Florentin Smarandache

Real-world phenomena frequently involve vagueness, partial truth, and incomplete information. To capture such uncertainty in a mathematically rigorous manner, numerous generalized set-theoretic frameworks have been introduced, including Fuzzy Sets [1], Intuitionistic Fuzzy Sets [2], Neutrosophic Sets [3, 4], Vague Sets [5], Hesitant Fuzzy Sets [6], Picture Fuzzy Sets [7], Quadripartitioned Neutro-sophic Sets [8], PentaPartitioned Neutrosophic Sets [9], Plithogenic Sets [10], HyperFuzzy Sets [11], and HyperNeutrosophic Sets [12]. Within these frameworks, a vast number of concepts have been proposed and studied, especially in the contexts of Fuzzy, Intuitionistic Fuzzy, Neutrosophic, and Plithogenic Sets. This extensive body of work highlights both the importance of these theories and the breadth of their application domains. Consequently, many ideas, constructions, and structural patterns recur across these four families of uncertainty-oriented models. In this book, we present a comprehensive, large-scale survey of Fuzzy, Intuitionistic Fuzzy, Neutro-sophic, and Plithogenic Sets. Our aim is to offer r eaders a s ystematic overview of existing develop-ments and, through this unified exposition, to foster new insights, further conceptual extensions, and additional applications across a wide range of disciplines.

A Neutrosophic Set assigns to each element independent degrees of truth, indeterminacy, and falsity, thereby extending classical uncertainty models. It is widely recognized as a generalization of both Fuzzy Sets and Intuitionistic Fuzzy Sets. Neutrosophic and fuzzy logics have been employed across sociology, psychology, the social sciences, biology, chemistry, physics, and philosophy. This paper revisits and systematizes these applications of Neutrosophic Logic, presenting rigorous mathematical definitions alongside concrete, domain–specific ex am ples. Our aim is tw ofold: to promote broader understanding and dissemination of neutrosophic methods, and to provide a clear foundation that enables future theoretical development and practical deployment. By organizing existing concepts into a coherent framework and illustrating their use through reproducible constructions, we seek to broaden the scope of applications and to stimulate further research across disciplines.

Este artículo propone un marco de pluralismo lógico aplicado al análisis causal en inteligencia artificial (IA) y ciencias sociales. Basado en la tesis pluralista de que no existe un único concepto monolítico de causalidad, sino una familia de conceptos relacionados, confrontamos la premisa humeana de que “no observamos la causalidad” con el contraargumento de Anscombe de que, de hecho, percibimos acciones causales como empujar, golpear y cortar. Sobre esta base, presentamos un estudio ilustrativo que compara el Análisis Comparativo Cualitativo de conjuntos nítidos (csQCA), el de conjuntos difusos (fsQCA) y el neutrosófico (nQCA). De esta comparación, derivamos implicaciones metodológicas y sustantivas. Metodológicamente, encontramos que: (i) la dicotomización estricta (csQCA) puede subestimar las relaciones causales; (ii) la pertenencia gradual (fsQCA) captura más eficazmente la fuerza y relevancia empírica; y (iii) la descomposición neutrosófica (nQCA) considera explícitamente la verdad, la indeterminación y la falsedad, ofreciendo así un diagnóstico pluralista de la relación causal. Enriquecemos aún más este análisis incorporando una visión pluralista de la causalidad, que abarca la producción mecánica, la diferencia contrafactual, las capacidades/disposiciones y los mecanismos.

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 analyzes cause-and-effect relationships among critical factors that influence businesses’ adaptation to AI, smart cities, and Society 5.0. The results offer a holistic decision-support framework to guide policymakers, businesses, and urban planners toward inclusive, sustainable, and technologically integrated societies.

This study addresses the challenges of uncertainty, vagueness, and imprecision in real-world decision-making, particularly for small-scale farmers selecting short-term crops. The central problem is the lack of a systematic framework to evaluate conflicting criteria such as investment, yield, market demand, and soil requirements. To solve this, a Multi-Criteria Decision-Making (MCDM) framework is introduced, which integrates Cubic Spherical Neutrosophic Sets (CSNS) and Neutrosophic Hyper Soft Sets (NHSS). The research also proposes a novel cubic spherical neutrosophic Bonferroni mean operator for aggregating neutrosophic sets. The effectiveness of this approach is demonstrated through a case study in Tamil Nadu, focusing on selecting the most suitable crop for different climatic zones. A sensitivity analysis confirms the model's robustness and reliability. The tool aims to improve resource utilization, reduce risks, and promote agricultural sustainability.

