing all its predators, thereby encoding multi-way competition in ecological networks. In this work, we introduce the competition super-hypergraph, which lifts the competition concept to higher tiers of aggregation. We present its formal definition, explore theoretical properties, and illustrate its practical use in real-world …
A New Simulation Framework For Analyzing Neutrosophic Data In Experimental Design, Muhammad Aslam, Nasrullah Khan, Florentin Smarandache
A New Simulation Framework For Analyzing Neutrosophic Data In Experimental Design, Muhammad Aslam, Nasrullah Khan, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
A recent simulation-based classical analysis has been developed for interval data. However, a review of the literature indicates that these existing simulations have notable limitations and fail to conform to the neutrosophic statistical framework. In this paper, we propose a novel simulation process designed to analyze neutrosophic data within an appropriate and rigorous neutrosophic framework. We demonstrate that the proposed simulation is more comprehensive and aligns closely with the principles of neutrosophic theory. The results will be obtained through simulation and compared with those of existing methods, with the expectation that the proposed approach provides substantial improvements and is better …