Florentin Smarandache

This book develops a comprehensive and unified theory of SuperHyperStructures and their uncertain extensions, introducing a new paradigm for modeling multi-level, hierarchical, and non-deterministic systems. Extending classical structures and hyperstructures, the framework generalizes operations from single-valued mappings to higher-order mappings of the form f:X^n→P^k (X), enabling the representation of sets of sets and recursively organized relational systems. SuperHyperStructures were introduced by Florentin Smarandache. At its core, the theory addresses fundamental limitations of traditional mathematical models, which are often inadequate for describing systems characterized by hierarchy, interdependence, and uncertainty. By integrating concepts from set theory, hyperstructures, n-ary operations, and neutrosophic logic, the book establishes a rigorous foundation for Uncertain SuperHyperStructures, incorporating truth, indeterminacy, and falsity within a unified formalism. The work systematically develops the theory across multiple domains, including SuperHyperAlgebra, SuperHyperGeometry, SuperHyperLogic, SuperHyperGraphs, and SuperHyperCalculus, and introduces corresponding uncertain and neutrosophic extensions. A comparative framework is provided to position SuperHyperStructures relative to classical structures and hyperstructures, highlighting their increased expressive power and structural depth. Beyond theoretical development, the book demonstrates the applicability of the framework to a wide range of disciplines, including artificial intelligence, complex systems, data science, and physics. In these contexts, SuperHyperStructures enable the modeling of systems-of-systems, multi-agent interactions, hierarchical networks, and multi-scale phenomena under uncertainty. The final chapters explore advanced directions such as SuperHyperCategory Theory and outline open problems, emphasizing the foundational nature of the theory and its potential to support a broad research program. Overall, this work proposes a conceptual and mathematical shift—from flat, deterministic representations to hierarchical, multi-level, and uncertainty-aware structures—offering a unified approach to complexity across scientific domains.

This book presents a comprehensive and systematic survey of fuzzy and uncertain logical operators developed to model reasoning under imprecision, incompleteness, and partial reliability. Building upon foundational frameworks such as fuzzy sets, intuitionistic fuzzy sets, neutrosophic sets, vague sets, and hesitant fuzzy sets, the work focuses on the extension of classical logical connectives into uncertainty-aware environments. It provides a structured overview of a wide range of operators, including basic set-theoretic operations, conjunctive–disjunctive families (t-norms, t-conorms, uninorms), relational and inferential operators, aggregation mechanisms, and integral-based models such as Choquet and Sugeno integrals. The book organizes these operators within a unified uncertain-set framework, clarifying their mathematical properties, interrelationships, and functional roles in reasoning processes. By developing a coherent taxonomy and highlighting connections across different uncertainty paradigms, it establishes a solid theoretical foundation for future research. The survey also emphasizes applications in approximate reasoning, decision-making systems, control theory, and artificial intelligence, making it a valuable reference for both theoretical investigation and practical implementation of uncertainty-based logic.

Florentin Smarandache întreprinde o (nouă) incursiune radicală în logica paradoxului în volumul “Țara oamenilor care merg în cap”, un “experiment superparadoxist” care sfidează toate convențiile. Lucrarea nu se rezumă la o simplă poveste, ci se constituie ca un dispozitiv complex de deconstrucție a realității, alcătuit dintr-un “roman întors pe dos”, un “raport strict secret” de teren și un “studiu științific incorect”. Această succesiune nu este o simplă aglomerare de texte, ci o progresie deliberată a absurdului, de la experiența subiectivă a eroului, la instituționalizarea acestuia prin birocrație și, în final, la teoretizarea sa ca o realitate ontologică validă.

Uncertainty, indeterminacy, and inconsistency are intrinsic features of real-world systems, requiring mathematical and conceptual frameworks that extend beyond classical binary logic. Building upon earlier developments in fuzzy sets and intuitionistic fuzzy sets, neutrosophy introduces a triadic structure in which each element is characterized by independent degrees of truth, indeterminacy, and falsity. This book represents a revised and expanded synthesis of prior work, particularly the volume Neutrosophy Revisited, while incorporating further developments inspired by the Nidus idearum series and related research. It systematically re-formalizes and consolidates a wide spectrum of concepts in neutrosophic logic, plithogenic set theory, and associated mathematical structures. The work emphasizes the transition from exploratory and conceptual formulations toward coherent, rigorous, and unified theoretical frameworks. It presents refined definitions, extended structures (including n-refined and multi-valued neutrosophic systems), and connections to diverse domains such as discrete mathematics, algebra, applied sciences, and emerging neutrosophic technologies. By organizing and clarifying previously scattered or partially developed ideas, this volume aims to provide a solid foundation for further theoretical advancement and to stimulate interdisciplinary applications in mathematics, physics, computer science, and complex systems analysis.