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 are necessary, though not sufficient, for learning improvements, but generate significant uncertainty. The study concludes that the neutrosophic-fsQCA framework is a viable technique for synthesizing ambiguous findings and provides empirical evidence that digital equity and high-quality design are crucial for the successful integration of AI in education.

A multitude of uncertainty models, such as fuzzy, neutrosophic, and plithogenic sets, have emerged in the domain of fuzzy sets and their extensions. This diversity, while reflecting an active research community, can lead to conceptual overlap. To address this, the authors propose a unified framework for the systematic management of these "Uncertain Sets" by defining the Uncertain Model, the U-Structure, and the U-Off Structure. The paper revisits and extends the definitions of HyperUncertain, SuperUncertain, SuperHyperUncertain, Tree Uncertain, and Forest Uncertain structures, along with their "Off" variants. To encompass systems beyond Uncertain Sets, the concepts of Functorial Set and Functorial Structure are also introduced. This comprehensive approach aims to establish a robust foundation for organizing and applying uncertainty models across various mathematical and applied domains.

"Neutrosophic Computing and Machine Learning" (NCML) es una revista académica dedicada a la publicación de estudios avanzados en neutrosofía, conjuntos neutrosóficos, lógica neutrosófica, probabilidad neutrosófica, estadística neutrosófica y enfoques neutrosóficos para el aprendizaje automático y sus aplicaciones en diversos campos. La revista da la bienvenida a trabajos profesionales en inglés o español que incluyan un breve resumen de un problema y los resultados obtenidos. Este número (36) de "Neutrosophic Computing and Machine Learning" (NCML) presenta una colección focalizada de artículos que exploran la aplicación práctica de la teoría neutrosófica en varios dominios. Los trabajos abordan desafíos clave en áreas como el diagnóstico médico, el análisis de riesgos y el análisis de redes sociales, demostrando cómo los enfoques neutrosóficos pueden manejar eficazmente la incertidumbre y la indeterminación. Un tema central es el desarrollo de modelos neutrosóficos novedosos para resolver problemas del mundo real. El número presenta investigaciones sobre mapas cognitivos neutrosóficos para la evaluación multicriterio, un enfoque integrado neutrosófico-TOPSIS para la selección de personal y un modelo neutrosófico único para la detección del cáncer de mama. Además, los artículos profundizan en el uso de conjuntos neutrosóficos refinados para analizar el sentimiento en las redes sociales y su aplicación en la clasificación de rasgos de personalidad. Esta colección de investigaciones demuestra la utilidad en expansión de la computación neutrosófica en la creación de soluciones más robustas y matizadas para sistemas complejos.

"Neutrosophic Computing and Machine Learning" (NCML) es una revista académica dedicada a la publicación de estudios avanzados en neutrosofía, conjuntos neutrosóficos, lógica neutrosófica, probabilidad neutrosófica, estadística neutrosófica y enfoques neutrosóficos para el aprendizaje automático y sus aplicaciones en diversos campos. La revista da la bienvenida a trabajos profesionales en inglés o español que incluyan un breve resumen de un problema y los resultados obtenidos. Este número (37) de "Neutrosophic Computing and Machine Learning" (NCML) presenta una colección diversa de investigaciones que demuestran la extensa aplicación de la teoría neutrosófica para abordar complejos desafíos sociales, legales y de salud, con un enfoque particular en temas de Ecuador. Los artículos utilizan una variedad de métodos neutrosóficos, incluyendo evaluación multicriterio, mapas cognitivos y procesos analíticos, para analizar problemas del mundo real. Las contribuciones clave incluyen un análisis legal y social, con varios trabajos que aplican métodos neutrosóficos para evaluar los desafíos legales relacionados con la telemedicina, evaluar el impacto de las herramientas digitales en el derecho notarial y analizar los factores que influyen en los homicidios utilizando datos abiertos. El número también examina problemas como la violencia de género y la migración, los derechos de las víctimas menores de violencia sexual y los desafíos legales del "porno de venganza". En cuanto a las aplicaciones médicas y de salud, la investigación profundiza en los campos de la medicina y la odontología, con artículos sobre la evaluación de la eficacia de las estrategias para prevenir la hepatitis B en mujeres embarazadas, el análisis de los factores de riesgo para la diabetes tipo II y la optimización del tratamiento para el Alzheimer. Otros estudios se centran en la salud animal, como la evaluación del impacto de la brucelosis y la mastitis en el ganado y la evaluación del raquitismo canino. El número también incluye estudios ambientales y económicos, con aplicaciones de la lógica neutrosófica para evaluar el impacto de los plásticos oceánicos y analizar la contaminación del agua. Adicionalmente, los trabajos evalúan temas económicos como la rentabilidad hotelera y el impacto del impuesto a la moneda en el desarrollo económico de Ecuador.

