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Plithogenic Superhypersoft Set And Plithogenic Forest Superhypersoft Set, Takaaki Fujita, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Reconsideration Of Neutrosophic Social Science And Neutrosophic Phenomenology With Non-Classical Logic, Takaaki Fujita, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Body-Mind-Soul-Spirit Fluidity is a concept rooted in psychology and phenomenology, offering significant insights into human decision-making and well-being. Similarly, in social analysis and social sciences, frameworks such as PDCA, DMAIC, SWOT, and OODA have been established to enable structured evaluation and effective p roblem-solving. Furthermore, in phenomenology and social sciences, various logical systems have been developed to address specific objectives and practical applications. This paper extends these concepts using the Neutrosophic theory, revisiting their mathematical definitions and exploring their properties. The Neutrosophic Set, an extension of the Fuzzy Set, is a highly flexible framework that has been widely studied in …

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 …

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 …

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, …

A Novel Bipolar Valued Fuzzy Group Based On Dib’S Approach, Fadi Al-Zu’Bi, Abdul Ghaffur Ahmad, Abd Ulazeez Alkouri, Maslina Darus

All Works

The numerous extensions of fuzzy groups (FG) and fuzzy subgroups are complicated. Several results depending on different approaches of FG theory were introduced. This study introduces a novel extension, named bipolar-valued fuzzy groups (BVF-groups), which are based on bipolar-valued fuzzy space (BVF-space) and are created using Dib’s methodology. The BVF-space replaces the universal set in conventional set theory. The BVF-space generalizes the notion of fuzzy space (F-space) from [0, 1] to [−1, 0] × [0, 1] for the range of membership function. The novel theory of BVF-group is achieved through the BVF-space and bipolar valued binary operation (BVFBO) to build …

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.

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 …

(R2082) Two New Operations And Extended Modal Operators On Bipolar Pythagorean Fuzzy Matrices, S. Sriram, K. Sivaranjani

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, two novel binary operations concerning bipolar Pythagorean fuzzy matrices are delineated. Several algebraic properties, such as commutativity and associativity, are explored. Additionally, extended modal operators for Bipolar Pythagorean fuzzy matrices are introduced. Subsequently, these methodologies are applied to a decision-making scenario wherein a scoring matrix is formulated and alternatives are ranked according to their cumulative score values.

Integrating Contradictory Perspectives In Latin American Philosophy: A Multialism Approach, Maikel Yelandi Leyva Vázquez, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This study explores the integration of indigenous philosophies and postcolonial modernist theories within the framework of MultiAlism, highlighting the potential for dialogue and synthesis between these diverse philosophical traditions in Latin America. MultiAlism, a concept developed by Florentin Smarandache, is utilized to bridge the gaps and contradictions between these systems by focusing on areas of neutrality such as cultural diversity and power structure critiques. The research emphasizes the importance of incorporating both ancestral wisdom and modern critiques to foster a deeper understanding and appreciation of Latin America’s rich philosophical heritage. This integrative approach offers practical insights for developing inclusive policies …

Survey Of Planar And Outerplanar Graphs In Fuzzy And Neutrosophic Graphs, 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 explores networks made up of nodes and edges, focusing on their paths, structures, and properties [196]. A planar graph is one that can be drawn on a plane without any edges intersecting, ensuring planarity. Outerplanar graphs, a subset of planar graphs, have all their vertices located on the boundary of the outer face in their planar embedding. In recent years, outerplanar graphs have been formally defined within the context of fuzzy graphs. To capture uncertain parameters and concepts, various graphs such as fuzzy, neutrosophic, Turiyam, and …

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, …

Foundation Of Appurtenance And Inclusion Equations For Constructing The Operations Of Neutrosophic Numbers Needed In Neutrosophic Statistics Foundation Of Appurtenance And Inclusion Equations For Constructing The Operations Of Neutrosophic Numbers Needed In Neutrosophic Statistics, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

We introduce for the first time the appurtenance equation and inclusion equation, which help in understanding the operations with neutrosophic numbers within the frame of neutrosophic statistics. The way of solving them resembles the equations whose coefficients are sets (not single numbers).