This book addresses a fundamental epistemological limitation of contemporary artificial intelligence systems: their inability to represent and communicate uncertainty. Current AI architectures, particularly large language models, generate outputs based on probabilistic pattern matching without an intrinsic mechanism to distinguish between verified knowledge, partial knowledge, and fabricated information. This results in what the authors define as “confident machines,” capable of producing fluent yet potentially unreliable responses without signaling epistemic boundaries. To address this structural deficiency, the book introduces a practical and conceptual framework grounded in neutrosophic logic, a triadic system developed by Florentin Smarandache, in which every proposition is characterized by degrees of truth (T), indeterminacy (I), and falsity (F). The authors extend this formalism beyond mathematics, integrating it with philosophical traditions from Latin America and other non-Western epistemologies that embrace ambiguity, complementarity, and productive doubt. The work develops an operational methodology—referred to as “The Third Answer”—which enables users to critically evaluate AI-generated outputs through structured questioning, classification of uncertainty, and decision protocols. By translating abstract logical principles into accessible tools (e.g., decision frameworks, uncertainty mapping, and prompt strategies), the book provides a practical guide for professionals interacting with AI systems across domains. Ultimately, the book argues that improving AI reliability is not merely a matter of increasing data or model size, but requires a paradigm shift toward uncertainty-aware reasoning. It positions neutrosophic logic as a bridge between ancient philosophical insights and modern computational systems, offering a pathway toward more transparent, trustworthy, and epistemically responsible artificial intelligence.

In this paper, for the first time, we extend the Over/Under/Off Set/Logic/Probability used in uncertain theories (such as: fuzzy, neutrosophic and extensions) to the Over/Under/Off Mass that could be used in information fusion. The approach is exemplified in three scenarios: (1) wildfire evacuation and resource allocation with satellite, IoT, and social media; (2) coverage gaps where indeterminacy must be managed; and (3) security monitoring where contradictory or erroneous reports are discounted.

This book provides a comprehensive and systematic survey of modern set-theoretic frameworks developed to model uncertainty, vagueness, indeterminacy, and partial truth in real-world phenomena. It synthesizes a wide spectrum of classical and advanced theories, including fuzzy sets, intuitionistic fuzzy sets, neutrosophic sets, plithogenic sets, and numerous related extensions. The work organizes these concepts across multiple structural and conceptual dimensions-such as interval, granular, probiliistic, and complex extensions-highlighting their mathematical foundations, interrelations, and distinguishing characteristics. By unifying diverse approaches under a coherent analytical perspective, the book clarifies how different uncertainty models A complement or generalize one another. It also explores emerging directions in set theory, including hybrid and dynamic frameworks, offering insights into their applicability in fields such as decisionmaking, control systems, artificial intelligence, and data analysis.

Rough set theory models uncertainty by approximating target concepts via lower and upper sets induced by indiscernibility (or more general granulation) relations in data tables. This perspective captures vagueness caused by limited observational resolution and supports settheoretic reasoning about what can be determined with certainty versus what remains only possible. The present book is written as a model map: rather than developing a single algorithmic pipeline in depth, we provide a systematic survey of the main rough-set paradigms and their extension routes. Concretely, we organize representative variants according to (i) the underlying granulation mechanism (e.g., equivalence-, tolerance-, covering-, neighborhood-, and probabilistic-based approximations) and (ii) the uncertainty semantics attached to data and relations (e.g., crisp, fuzzy, intuitionistic fuzzy, neutrosophic, and plithogenic settings), and we explain how each choice changes the form of approximations and the interpretation of boundary regions. Throughout, small illustrative examples are used to clarify modeling intent and typical use-cases in classification and decision support. Finally, we note an important scope clarification: if the purpose of this book is limited to a model map, then the Abstract/Introduction should not lead readers to expect that feature reduction and rule induction are primary goals. Those topics are central in the rough-set literature, but here they are discussed mainly as motivating applications and as pointers to the broader ecosystem; the main objective is to align the book’s stated aim with its actual focus on surveying and positioning rough-set models and extensions.

Decision-making in real applications is often affected by vagueness, incomplete information, heterogeneous data, and conflicting expert opinions. This survey reviews uncertainty-aware multi-criteria decision-making (MCDM) and organizes the field into a concise, task-oriented taxonomy. We summarize problem-level settings (discrete, group/consensus, dynamic, multi-stage, multi-level, multi agent, and multi-scenario), weight elicitation (subjective and objective schemes under fuzzy/linguistic in puts), and inter-criteria structure and causality modelling. For solution procedures, we contrast compen satory scoring methods, distance-to-reference and compromise approaches, and non-compensatory outrank ing frameworks for ranking or sorting. We also outline rule/evidence-based and sequential decision models that produce interpretable rules or policies. The survey highlights typical inputs, core computational steps, and primary outputs, and provides guidance on choosing methods according to robustness, interpretability, and data availability. It concludes with open directions on explainable uncertainty integration, stability, and scalability in large-scale and dynamic decision environments.

This book presents a systematic survey of the concepts of Z-Numbers, D-Numbers, and ZD-Numbers, which represent advanced mathematical frameworks for modeling uncertainty, imprecision, and incomplete information. Building upon classical uncertainty theories such as fuzLy sets, intuitionistic fuzzy sets, and neutrosophic sets, the work examines how Z-Numbers and D-Numbers extend traditional approaches by incorporating reliability assessments and flexible belief structures. The book reviews a wide range of extensions and variants, including linguistic, probabilistic, multidimensional, hyper, and plithogenic ZNumber models, as well as numerous D-Number generalizations designed to address non-exclusive hypotheses and incomplete knowledge. In addition to surveying existing developments, the book introduces the concept of the ZD-Number, which integrates the perspectives of Z-Numbers and D-Numbers into a unified representation capable of capturing both value-reliability relations and flexible evidence structures. Through definitions, comparisons, and illustrative examples, the book clarifies the relationships among these models and highlights their relevance in areas such as decision-making, information fusion, artificial intelligence, and complex systems analysis. The resulting survey provides both a reference for researchers and a foundation for further theoretical and applied developments in uncertainty modeling.