"Neutrosophic Computing and Machine Learning" (NCML) es una revista académica dedicada a la publicación de estudios avanzados en neutrosofía, conjuntos neutrosóficos, lógica neutrosófica, probabilidad neutrosófica, estadística neutrosófica y enfoques neutrosóficos para el aprendizaje automático y sus aplicaciones en diversos campos. La revista da la bienvenida a trabajos profesionales en inglés o español que incluyan un breve resumen de un problema y los resultados obtenidos. Este número (38) de "Neutrosophic Computing and Machine Learning" (NCML) es una edición especial dedicada a explorar la "Neutrosofía aplicada a los dilemas bioéticos: una mirada transdisciplinaria desde la medicina, el derecho y la educación". Los artículos del número utilizan una variedad de métodos neutrosóficos para abordar una amplia gama de problemas complejos, principalmente en el contexto de la sociedad ecuatoriana. El número se centra en gran medida en los desafíos legales y sociales, presentando análisis neutrosóficos de temas críticos como los derechos de la familia y personales, la eficacia legal de la adopción homoparental, la revictimización de las víctimas de violencia sexual y la protección de los derechos de los niños durante los procedimientos de divorcio y cuando nacen en penitenciarías. También se abordan temas relacionados con el sistema de justicia, como la eficacia de la justicia restaurativa, la despenalización del aborto, el impacto de los medios en los "juicios paralelos" y la exclusión de las mujeres indígenas del sistema de justicia. En cuanto a los asuntos civiles y públicos, se analizan los derechos de los migrantes, la discriminación contra los Testigos de Jehová, la seguridad jurídica del comercio digital y las cuestiones procesales relacionadas con los casos de pensión alimenticia y la adjudicación de bienes abandonados. Además de los asuntos legales, la investigación se extiende a otros campos, demostrando la versatilidad de los enfoques neutrosóficos. Los artículos evalúan la reforma del sistema penitenciario, analizan las lagunas legales en la gestión de áreas de conservación y evalúan el derecho a la educación en Ecuador. La investigación en salud y bienestar aplica métodos neutrosóficos para evaluar la eficacia de los adhesivos dentales y el impacto de la leucemia viral felina. En los campos de negocios y economía, los trabajos exploran estrategias comerciales para cafeterías especializadas, analizan la viabilidad financiera para pequeñas empresas y proponen un modelo de innovación gastronómica para la cocina vegetariana. El número también incluye un análisis de la aplicación de la inteligencia artificial en la lucha contra el terrorismo y un estudio sobre el uso de la lógica neutrosófica para evaluar los marcos legales para el ciberacoso.