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, …

Generating Neutrosophic Random Variables Based Gamma Distribution, Maissam Ahmad Jdid, Florentin Smarandache, Khalifa Al Shaqsi

Branch Mathematics and Statistics Faculty and Staff Publications

In practical life, we encounter many systems that cannot be studied directly, either due to their high cost or because some of these systems cannot be studied directly. Therefore, we resort to the simulation method, which depends on applying the study to systems similar to real ones and then projecting these results if they are suitable for the real system. The simulation process requires a good understanding of probability distributions and the methods used to transform random numbers that follow a regular distribution in the field [0,1] into random variables that follow them, so that we can achieve the greatest …

Partial Collisions Of Unmater-Matter, Unmatter-Antimatter, And Unmatter1-Unmatter2 To Generate High Energy, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we present the possibility of partial collisions between unmatter with matter, and unmatter with antimatter, and two or more different types of unmatters colliding between themselves to create high energy. In general, the collisions between unmatter with matter, or with antimatter, or with other type of unmatter, because being partial, they release less energy than the matter-unmatter collision which is a total collision. But the unmatter may be easier to produce in laboratory than antimatter.

Ermakov Equations Can Be Derived From Zel’Dovich Pancake, And They Are Cold And Nonlocal Through Using Neutrosophic Venn Diagram, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

As we argue in a previous article, the labyrinthine worlds of Jorge Luis Borges are more than captivating narratives; they are portals to a deeper understanding of existence. By weaving elements of science-fiction fantasy with philosophical and ethical inquiries, Borges's short stories bridge the seemingly disparate realms of physics and the humanities, offering fertile ground for contemporary physics research. The present-day universe consists of galaxies, galaxy clusters, one-dimensional filaments and two-dimensional sheets or pancakes, all of which combine to form the cosmic web. The so called ”Zeldovich pancakes”, are very difficult to observe, because their overdensity is only slightly greater …

New Trends In Neutrosophic Theories And Applications, Volume Iii, Florentin Smarandache, Surapati Pramanik

Branch Mathematics and Statistics Faculty and Staff Publications

The field of neutrosophic set theory and its applications has been rapidly expanding, particularly since the introduction of the journal "Neutrosophic Sets and Systems." New theories, techniques, and algorithms are being developed at a very high rate. One of the most notable trends in neutrosophic theory is its hybridization with other set theories such as rough set theory, bipolar set theory, soft set theory, hesitant fuzzy set theory, and more. Various hybrid structures like rough neutrosophic sets, neutrosophic soft set, single valued neutrosophic hesitant fuzzy sets, among others, have been proposed in a short period. Neutrosophic sets have proven to …

The Cardinal Of The M-Powerset Of A Set Of N Elements Used In The Superhyperstructures And Neutrosophic Superhyperstructures, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we find a formula for computing the cardinal of the m-th powerset of a set of n elements, which is needed in the SuperHyperStructures.

Combined Plithogenic Hypersoft Sets In Decision Making On Supplier Selection With Different Mcdm Approaches., Sikkanan Sudha, Ravi Priya, Nivetha Martin, Said Broumi, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Decision making methods integrated with Plithogenic sets are highly feasible and resilient in designing optimal solutions. This research work identifies the research gaps of limited applications of combined plithogenic hypersoft sets (CPHSS) and hence proposes a supplier selection decision problem with an integrated approach combining CPHSS with MCDM methods. A generalized form of Plithogenic accuracy function is used in determining the plithogenic accuracy matrix to which the prominent ranking methods of TOPSIS, ELECTRE, VIKOR and MAIRCA are applied. The proposed hybrid decision approach is illustrated using supplier selection decision problem as a case study. The ranking results are compared with …

Introduction To Upside-Down Logic: Its Deep Relation To Neutrosophic Logic And Applications, Takaaki Fujita, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In the study of uncertainty, concepts such as fuzzy sets [113], fuzzy graphs [79], and neutrosophic sets [88] have been extensively investigated. This paper focuses on a novel logical framework known as Upside-Down Logic, which systematically transforms truths into falsehoods and vice versa by altering contexts, meanings, or perspectives. The concept was first introduced by F. Smarandache in [99]. To contribute to the growing interest in this area, this paper presents a mathematical definition of Upside-Down Logic, supported by illustrative examples, including applications related to the Japanese language. Additionally, it introduces and explores Contextual Upside-Down Logic, an advanced extension that …