Applied Mathematics Commons^™

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 …

Local-Neutrosophic Logic And Local-Neutrosophic Sets: Incorporating Locality With Applications, Florentin Smarandache, Takaaki Fujita

Branch Mathematics and Statistics Faculty and Staff Publications

The study of uncertainty has been a significant area of research, with concepts such as fuzzy sets [87], fuzzy graphs [51], and neutrosophic sets [58] receiving extensive attention. In Neutrosophic Logic, indeterminacy often arises from real-world complexities. This paper explores the concept of locality as a key factor in determining indeterminacy, building upon the framework introduced by F. Smarandache in [73]. Locality refers to processes constrained within a specific region, where an object or system is directly influenced by its immediate surroundings. In contrast, nonlocality involves effects that transcend spatial or temporal boundaries, where changes in one location have direct …

Soft Directed N-Superhypergraphs With Some Real-World Applications, Takaaki Fujita, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This paper introduces the Directed Soft Super Hyper Graph, a unified framework for modeling complex, multi-layered directed networks. It combines directionality, recursive hyperstructure, and soft-set parameterization to address the integration of Soft Super HyperGraphs and Directed SuperHyperGraphs, which remains largely unexplored. The paper provides formal definitions, core operations, and real-world examples, such as urban infrastructure and transportation networks, to demonstrate the framework's effectiveness in managing deep hierarchies and uncertain relationships simultaneously.

Beyond Dialectics, Paradoxes, And Binary Logic, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Philosophy, long defined by its pursuit of truth, has historically been a battleground for dichotomies: truth vs. falsehood, materialism vs. idealism, reason vs. emotion. These oppositions often provide a framework for understanding philosophical discourse, but they fail to capture the full nuances of reality. To challenge these binary oppositions, I introduced the neutrosophic perspective in philosophy, rooted in Mathematics, and Many-Valued Logics.1 By emphasizing the interrelation of affirmation, negation, and neutrality, neutrosophy allows for the reconciliation of seemingly irreconcilable viewpoints, providing a new lens through which to reinterpret age-old philosophical questions.

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 …

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.

Exploring Concepts Of Hyperfuzzy, Hyperneutrosophic, And Hyperplithogenic Sets (I), Florentin Smarandache, Takaaki Fujita

Branch Mathematics and Statistics Faculty and Staff Publications

This work investigates the evolution of traditional set theory to address complex and ambiguous real-world phenomena. It introduces hierarchical hyperstructures and superhyperstructures, where superhyperstructures are formed by iteratively applying power sets to create nested abstractions. The focus is placed on three foundational set-based frameworks—Fuzzy Sets, Neutrosophic Sets, and Plithogenic Sets and their extensions into Hyperfuzzy Sets, HyperNeutrosophic Sets, and Hyperplithogenic Sets. These extensions are applied to various domains, including Statistics, TOPSIS, K-means Clustering, Evolutionary Theory, Topological Spaces, Decision Making, Probability, and Language Theory. By exploring these generalized forms, this paper seeks to guide and inspire further research and development in …

Exploring Concepts Of Hyperfuzzy, Hyperneutrosophic, And Hyperplithogenic Sets (Ii), Takaaki Fujita, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This paper delves into the advancements of classical set theory to address the complexities and uncertainties inherent in real-world phenomena. It highlights three major extensions of traditional set theory - Fuzzy Sets [288], Neutrosophic Sets [237], and Plithogenic Sets [243] - and examines their further generalizations into Hyperfuzzy [106], HyperNeutrosophic [90], and Hyperplithogenic Sets [90]. Building on previous research [83], this study explores the potential applications of HyperNeutrosophic Sets and SuperHyperNeutrosophic Sets across various domains. Specifically, it extends f undamental c oncepts such as Neutrosophic Logic, Cognitive Maps, Graph Neural Networks, Classifiers, and Triplet Groups through these advanced set structures …

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.

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.

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 …

Modelado Causal De La Violencia En El Área Metropolitana De Guayaquil: Evidencia Neutrosófica Y Análisis De Condiciones Necesarias, Maikel Y. Leyva Vázquez, Lorenzo Cevallos-Torres, Alfonso Guijarro Rodríguez, Douglas Iturburu-Salvador, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

La violencia urbana en el área metropolitana de Guayaquil plantea desafíos persistentes para el bienestar social y la gobernanza. Este estudio integra tres fuentes de evidencia para clarificar qué factores son necesarios y qué niveles mínimos habilitan altos niveles de violencia. Primero, se aplica stance detection con representación neutrosófica para construir un prior (T, I, F) de la literatura. Luego, evaluamos condiciones necesarias mediante fsQCA (inclusión difusa 𝑌⊆𝑋, umbral de consistencia ≥ 0.90) y estimamos umbrales (bottlenecks) con NCA (CE-FDH, CR-FDH, permutaciones). Usamos la misma matriz fuzzy en ambos métodos para asegurar coherencia. Con una encuesta a 179 jóvenes de …