"Neutrosophic Computing and Machine Learning" (NCML) es una revista académica dedicada a la publicación de estudios avanzados en neutrosofía, conjuntos neutrosóficos, lógica neutrosófica, probabilidad neutrosófica, estadística neutrosófica y enfoques neutrosóficos para el aprendizaje automático y sus aplicaciones en diversos campos. La revista da la bienvenida a trabajos profesionales en inglés o español que incluyan un breve resumen de un problema y los resultados obtenidos. Este número (39) de "Neutrosophic Computing and Machine Learning" (NCML) presenta una amplia gama de investigaciones que demuestran la vasta aplicación de la teoría neutrosófica en múltiples campos, con un enfoque significativo en la resolución de problemas complejos del mundo real que implican incertidumbre e indeterminación. La colección comienza con una discusión fundamental sobre el concepto de indeterminación en las teorías neutrosóficas. A partir de esta base teórica, los trabajos aplican métodos neutrosóficos a una amplia variedad de dominios. En medicina y salud, la investigación incluye la evaluación de la función respiratoria en atletas profesionales, la comparación de procedimientos quirúrgicos para la obesidad mórbida y una revisión sistemática del impacto del sistema neuroendocrino en la función inmunológica. El número también profundiza en el análisis legal y social, con artículos sobre el poder discrecional en el derecho tributario, los aspectos legales de la familia y las pensiones alimenticias, y la responsabilidad del estado con respecto a las víctimas de feminicidio. Un tema importante en este volumen es el uso de modelos neutrosóficos para el análisis estratégico y la toma de decisiones, especialmente en negocios y políticas públicas. Los trabajos cubren la aplicación de modelos neutrosóficos PEST-FODA para pequeñas y medianas empresas (PyMEs) y para analizar la industria audiovisual cubana. Otras contribuciones exploran tecnología y educación, como el uso de métodos neutrosóficos para la gestión de procesos municipales, el desarrollo de sistemas de recomendación para estudiantes y el análisis de expresiones emocionales en la educación de estudiantes con Trastorno del Espectro Autista (TEA). En general, el número muestra la versatilidad de la computación neutrosófica al proporcionar soluciones sólidas para sistemas complejos tanto en un contexto teórico como aplicado.

The Neutrosophic Set offers a robust mathematical framework for handling uncertainty by incorporating three key membership functions: truth, indeterminacy, and falsity [36]. To address the growing complexity of real-world problems, advanced extensions such as the HyperNeutrosophic Set and the SuperHyperNeutrosophic Set have been developed. These higher-dimensional models provide an enhanced representation of uncertainty and are formally defined in [20, 21, 22, 24, 23, 37, 19]. In addition, the TreeNeutrosophic Set and ForestNeutrosophic Set are well-established extensions of the Neutrosophic Set, broadening its applicability to structured and hierarchical data[16]. This paper explores the practical applications of the Neutrosophic Set in livestock management [28, 11, 2], highlighting its potential to enhance decision-making processes in this field. Additionally, we introduce several new variations of the Neutrosophic Set and the ForestNeutrosophic Set [16], further extending their theoretical framework and practical applicability.

The Neutrosophic Set provides a flexible mathematical framework for handling uncertainty by incorporating three distinct membership functions: truth, indeterminacy, and falsity [50]. In response to the growing complexity of real-world problems, advanced extensions such as the Hyperneutrosophic Set and the SuperHyperneutrosophic Set have been introduced. These extensions offer a higher-dimensional approach to modeling uncertainty and can be formally defined in [33, 34, 35, 37, 36, 51, 32]. Since the Hyperneutrosophic Set and the SuperHyperneutrosophic Set have only been recently defined, there remains a lack of concrete examples demonstrating their applicability. This paper aims to bridge this gap by exploring practical examples of these concepts in the field of agriculture. Additionally, we introduce two novel extensions, the Forest Hyperneutrosophic Set and the Forest SuperHyperneutrosophic Set, which further generalize the existing models to accommodate hierarchical and interconnected uncertainty structures in complex systems.

The pursuit of human knowledge has traditionally been organized into distinct disciplines—such as physics, philosophy, biology, and mathematics. This compartmentalization, while useful in many contexts, fails to capture the complexity and fluidity of reality. Neutrosophic Transdisciplinarity, a framework rooted in the principles of neutrosophy, offers a paradigm shift, enabling us to bridge these gaps. By focusing on the intersections where uncertainty and complexity thrive, neutrosophic transdisciplinarity challenges conventional disciplinary boundaries and facilitates the exploration of knowledge in its interconnected, evolving form.

The world, as we experience it, is suffused with indeterminacy. From the behavior of subatomic particles to the complexities of human thought and social systems, ambiguity and uncertainty are not exceptions but intrinsic properties of reality. Classical frameworks—whether grounded in strict probabilities, binary logic, or clear set membership—often falter in their ability to grapple with this pervasive indeterminacy. That is why Neutrosophy seeks to lay the groundwork for a paradigm shift across disciplines.