Many real-world phenomena are naturally modeled by graphs and networks. However, classical graph models are often limited to pairwise interactions and may not adequately capture the richer structures that arise in practice. Higher-order graph formalisms extend this framework by incorporating multiway, hierarchical, temporal, multilayer, recursive, and tensor-based interactions, thereby providing more expressive representations of complex systems. This book presents a comprehensive overview of mathematical notions that can be used to model higher-order networks. It surveys foundational concepts, extensional frameworks, and newly introduced formalisms, with an emphasis on their structural principles, relationships, and modeling roles. The aim is to provide a unified perspective that helps readers compare diverse higher-order network models and identify appropriate tools for theoretical study and practical applications. This book is Edition 2.0. It mainly includes the addition of several concepts, as well as corrections and improvements of typographical errors and explanations. Keywords: Hypergraph, Superhypergraph, Higher-Order Graphs MSC2010 (Mathematics Subject Classification 2010): 05C65 - Hypergraphs, 05C82 - Graph theory with applications

Waves are among the most fundamental phenomena in nature. From sound in air and light in vacuum to seismic tremors and quantum matter waves, their mathematical descriptions are traditionally expressed through continuum field equations. Yet every measurement of a wave ultimately yields discrete outcomes. Infinitesimally Punctured Waves proposes a unifying framework in which this apparent tension between continuity and discreteness is resolved at a structural level. The Infinitesimally Punctured Wave (IPW) approach models a wavefield as the macroscopic limit of an ultra-dense lattice of interacting “punctures”—elementary carriers of physical quantities coupled through local dynamical rules. In the limit of vanishing lattice spacing, the familiar partial differential equations of acoustics, elasticity, electromagnetism, gravity, and quantum mechanics emerge. For finite spacing, the same formalism predicts systematic corrections, controlled dispersion, and experimentally testable deviations. Developed rigorously and applied across multiple physical domains, the IPW framework connects: • acoustic and elastic wave propagation, • electromagnetic and optical phenomena, • linearised gravitational dynamics, • quantum wave evolution and measurement theory, and • nonlinear effects including shocks and solitons. Beyond conceptual unification, the lattice structure provides a transferable computational methodology applicable to multiphysics metamaterials, analogue gravity systems, and high-frequency wave engineering. The book integrates theoretical development with proposed experimental tests, offering concrete pathways to probe finite-scale effects. Written for researchers and advanced students in physics, applied mathematics, and engineering, Infinitesimally Punctured Waves presents a coherent, cross-disciplinary language for wave phenomena and outlines a research programme extending from practical device design to foundational questions in spacetime physics.

infinitesimally punctured geometry formulated within Extended Nonstandard Analysis (ENSA). It introduces the MoBiNad manifold as a hyperreal extension of classical differential geometry, where monads, binads, and infinitesimal punctures generate structured micro-deviations in metric, connection, and curvature operators. Through neutrosophic logic, each geometric and physical quantity acquires a triplet valuation (truth, indeterminacy, falsity), allowing curvature, topology, and field dynamics to encode graded logical structure at the infinitesimal level. Building on this foundation, the book develops MoBiNad differential operators, supersymmetric extensions, Smarandache curves and surfaces, and a neutrosophic Gauss–Bonnet theorem, demonstrating how mixed geometric regimes emerge as standard-part projections of a rigorously defined hyperreal substratum. Gauge–gravitational coupling, curvature oscillations, and topological invariants are reformulated within this punctured continuum, providing a deterministic infinitesimal basis for phenomena traditionally attributed to quantum fluctuation. The result is a coherent bridge between differential geometry, topology, logic, and high-energy physics: classical geometry appears as the macroscopic limit of a structured infinitesimal network, while Smarandache geometries arise naturally from local curvature sign alternations induced by monadic asymmetries. This work lays the analytical groundwork for a neutrosophic Chern–Weil theory and higher-dimensional topological invariants in hyperreal spacetime.

For more than a century, singularities and ultraviolet divergences have stood at the frontiers of modern theoretical physics, marking points where our most successful theories cease to be mathematically well defined. Infinitesimal Punctures proposes a structural shift in perspective: instead of inserting point-like sources into smooth manifolds, matter and physical attributes are interpreted as intrinsic geometric defects—measure-zero punctures—within spacetime itself. In this framework, curvature, charge, and quantum behavior arise not as external additions but as distributionally supported features of geometry. The series develops this idea systematically, moving from foundational geometry, through dynamical physical laws, to a unified S-MultiSpace and S-MultiStructure structural formalism. This volume elevates the framework to a unified structural and meta-geometric level. Drawing on Smarandache multi-space concepts and Neutrosophic logic, it develops a rigorous theory of S-MultiSpaces and S-MultiStructures in which multiple geometric regimes coexist within a single manifold. Neutrosophic differential geometry, hybrid connections, and generalized curvature tensors are constructed, together with modified Gauss–Codazzi relations and Smarandache variational principles. This volume situates infinitesimally punctured geometry within a broader mathematical landscape that includes topology, holonomy, generalized algebras, and spectral reconstruction of geometry. It provides the formal completion of the trilogy, demonstrating how the structural triad underlying punctured manifolds leads to a coherent, logically consistent framework for matter, fields, and spacetime.