Ppg-Based Sleep Stage Classification Using Pulse Wave Feature Fusion And Explainable Ai, Florentin Smarandache, Satyasri Akula, Saleh Alzahrani, Farrukh Arslan, Amir Ijaz

Branch Mathematics and Statistics Faculty and Staff Publications

Sleep monitoring plays a crucial role in understanding and managing various health conditions, including sleep disorders, cardiovascular diseases, and mental health. Traditional sleep monitoring methods rely on Electroencephalography (EEG) and Polysomnography (PSG) in clinical settings. However, these methods are expensive, difficult to administer, and unsuitable for home-based monitoring. In recent years, photoplethysmogram (PPG) has emerged as a promising noninvasive technology that is widely used in wearable devices and holds great potential for sleep assessment. Yet, most current sleep monitoring methods rely on deep learning models, which are inherently "black-box" and challenging in the clinical decision-making process. In this paper, we …

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 …

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 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 …

Prólogo Al Número Especial “Neutrosophic Computing And Machine Learning”, Vol. 40, 2025, Florentin Smarandache, Maikel Y. Leyva Vázquez, Mohamed Abdel Basset

Branch Mathematics and Statistics Faculty and Staff Publications

Esto es un prólogo al número especial de "Neutrosophic Computing and Machine Learning" presenta una selección de trabajos significativos sobre enfoques neutrosóficos y plitogénicos en ciencia de datos y análisis multivariante de la IX Conferencia Iberoamericana de Biometría. La conferencia, celebrada en Quito, Ecuador, del 8 al 9 de julio de 2025, reunió a más de 250 expertos de 13 países. El éxito del evento fue resultado de la colaboración entre la Universidad Estatal de Milagro (UNEMI) de Ecuador y la Universidad de Salamanca (USAL) de España. Los artículos de este volumen exploran la relación entre la estadística clásica y …

Neutrosophic Stance Detection And Fsqca-Based Necessary Condition Analysis For Causal Hypothesis Assessment In Ai-Enhanced Learning, Jesús Rafael Hechavarría-Hernández, Maikel Y. Leyva Vazquez, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This study addresses the ambiguities in empirical findings on artificial intelligence (AI) in education by proposing a new methodological framework that combines neutrosophic stance detection and Fuzzy Set Qualitative Comparative Analysis (fsQCA). This approach explicitly models truth, indeterminacy, and falsity, allowing for the synthesis of contradictory research. The authors evaluated four causal hypotheses related to AI-based learning, using a survey of 24 university participants to explore the necessary conditions for perceived learning improvements. The results indicate that the digital divide is a perfectly necessary condition for effective AI-enhanced learning. The findings also reveal that AI feedback and AI platform use …

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.

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.

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 …

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 …

Cvitlnn: A Hybrid Approach Based On Vision Transformer And Liquid Neural Network For Covid-19 Detection, Muhammad Waqaq, Florentin Smarandache, Muhammad Yasir, Farrukh Arslan, Anum Ali

Branch Mathematics and Statistics Faculty and Staff Publications

The COVID-19 pandemic has underscored the need for accurate and rapid diagnostic tools to assist clinical decision-making. Conventional deep learning models for COVID-19 detection in Chest X-Ray (CXR) images face challenges in poor generalization across imaging conditions and high computational demands. To address these issues, this study proposes CviTLNN, a novel hybrid model combining Vision Transformers (ViTs) and Liquid Neural Networks (LNNs) to improve feature extraction and classification. Specifically, CviTLNN employs a ViT with 24 transformer encoder blocks for efficient extraction of spatial features. The self-attention mechanism of ViTs effectively captures global and local dependencies in CXR images. Furthermore, …

Nidus Idearum. Scilogs, Xiv: Superhyperalgebra, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this fourteenth book of scilogs – one may find topics on examples where neutrosophics works and others don’t, law of included infinitely-many-middles, decision making in games and real life through neutrosophic lens, sociology by neutrosophic methods, Smarandache multispace, algebraic structures using natural class of intervals, continuous linguistic set, cyclic neutrosophic graph, graph of neutrosophic triplet group , how to convert the crisp data to neutrosophic data, n-refined neutrosophic set ranking, adjoint of a square neutrosophic matrix, neutrosophic optimization, de-neutrosophication, the n-ary soft set relationship, hypersoft set, extending the hypergroupoid to the superhypergroupoid, alternative ranking, Dezert-Smarandache Theory (DSmT), reconciliation between …

Nidus Idearum. Scilogs, Xiii: Structure / Neutrostructure / Antistructure, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this thirteenth book of scilogs – one may find topics on Neutrosophy, Plithogeny, Physics, Mathematics, Philosophy – email messages to research colleagues, or replies, notes, comments, remarks about authors, articles, or books, spontaneous ideas, and so on. It presents new types of soft sets and new types of topologies.