Materialism, as a philosophical outlook, has undergone several evolutionary transformations from classical metaphysical materialism to the more dynamic and socially-conscious dialectical materialism proposed by Marx. In this short essay, I propose the concept of Neutrosophic Materialism, which extends and refines dialectical materialism. Neutrosophic Materialism offers a broader, more nuanced framework for understanding the material conditions, social forces, and ideas in shaping human history and social reality.

When students first encounter logic, their journey often begins with classical logic, a foundational framework widely applied in fields such as mathematics, computer science, and philosophy. The classical logic is a rigid structure with binary distinctions between true and false, frequently regarded as the default system of reasoning. However, deeper exploration into symbolic logic reveals a more complex landscape, where no single, universally accepted system prevails. Instead, an array of logical frameworks emerges, each offering multifaceted perspectives on truth, validity, or inference.

The Javanese philosophical concept of “Gemah Ripah Loh Jinawi” paints a vivid picture of a dreamed utopia, often translated as a land of abundant natural wealth, fertility, and profound peace and prosperity. While this vision frequently appears to remain an elusive ideal in contemporary reality, this article argues for a re-evaluation of its essence, moving beyond a purely materialist interpretation. We draw parallels between “Gemah Ripah Loh Jinawi” and concepts such as the Judaic notion of “Shalom” and the “pursuit of happiness” embedded in Thomas Jefferson’s Declaration of Independence, demonstrating a shared yearning for a holistic well-being that transcends mere economic prosperity. Furthermore, by employing Neutrosophic Logic, we aim to analyze “Gemah Ripah Loh Jinawi” as a complex, multi-dimensional aspiration, acknowledging its degrees of truth, falsity, and inherent indeterminacy. This framework allows for a nuanced understanding of how this Javanese ideal seeks a complete abundance, blending material wealth with profound spiritual growth, offering a potent vision for human flourishing beyond the confines of modern materialism.

Cet article aborde le défi de modéliser formellement les systèmes de connaissance complexes, souvent contradictoires, propres à la pensée décoloniale latino-américaine. Il introduit le MultiPerspectivisme Neutrosophique, un cadre théorique qui opérationnalise le perspectivisme philosophique à l’aide de la logique neutrosophique. Nous posons comme postulat que la connaissance est située et que la vérité est médiée par le point de vue de l’observateur — un concept enraciné dans la philosophie nietzschéenne mais qui trouve une expression singulière dans les cosmologies amérindiennes et les systèmes juridiques pluralistes. La méthode principale consiste à proposer un Modèle de MultiPerspectivisme Neutrosophique, utilisant des ensembles multi-neutrosophiques pour représenter les perspectives subjectives sous forme de triplets de séquences de vérité, d’indétermination et de fausseté ⟨T, I, F⟩. Un résultat clé est le développement d’une fonction de similarité permettant de quantifier l’affinité entre différentes perspectives, transformant ainsi des points de vue qualitatifs en données analysables. Ce modèle est appliqué à une étude de cas portant sur un conflit foncier juridique, où il permet de révéler des similitudes structurelles cachées — telles qu’un style de raisonnement absolutiste partagé entre des parties opposées — et d’identifier des alliances stratégiques potentielles. La conclusion principale est que la logique neutrosophique offre un outil mathématique robuste pour naviguer à travers l’ambiguïté et la pluralité des réalités perspectivistes, allant au-delà de la simple reconnaissance de la différence vers son analyse formelle et son intégration possible..

Philosophy is characterized by its rich diversity of methods and schools of thought. Beneath this diversity, however, lies a subtle but profound unity: the interrelation of affirmation, negation, and neutrality. A neutrosophic perspective reveals that philosophical movements are not isolated ruptures from tradition but are dynamic threads interwoven into a larger intellectual tapestry. This short essay birelfy examines six philosophical movements—revisionism, inspirationalism, recur-rentism, sophisticalism, rejectivism, and paradoxism—through the lens of neutrosophy, illustrating how each contributes to the evolving landscape of philosophy.