For more than a century, singularities and ultraviolet divergences have stood at the frontiers of modern theoretical physics, marking points where our most successful theories cease to be mathematically well defined. Infinitesimal Punctures proposes a structural shift in perspective: instead of inserting point-like sources into smooth manifolds, matter and physical attributes are interpreted as intrinsic geometric defects—measure-zero punctures—within spacetime itself. In this framework, curvature, charge, and quantum behavior arise not as external additions but as distributionally supported features of geometry. The series develops this idea systematically, moving from foundational geometry, through dynamical physical laws, to a unified S-MultiSpace and S-MultiStructure structural formalism. Building on the geometric framework of Infinitesimally Punctured Geometry, this volume develops the dynamical laws governing infinitesimally punctured spacetime. A hybrid variational principle is introduced in which smooth curvature, defect-supported curvature, and an indeterminate transition sector enter on equal footing. Variation of this action yields a master field equation that generalizes the Einstein equations and naturally incorporates defect density as a geometric source rather than an externally prescribed stress-energy tensor. Within this setting, an approach termed Infinitesimally Punctured Quantum Physics is proposed, in which a quantum object is visualized as an aggregation of infinitely many infinitesimally spaced constituents. When these constituents are densely packed, the ensemble manifests as a continuous wave, surface, space, or manifold; when a measurement effectively isolates a single constituent, particle-like behavior emerges. This picture is linked to Neutrosophic Quantum Theory, which supplies a logical framework for handling indeterminacy in the transition between continuous and discrete regimes. Applications include regularised black hole geometries, punctured wave and Schrödinger equations, modified cosmological evolution, and geometric interpretations of dark matter and dark energy. This volume centralizes the predictive content of the theory and develops its phenomenological and observational consequences.

For more than a century, singularities and ultraviolet divergences have stood at the frontiers of modern theoretical physics, marking points where our most successful theories cease to be mathematically well defined. Infinitesimal Punctures proposes a structural shift in perspective: instead of inserting point-like sources into smooth manifolds, matter and physical attributes are interpreted as intrinsic geometric defects—measure-zero punctures—within spacetime itself. In this framework, curvature, charge, and quantum behavior arise not as external additions but as distributionally supported features of geometry. The series develops this idea systematically, moving from foundational geometry, through dynamical physical laws, to a unified S-MultiSpace and S-MultiStructure structural formalism. This volume establishes the geometric and analytic foundations of infinitesimally punctured manifolds. It introduces the weak–strong decomposition of geometry, in which smooth differential structure coexists with defect-supported distributional curvature on measure-zero sets. Classical singularities are reinterpreted as punctures carrying finite, integrable curvature, replacing divergent invariants with well-defined distributional objects. The book develops codimension-based classification of defects, holonomy effects, regularisation via smooth metric families, and the structural Neutrosophic triad as a geometric—not yet dynamical—decomposition. A substantial portion of the volume is devoted to operator theory on punctured manifolds, including self-adjoint extensions of Laplace-type operators, spectral stability, defect-induced bound states, and scattering without external potentials. Explicit low-dimensional toy models—punctured circles, conical planes, and point defects in three dimensions—demonstrate how geometry alone generates observable analytic consequences. This book contains no field equations and no cosmological models; its purpose is to provide a rigorous, self-contained mathematical groundwork upon which the subsequent volumes build.

Soft set theory provides a direct framework for parameterized decision modeling by assigning to each attribute (parameter) a subset of a given universe, thereby representing uncertainty in a structured way [1, 2]. Over the past decades, the theory has expanded into numerous variants— including hypersoft sets, superhypersoft sets, TreeSoft sets, bipolar soft sets, and dynamic soft sets—and has been connected to diverse areas such as topology and matroid theory. In this book, we present a survey-style overview of soft sets and their major extensions, highlighting core definitions, representative constructions, and key directions of current development.

This volume presents some original research on SuperHyperStructures and SuperHyperTopologies, new branches of mathematics with applications in applied sciences. These frameworks extend classical notions of sets, graphs and topologies by incorporating uncertainty, indeterminacy and multivalued membership, rooted in neutrosophic and Plithogenic logic. They provide non-rigorous methods for the analysis of complex systems in which ambiguity and dynamic interactions are fundamental. The book is largely deals with 3 main subject-matters. The first one introduces mathematical foundations, including SuperHyperTopologies, Neutrosophic and Plithogenic extensions, fuzzy and soft set frameworks, and links with Łukasiewicz algebras. The second one develops structural perspectives through SuperHyperGraphs, weighted hyperedges, fuzzy neural networks, and neutrosophic automata. The third subject-matter illustrates interdisciplinary applications in medicine, finance, agriculture, tourism, economics, and data science. An important feature of the volume is its interdisciplinary orientation. Mathematical theories are linked to practical problems, showing how SuperHyper concepts can support decision-making, optimize resources and model uncertainty in different fields. By combining fuzzy, neutrosophic and plithogenic logics within hyperstructural frameworks, the book highlights innovative approaches to indeterminate and multilayered phenomena. The subject-matters and content of this volume is aimed not only at researchers but also graduate students and professionals in mathematics, computer science and related disciplines. It offers a comprehensive reference and several practical research avenues, paving the way for further interdisciplinary research and applications. In this volume, there are 25 research studies with different approaches, results and findings.