Exchanging ideas with Mohammad Abobala, Ishfaq Ahmad, Ibrahim M. Almanjahie, Fatimah Alshahrani, Nizar Altounji, Muhammad Aslam, Said Broumi, Victor Christianto, R. Diksh, Feng Liu, Frank Julian Gelli, Erick Gonzalez Caballero, Riad Hamido, Yaser Al-Hasan, Ahmed Hatip, Yasin Karmouta, Nivetha Martin, Preda Mihăilescu, V. Lakshmana Gomathi Nayagam, Ze Carlos Tiago de …

Fundamental Computational Problems And Algorithms For Superhypergraphs, Takaaki Fujita, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Hypergraphs extend traditional graphs by allowing edges (known as hyperedges) to connect more than two vertices, rather than just pairs. This paper explores fundamental problems and algorithms in the context of SuperHypergraphs, an advanced extension of hypergraphs enabling modeling of hierarchical and complex relationships. Topics covered include constructing SuperHyperGraphs, recognizing SuperHyperTrees, and computing SuperHyperTree-width. We address a range of optimization problems, such as the SuperHy-pergraph Partition Problem, Reachability, Minimum Spanning SuperHypertree, and Single-Source Shortest Path. Furthermore, adaptations of classical problems like the Traveling Salesman Problem, Chinese Postman Problem, and Longest Simple Path Problem are presented in the SuperHypergraph framework.

Enhancing Set-Theoretic Research Methods With Neutrosophic Sets, Maikel Yelandi Leyva Vázquez, Jesús Estupiñán Ricardo, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This study employed the integration of neutrosophic set theory with set-theoretic methods and Qualitative Comparative Analysis (QCA) to examine intricate social phenomena. Participants' opinions and attitudes were captured using neutrosophic Likert scales, which reflected elements of truth, indeterminacy, and falsity. This proposal is illustrated in a case study facilitated a more comprehensive and subtle examination, emphasizing the significance of variables such as motivation, instructional excellence, and educational resources in achieving academic accomplishment. The results of the necessary condition analysis and set coincidence analysis indicated that motivation and teaching quality have the highest individual impact. Nevertheless, the convergence of scholarly resources, …

Numerical Solution Of Hybrid Nanofluid And Its Stability Over Permeable Wedge Sheet With Heat Transfer Analysis, Aisha M. Alqahtani, Zeeshan, Waris Khan, Florentin Smarandache, Nidhal Becheikh, Roobaea Alroobaea, Taseer Muhammad

Branch Mathematics and Statistics Faculty and Staff Publications

The inclusion of nanoparticles has the potential to improve the thermal efficiency of the base fluid. The field of nanofluid (NF) dynamics has attracted important attention due to its extensive range of practical uses like fuel cells, solar energy, medication administration, heat transfer, microfabrication, coolant applications, and other related domains. The aim of this study is to scrutinize the impact of Lorentz force, thermal energy, joule heating, heat source and injection parameters, and Brownian and thermoporetic diffusions on the hybrid nanofluid over the moving wedge. The stability inquiry is reported for the existing work in order to confirm the stable …

A Review Of The Hierarchy Of Plithogenic, Neutrosophic, And Fuzzy Graphs: Survey And Applications, Takaaki Fujita, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

As many readers may know, graph theory is a fundamental branch of mathematics that examines networks consisting of nodes and edges, with a focus on their paths, structures, and properties [157]. A Fuzzy Graph extends this concept by assigning a membership degree between 0 and 1 to each edge and vertex, capturing the level of uncertainty. Expanding on this idea, the Turiyam Neutrosophic Graph was introduced as an extension of both Neutrosophic and Fuzzy Graphs. Plithogenic graphs, in turn, offer a powerful approach for managing uncertainty. In this paper, we explore the relationships among various graph classes, including Plithogenic graphs, …

Beyond Cryptic Equations: Reimagining Concepts In Physics Through Metaheuristics And Fantasy Stories Using Neutrosophic Venn Diagram, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Physics, the grand narrative of the universe, bas long been viewed as realm of cold, hard equations. But what if we looked beyond the formulas and considered a more imaginative origin for some of its concepts? This article explores the intriguing possibility that physics, and even cosmology, might share a surprising kinship with metaheuristics and fantastical fiction.