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.

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 intrinsic in a given philosophical system.

This special issue of the journal “Neutrosophic Sets and Systems” compiles a selection of notable works from the IX Ibero-American Biometry Meeting, held in Quito, Ecuador. The collection focuses on the application of neutrosophic and plithogenic approaches to data science and multivariate analysis. The papers explore advanced studies in neutrosophy, which is a branch of philosophy examining the origin, nature, and scope of neutralities. Neutrosophic theory generalizes classic logic by introducing a degree of indeterminacy, alongside degrees of truth and falsity. The articles within this volume demonstrate the application of these concepts to diverse fields, including financial dynamics, psychological treatments, cryptocurrency regulation, sentiment analysis, and the evaluation of public policies.

The domain of neutrosophic set theory has been undergoing significant and rapid expansion. New approaches, theories, strategies, and optimization techniques are developed at a swift rate. An important development in neutrosophic theory is its integration with existing set theories, such as soft set theory, rough set theory and more. Neutrosophic set has been extended to neutrosophic hyperset which is vast and extends across multiple disciplines and problem domains, from decision support and Artificial Intelligence (AI) to data analysis and complex systems modelling. A neutrosophic hypersoft set extends the flexibility of neutrosophic logic and soft set theory by considering multidimensional or hypersoft sets to address real-world complexities where information is incomplete, uncertain, or inconsistent. Neutrosophic theories have emerged as essential tools in a diverse range of disciplines, including, MCDM, data mining, biomedical research, social studies, and beyond. The fourth volume of “New Trends in Neutrosophic Theories and Applications” focuses on theories, strategies, optimizing techniques for MCDM within neutrosophic frameworks. Some topics deal with introducing of Pythagorean hypersoft sets with possibility degree, quadripartitioned neutrosophic Lie-ideal of Lie-algebra, quadripartitioned neutrosophic quasi coincident topological space, neutrosophic supra-open set in neutrosophic supra topological space and neutrosophic soft matrices. Some topics deal with medical diagnosis, organ transplantation success using neutrosophic superhyperstructure and artificial intelligence. Some topics deal with revenue management, social situation. Some topics deal with MCDM in single valued neutrosophic set environment, rough set environment, and interval trapezoidal neutrosophic environment.

This book explores the development and importance of these mathematical approaches in managing uncertainty and imprecision in decision-making, and focuses on the practical applications of these theories in decision-making, demonstrating how they improve uncertainty modeling and facilitate more effective decision-making across various fields. By leveraging these frameworks, decision-makers can better navigate complexity, leading to more accurate and dependable outcomes. Ultimately, it highlights the progression from fuzzy to intuitionistic fuzzy to neutrosophic set theories as a significant advancement in capturing and analyzing uncertainty within decision-making contexts.

Young people’s skills and attitudes must be observed, studied and evaluated in order to create appropriate models that would serve an educational purpose. In this paper, we propose a decision-making model with the aim to detect certain attitudinal and behavioral patterns of actively engaged young people. The data used in this research resulted from a questionnaire drawn up by a group of researchers from six European countries with the aim to investigate the youth’s awareness about the Sustainable Development Goals and their engagement as active agents of development and change at regional level. For the purpose of this study, we selected the regional results obtained from administering this questionnaire in Dolj County (Romania) and La Rioja (Spain). We developed a neutrosophic model that determines the Mindchanger profile of the respondents based on a minimal set of questions, which is dependent on the inclusion or exclusion of the nationality-specific traits. The resulting decisions were then compared with the respondents’ self-evaluations, yielding high precisions (more than 0.83) for all the investigated evaluation scenarios. Our results were significantly better than the ones provided by several machine learning models applied on the same set of data. A direct impact of our model is that it can be applied to questionnaires which include linguistic responses that express, among others, unclear or vague thoughts. Additionally, it offers the possibility to identify the minimal set of questions that impact the respondent’s answer choice to a target question.