Collected Papers, Vol. XVII – A Multi-Disciplinary Approach to Uncertainty, Indeterminacy, and Complex Systems is a substantial and wide-ranging volume, bringing together 74 articles across nearly 1,000 pages. The contributions, originally published in a variety of international scientific journals, reflect the breadth and maturity of contemporary research in neutrosophy and its related domains. The volume explores a rich spectrum of interdisciplinary fields, including logic, philosophy, physics, mathematics, statistics, information fusion, artificial intelligence, decision theory, complex systems, and robotics, offering both foundational developments and applied methodologies for modeling uncertainty, indeterminacy, and contradiction. All papers are authored or co-authored by Florentin Smarandache, either individually or in collaboration with 69 distinguished co-authors from 18 countries (Ahmed Abdelhafeez, Mohamed Abdel Basset, Hamiden Abd El-Wahed Khalifa, Ijaz Ahmad, Muhammad Ahsan, Alhanouf Alburaikana, Ahmed M. Ali, Anum Ali, Mubashir Ali, Wajid Ali, Sulaiman Al Amro, Rafif Alhabib, Saleh I. Alzahrani, Farrukh Arslan, Muhammad Arshad, Büşra Aydoğan, Robert N. Boyd, Victor Christianto, Ajoy Kanti Das, Rakhal Das, Suman Das, Rama Debbarma, Srila Dey, Dinh Van Dzung, Alaa Elmor, Takaaki Fujita, Daniela Gifu, Mohammad Hamidi, Hoang Anh Tuan, A. Kalavathi, Khuram Ali Khan, S. Krishnaprakash, Duraisamy Kumar, Luong Thi Hong Lan, Le Nhu Dieu Huon, Maikel Yelandi Leyva-Vázquez, Priyanka Majumder, Ahmed A. Metwaly, Mona Mohamed, Noreen Mushtaq, Ion Nălbitoru, Nguyen Long Giang, Nguyen Thi Hien, Nguyen Thi Lan Nhi, Nguyen Thien Luong, Nguyen Tho Thong, Nguyen Thu Huong, Murat Olgun, Gabrijela Popovic, Michael Angelo B. Promenti, Afshan Qayyum, Atiqe Ur Rahman, Shazia Rana, Muhammad Saeed, Alaa Salem, A. Saranya, Alexandra Şandru, Ovidiu Ilie Şandru, Tanzeela Shaheen, Dragisa Stanujkic, Maja Stanujkic, Mohadeseh Taghinezhad, John Frederick D. Tapia, Mehmet Ünver, Vo Si Nam, Michael Voskoglou, Muhammad Waqas, Muhammad Yasir, Badria Almaz Ali Yousif), underscoring the global reach and collaborative nature of neutrosophic research, and revealing a coherent yet diverse intellectual landscape, ranging from theoretical frameworks—such as neutrosophic logic, hypersoft sets, superhyperstructures, and revolutionary topologies—to practical applications in healthcare analytics, artificial intelligence, sustainability, engineering, and decision-making under uncertainty. Together, the works collected in this seventeenth volume provide both a comprehensive reference and a forward-looking perspective on the evolving role of neutrosophic and multi-valued approaches in addressing complex real-world problems.

This sixteenth volume of Collected Papers is an extensive work, comprising 78 articles that span almost 1000 pages. The papers, originally published in various scientific journals, cover the broad and interdisciplinary fields of neutrosophics and other areas of study, including logic, philosophy, physics, mathematics, statistics, information fusion, and robotics. The volume features articles authored by Florentin Smarandache, either alone or in collaboration with 81 co-authors (from 21 different countries): Shumaila Abbas, Mohammed Abdel-Sattar, M. Modather M. Abdoug, Usama Afzal, Daud Ahmad, Abdulrahman AlAita, Shahbaz Ali, Fahad Alsharari, Suriana Alias, Saima Anis, Muhammad Aslam, Hamdi Ayed, M.B. Bera, Noel Batista-Hernández, Robert N. Boyd, Said Broumi, Claudia Camacho-Zuñiga, T. Daniel Chandra, Ebenezer Chifu, Victor Christianto, Mihaela Colhon, Shrouk El-Amir, Ibrahim El-Henawy, Takaaki Fujita, Nguyen Long Giang, Ana González-Marcos, Phung The Huan, Sadia Iqbal, Azhar Ali Janjua, Maissam Jdid, Madad Khan, Waris Khan, Muhammad Shahid Khan, Anamika Kumari, Luong Thi Hong Lan, M. Lathamaheswari, B.S. Mahapatra, G.S. Mahapatra, Muhammad Khalid Mahmood, Nivetha Martin, Pierre Millette, Mona Mohamed, M.K. Mondal, Bahnishikha Roy Muhuri, Norzieha Mustapha, Fermín Navaridas-Nalda, Tran Thi Ngan, Antonios Paraskevas, P. Prabakaran, Madiha Qayyum, Shazia Rana, Alina Reșceanu, Jesus Estupiñan Ricardo, Andreas Ries, Yaser Saber, Muhammad Saeed, Taoufik Saidani, P. Sathya, Noorazliyana Shafii, Muhammad Ahmed Shehzad, Rehan Ahmad Khan Sherwani, Rajesh Singh, Le Hoang Son, S. Sudha, Vu Duc Thai, Hugo Terashima-Marin, Nguyen Tho Thong, Pham Huy Thong, Monica Tilea, Tran Manh Tuan, Yunita Umniyati, Maikel Leyva Vázquez, Michael Gr. Voskoglou, Mohammad Kaif Wajid, Mohammad Saif Wajid, Mohd Anas Wajid, Roliza Md Yasin, Shouzhen Zeng, Muhammad Zeeshan, Alia Nur Izzah Zulkifli.