In this volume, I delve into a wide spectrum of topics, spanning mathematics, physics, philosophy, artificial intelligence, and social dynamics. A significant portion of the book is dedicated to neutrosophy and its extensions, including refined and quadripartitioned neutrosophic sets, neutrosophic determinants, and their applications in decision-making, evolutionary biology, and algebraic structures. The plithogenic approach, with its focus on multi-valued, multi-attributed frameworks, is also examined through concepts such as plithogenic derivatives and constants. Additionally, this volume explores the Dezert-Smarandache Theory (DSmT) and its implications for sensor fusion and probability assessment. The rank preservation, Bayesian masses, and decision fusion rules is considered, shedding light on critical aspects of belief representation and reasoning under uncertainty. Beyond mathematics and theoretical physics, I reflect on broader philosophical and societal questions: the spectrum of moral and social dynamics, the nature of free will, and the implications of population growth. The philosophical underpinnings of paradoxism, indeterminacy, and the evolving nature of logic are also explored. Technological advancements, including neutrosophic control in robotics and the impact of digital proliferation on learning and cognition, form another key theme of this volume. As artificial intelligence and automation continue to shape our world, I examine their implications through a neutrosophic and plithogenic lens. This book is not meant to provide definitive answers but rather to serve as a repository of ideas, questions, and intellectual provocations. I invite you, the reader, to engage, challenge, and expand upon these concepts, using them as a foundation for further inquiry and innovation. Exchanging ideas with Mayada Abualhomos, R. Alagar, Y. AlHasan, Mai Mousa Mahmoud Alhejoj, Abdallah Al-Husban, Norah Mousa Alrayes, G. Albert Asirvatham, Mahmut Baydaș, Octavian Blaga, Said Broumi, Victor Christianto, Jean Dezert, Dan Florin Lazăr, Feng Liu, Mohammad Hamidi, Ion Marinică, Nivetha Martin, Sagvan Y. Musa, Mutaz Mohamed Abbas Ali, Antonios Paraskevas, Amani Shatarah, Takaaki Fujita, Michael Voskoglou (alphabetically ordered).

In this volume, I delve into a diverse array of topics, spanning mathematics, physics, philosophy, artificial intelligence, and even touching upon social dynamics, literature, arts, criminal justice, and history. A significant portion of the book is dedicated to the ongoing development and exploration of neutrosophy and its related concepts. Together with peer mates, we examine neutrosophic improper integrals, n-ary neutrosophic triplets, refined neutrosophic S-approximation spaces, and the application of neutrosophic statistics and probability. The links between neutrosophy and other fields, such as Grey System Theory, is also investigated. This volume further explores the breadth of neutrosophic applications, from its use in defining new mathematical structures like neutrosophic triplet hypertopology and exploring neutro-algebraic and anti-algebraic structures, to its application in areas like medical diagnosis with complex neutrosophic similarity measures. We also delve into more theoretical aspects, such as completeness and incompleteness in neutrosophy, the division of quadruple neutrosophic numbers, and the refinement of neutrosophy in relation to lattices, pair structures, and YinYang bipolar fuzzy sets. Beyond the core of neutrosophic theory, I reflect on a range of philosophical and societal questions. This includes discussions on dialectics, the concept of indeterminacy, the degree of democracy, the blending of capitalism and communism, and the principle of internal fragility in dynamic systems. We also explore the fascinating potential of the aging brain and the principle of interconvertibility of matter, energy, and information, touching upon consciousness and personality. The Scilogs are not meant to provide definitive answers but rather to serve as a repository of ideas, questions, and intellectual provocations. Exchanging ideas with Dan Florin Lazăr, Yaser Ahmad Alhasan, William H. Woodall, M. Karimi, M. R. Hooshmandasl, A. Shakiba, N. Zamani, Said Broumi, Saeid Jafari, Ronald Pinho, Robert Neil Boyd, Victor Christianto, Le Hoang Son, Luu Quoc Dat, Mumtaz Ali, Rafif Alhabib, Kalyan Mondal, Surapati Pramanik, Zhang Wenpeng, Ludi Jancy Jenifer, Peide Liu, Ganeshsree Selvachandran, Terman Frometa-Castillo, Mohammad Khoshnevisan, Maikel Leyva Vazquez, Akira Kanda, Andrușa Vătuiu, Octavian Blaga, Mustapha Kachchouh, Kawther Fawzi, Hamidreza Seiti, Ștefan Vlăduțescu (in the order they appear in the book).