This fifteenth volume of Collected Papers is an extensive work, comprising 77 articles that span almost 1000 pages. The papers, originally published in various scientific journals, cover the broad and interdisciplinary fields of neutrosophics and other areas of study, including mathematics, fuzzy sets, intuitionistic fuzzy sets, picture fuzzy sets, information fusion, robotics, statistics, and extenics. The volume features articles authored by Florentin Smarandache, either alone or in collaboration with 123 co-authors. A complete list of these co-authors is provided below, arranged alphabetically: Shumaila Abbas, Raja Abdullah Abdulfatah, Sabah S. Abdulrahman, Mohammad Abobala, Mohamed Abosalih, Sunday Adesina Adebisi, Lorenzo Affè, Abuobida Ahal, Ashik Ahirwar, Abuobida Alfahal, Yaser Ahmad Alhasan, Hanan Alohali, B. Ananda Priya, S. Angammal, N. Angel, T. Ashika, Faiza Asif, Muhammad Aslam, Aws A. Azzidan, Abdelaziz Babiker, Esam Bader, Assia Bakali, Ranulfo Paiva Barbosa, Noel Batista-Hernández, Sania Batool, Romualdas Bausys, Mahmut Can Bozyıgt, Said Broumi, Erick González Caballero, T. Chalapathi, Victor Christianto, Bing Cui, Tugrul Daim, Bijan Davvaz, Muhammet Deveci, Meghana Dirisala, Seyyed Ahmad Edalatpanah, Ahmed El-Massry, Tawfik Elmasry, A. Elrawy, Takaaki Fujita, N. Ramila Gandhi, Harish Garg, Mona Gharib, P. Gnanachandra, İlgin Gökasar, Hasan Gökbaş, Hannah Grace, S. Karunya Helen Gunaseeli, Mohammad Hamidi, Iftikhar Ul Haq, D. Harish Babu, Masooma Raza Hashmi, Farnaz Sheikh Hassani, Jesús Rafael Hechavarría-Hernández, K. Hemabala, A. Ibrahim, Sadia Iqbal, Mehtap Isik, Saeid Jafari, Maissam Jdid, Ilanthenral Kandasamy, Vasantha Kandasamy, Muthusamy Karthika, Huda E. Khalid, Neha Andaleeb Khalid, Rehan Ahmad Khan Sherwani, B. Srinivasa Kumar, K. Kumaraswamy Naidu, Anamika Kumari, Mukesh Kushwaha, Yingcang Ma, Madelaine Al Tahan, Nivetha Martin, Mohamed Talea, Mona Mohamed, Swaminathan Mohanaselvi, Alaa A. Mohammed, D. Nagarajan, Muhammad Ali Najjar, Giorgio Nordo, Murat Olgun, Dragan Pamucar, P. Pandiammal, Antonios Paraskevas, Mani Parimala, Aurimas Petrovas, S. Rajeswari, Muhammad Riaz, Rafael Rojas-Gualdron, Yaser Saber, Muhammad Saeed, Rajesh Kumar Saini, A. A. Salama, Muhammad Saleem, S. Sandhiya, Tanzeela Shaheen, Riya Eliza Shaju, Rehan Ahmad Khan Sherwani, Rajesh Singh, Ali Sorourkhah, B. Srinivasa Kumar, C. Sugapriya, Ayat A. Temraz, Hugo Terashima-Marin, Mahima Thakur, S. S. Thakur, A. Theeba, Shobh Nath Tiwari, Hamza Ghazanfar Toor, Selçuk Topal, Mehmet Ünver, Maikel Leyva Vázquez, Satya Bhushan Verma, Mohammad Kaif Wajid, Mohammad Saif Wajid, Mohd Anas Wajid, Tomasz Witczak, Subhash Kumar Yadav, Aws A. Zaidan, Kazimieras Edmundas Zavadskas, Dan Zhang, Hengdong Zhu.

The twentieth-century edifice of physics rests on a handful of foundational pillars: Newtonian mechanics, Maxwellian electrodynamics, quantum theory, and Einsteinian relativity. Within this framework, the vast majority of research proceeds by refining, extending, or experimentally testing the consequences of these established laws. Over the past three decades, however, a persistent current of inquiry has sought to probe the limits of this canonical paradigm, asking whether the logical and ontological foundations of the discipline might admit richer, more flexible structures. Central to this current is Neutrosophy, a meta-theory that offers a systematic way to treat truth (T), falsity (F), and indeterminacy (I) as mutually independent components of any physical proposition. This volume brings together, for the first time, a curated collection of abstracts submitted by the author (alone or in collaboration) to the American Physical Society (APS) meetings between 2008 and 2018. These entries, originally intended as invitations to oral and poster presentations, collectively map an ambitious agenda: to reinterpret familiar phenomena through the lens of Neutrosophic Physics. By gathering these dispersed records, we provide scholars and historians of science with a panoramic view of a research program that challenges the very "constancy" of universal constants and the locality of physical laws. In addition to the formal APS records, this collection includes a chapter of unsubmitted abstracts and exploratory drafts (2018–present). Unlike the preceding chapters, these entries were selected from the author’s private research archives to illustrate the continuing evolution of his theories. They explore the frontiers of Unmatter—matter-antimatter states motivated by neutrosophic neutrality—and the Neutrosophic Expansion Constant, which addresses emerging tensions in modern cosmology.

This book explores the theoretical and philosophical implications of transcending the speed of light limit, building upon Florentin Smarandache's "no speed barrier" hypothesis. This collection of works develops the hypothesis that no physical entity is fundamentally constrained by a speed barrier, suggesting a framework for extending classical and relativistic physics into the realms of Superluminal Physics and Instantaneous Physics. The book’s core technical argument centers on the phenomenon of quantum tunneling and the Hartman effect, where the tunneling time appears independent of barrier width, leading to seemingly superluminal results. The authors propose a novel interpretation of the Hartman effect, suggesting that it is a manifestation of the multivaluedness of solutions to the Schrödinger equation, implying a quantum entity can exist in multiple locations simultaneously and thus appear to tunnel instantaneously. To provide a plausible mechanism for this superluminal effect, the book considers soliton tunnelling, specifically the Falaco soliton, which is presented as a known exact solution to the three-dimensional Navier-Stokes equations and is proposed as a realistic mechanism for quantum tunneling. Ultimately, the research seeks to find a general theory, such as the S-Multispace Theory, that unites physics at subluminal, relativistic, superluminal, and instantaneous speeds. This theoretical path is explored as an alternative for deep space and interstellar travel, moving beyond conventional concepts like the Alcubierre warp drive or wormholes in General Relativity.

Education is the foundation of any progressive society and understanding the challenges within educational systems is crucial for their improvement. However, educational problems are often characterised by uncertainty, indeterminacy and incompleteness—factors that traditional methods sometimes struggle to address adequately. This book introduces neutrosophic theory as a powerful framework for investigating educational challenges. Neutrosophy, which deals with neutralities and indeterminacies, offers a unique perspective that goes beyond classical logic and fuzzy logic. It provides researchers and educators with tools to handle the ambiguities inherent in educational settings. Our motivation for writing this book stems from the recognition that educational research often encounters situations where data is incomplete, opinions are conflicting, or outcomes are uncertain. Traditional binary or fuzzy approaches may not fully capture these complexities. Neutrosophic methods, with their ability to represent truth, indeterminacy and falsity simultaneously, offer a more comprehensive approach. This book is designed for educational researchers, postgraduate students, policymakers and practitioners who wish to explore innovative methodologies for addressing educational problems. We have made conscious efforts to present the material in simple Indian English, making it accessible to a wide audience while maintaining academic rigour. The book is organised into ten chapters, beginning with an introduction to educational challenges and progressing through the theoretical foundations, mathematical frameworks and practical applications of neutrosophic approaches. We include numerous examples from the Indian educational context to illustrate concepts and demonstrate applicability.

Hypergraphs generalize this framework by allowing hyperedges that connect more than two vertices. Superhypergraphs further enrich the model through iterated powerset constructions, capturing hierarchical and self-referential structures among hyperedges. An (m,n)-SuperHyperGraph is a mathematical structure in which each vertex corresponds to an (m,n)-superhyperfunction defined on a base set, while the hyperedges group such functions together to represent higher-order relationships and contextual connections. Systematic research on SuperHyperGraphs is still relatively limited compared with the extensive literature on graphs and hypergraphs. To help bridge this gap, this book presents a survey of fundamental and advanced concepts related to SuperHy-perGraphs. Our aim is twofold: (i) to increase the visibility and accessibility of SuperHyperGraph theory and thereby stimulate further research, and (ii) to deepen the mathematical understanding of their structures among researchers and practitioners who work with graph- and hypergraph-based models.

En un mundo moldeado por contradicciones, incertidumbres y paradigmas en evolución, la Filosofía Neutrosófica emerge como un marco innovador que trasciende el pensamiento binario. Arraigada en el estudio de las neutralidades, las contradicciones y su interacción dinámica, esta filosofía redefine la lógica clásica, la epistemología y la ontología, ofreciendo un enfoque integral para comprender la realidad. A través de la lente de la Neutrosofía, este libro recopila artículos que exploran conceptos fundamentales como el continuo de neutralidades, el equilibrio de ideas y la tesis-antítesis-neutrotesis, desafiando las estructuras dialécticas tradicionales. Expande las fronteras de la filosofía al integrar la matematización, las lógicas multivaluadas y los enfoques transdisciplinarios al conocimiento. Desde la mecánica cuántica y la inteligencia artificial hasta la ética, la sociología y la literatura, las aplicaciones de la Neutrosofía son vastas y transformadoras. Ya sea reinterpretando paradojas, remodelando fundamentos filosóficos o explorando la naturaleza infinita de la verdad, esta obra allana el camino hacia una nueva forma de pensar: una que abraza la ambigüedad, la indeterminación y la coexistencia de opuestos. Al tender puentes entre disciplinas e introducir principios innovadores como la Lógica Neutrosófica, la Evolución Social Neutrosófica y el Materialismo Neutrosófico, este libro sirve como una base teórica y una guía práctica para académicos, investigadores y pensadores que buscan una comprensión más profunda de la complejidad en el mundo moderno. La Filosofía Neutrosófica no es solo una exploración del conocimiento, es una invitación a repensar la esencia misma de la verdad, la realidad y la comprensión humana.

Dans un monde façonné par les contradictions, les incertitudes et des paradigmes en constante mutation, la philosophie neutrosophique s'impose comme un cadre révolutionnaire qui transcende la pensée binaire. Enracinée dans l'étude des neutralités, des contradictions et de leur interaction dynamique, cette philosophie redéfinit la logique classique, l'épistémologie et l'ontologie, offrant une approche globale pour la compréhension de la réalité. Ce volume rassemble des articles explorant des concepts fondamentaux tels que le continuum des neutralités, l'équilibre des idées et la triade thèse-antithèse-neutrothèse, remettant en question les structures dialectiques traditionnelles. Les frontières de la philosophie sont élargies par l'intégration de la mathématisation, des logiques multivaleurs et des approches transdisciplinaires de la connaissance. De la mécanique quantique et l'intelligence artificielle jusqu'à l'éthique, la sociologie et la littérature, les applications de la neutrosophie sont vastes et transformatrices. Qu'il s'agisse de réinterpréter des paradoxes, de reconfigurer les fondements philosophiques ou d'explorer la nature infinie de la vérité, cet ouvrage ouvre la voie à un nouveau mode de pensée — un mode qui intègre l'ambiguïté, l'indétermination et la coexistence des contraires. En reliant les disciplines et en introduisant des principes innovants tels que la logique neutrosophique, l'évolution sociale neutrosophique et le matérialisme neutrosophique, ce livre sert à la fois de fondement théorique et de guide pratique pour les chercheurs, les penseurs et les spécialistes désireux d'approfondir leur compréhension de la complexité du monde contemporain. La philosophie neutrosophique n'est pas seulement une exploration du savoir — c'est une invitation à repenser l'essence même de la vérité, de la réalité et de la compréhension humaine.

Într-o lume modelată de contradicții, incertitudini și paradigme în continuă schimbare, filosofia neutrosofică se conturează ca un cadru revoluționar care transcende gândirea binară. Înrădăcinată în studiul neutralităților, al contradicțiilor și al interacțiunii lor dinamice, această filosofie redefinește logica clasică, epistemologia, ontologia, oferind o abordare cuprinzătoare a înțelegerii realității. Acest volum reunește articole care explorează concepte fundamentale precum continuumul neutralităților, echilibrul ideilor și triada teză–antiteză–neutroteză, provocând structurile dialectice tradiționale. Se extind granițele filosofiei prin integrarea matematizării, a logicilor multi-valorice și a abordărilor transdisciplinare asupra cunoașterii. De la mecanica cuantică și inteligența artificială, până la etică, sociologie și literatură, aplicațiile neutrosofiei sunt vaste și transformatoare. Fie că reinterpretăm paradoxuri, reconfigurăm fundamentele filosofice sau explorăm natura infinită a adevărului, această lucrare deschide drumul către un mod nou de a gândi—unul care integrează ambiguitatea, indeterminarea și coexistența contrariilor. Prin conectarea disciplinelor și introducerea unor principii inovatoare precum logica neutrosofică, evoluția socială neutrosofică și materialismul neutrosofic, această carte funcționează atât ca fundament teoretic, cât și ca ghid practic pentru cercetători, gânditori și specialiști interesați să aprofundeze înțelegerea complexității lumii contemporane. Filosofia neutrosofică nu este doar o explorare a cunoașterii—este o invitație de a regândi însăși esența adevărului, a realității și a înțelegerii umane.

Las plataformas tradicionales de mapeo de opinión emplean análisis de componentes principales (PCA) y agrupamiento para visualizar paisajes de opinión pública. Sin embargo, estos enfoques se basan en marcos lógicos binarios o difusos que pueden no capturar adecuadamente la ambigüedad inherente y la naturaleza multidimensional de las creencias humanas. Este artículo presenta una aplicación novedosa de la lógica neutrosófica al análisis de percepciones sobre el cambio climático, demostrando ventajas significativas sobre los métodos tradicionales de análisis de consenso. Utilizando una encuesta de 84 residentes en Guayaquil, Ecuador, empleamos una escala Likert neutrosófica que captura tres dimensiones independientes: verdad (T), indeterminación (I) y falsedad (F) para cada elemento de la encuesta. Nuestro análisis revela dos grupos de respondientes distintos: un grupo "Altamente Comprometido pero Conflictivo" (34.5% de los respondientes) caracterizado por puntuaciones elevadas en las tres dimensiones, y un grupo "Moderadamente Aceptante" (65.5%) con perfiles dominados por la verdad. Los hallazgos clave demuestran que el análisis neutrosófico descubre complejidad oculta en datos de opinión que los enfoques binarios o difusos obscurecerían, permitiendo estrategias de comunicación más dirigidas y efectivas.

Uncertainty permeates most real-world contexts, motivating mathematical frameworks that can faithfully represent vagueness, inconsistency, and incomplete information. Classical approaches include fuzzy sets and intuitionistic fuzzy sets. Extending these ideas, the neutrosophic framework introduces neutrosophic sets in which each element x is characterized by a triplet of independent degrees (T (x), I (x), F (x)) ∈ [0, 1]3 , representing, respectively, truth, indeterminacy, and falsity, typically subject to T (x) + I (x) + F (x) ≤ 3. This book concentrates on a selection of concepts developed and discussed in the Nidus idearum series, with particular emphasis on Neutrosophy, Plithogenic Sets, Physics, and related scientific domains. We focus on ideas that, despite their conceptual richness and potential applicability, have so far received relatively limited systematic treatment. Our aim is to present these notions in a coherent and accessible manner, in order to support further theoretical development and to encourage new applications in Neutrosophy, Plithogenic Set theory, Physics, and allied fields.