A Note On Antigeometry And Neutrogeometry And Their Application To Real Life
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A Note On Antigeometry And Neutrogeometry And Their Application To Real Life
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Author : Carlos Granados
language : en
Publisher: Infinite Study
Release Date : 2022-04-27
A Note On Antigeometry And Neutrogeometry And Their Application To Real Life written by Carlos Granados and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-27 with Antiques & Collectibles categories.
Dealing with NeutroGeometry in true, false, and uncertain regions is becoming of great interested for researchers. Not too many studies have been done on this topic, for that reason, aim of this work is to define a new method to deal with NeutroGeometry in true, false, and neutrogeometry (T,C,I,F). Furthermore, some real-life application examples in 3D computer graphics, Astrophysics, nanostructure, neutrolaw, neutrogender, neutrocitation, neutrohealth-food, neutroenvironment and quantum space are presented.
Applications Of Neutrogeometry And Antigeometry In Real World
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Author : Erick Gonzalez-Caballero
language : en
Publisher: Infinite Study
Release Date : 2023-01-01
Applications Of Neutrogeometry And Antigeometry In Real World written by Erick Gonzalez-Caballero and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-01 with Mathematics categories.
NeutroGeometries are those geometric structures where at least one definition, axiom, property, theorem, among others, is only partially satisfied. In AntiGeometries at least one of these concepts is never satisfied. Smarandache Geometry is a geometric structure where at least one axiom or theorem behaves differently in the same space, either partially true and partially false, or totally false but its negation done in many ways. This paper offers examples in images of nature, everyday objects, and celestial bodies where the existence of Smarandechean or NeutroGeometric structures in our universe is revealed. On the other hand, a practical study of surfaces with characteristics of NeutroGeometry is carried out, based on the properties or more specifically NeutroProperties of the famous quadrilaterals of Saccheri and Lambert on these surfaces. The article contributes to demonstrating the importance of building a theory such as NeutroGeometries or Smarandache Geometries because it would allow us to study geometric structures where the well-known Euclidean, Hyperbolic or Elliptic geometries are not enough to capture properties of elements that are part of the universe, but they have sense only within a NeutroGeometric framework. It also offers an axiomatic option to the Riemannian idea of Two-Dimensional Manifolds. In turn, we prove some properties of the NeutroGeometries and the materialization of the symmetric triad
Neutrogeometry Neutroalgebra And Superhyperalgebra In Today S World
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Author : Smarandache, Florentin
language : en
Publisher: IGI Global
Release Date : 2023-05-15
Neutrogeometry Neutroalgebra And Superhyperalgebra In Today S World written by Smarandache, Florentin and has been published by IGI Global this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-15 with Mathematics categories.
NeutroAlgebra and AntiAlgebra were extended to NeutroGeometry and AntiGeometry in order to catch the Non-Euclidean Geometries. In the real world, the spaces and the elements that populate them and the rules that apply to them are not perfect, uniform, homogeneous, or complete. They are fragmentary and disparate, with unclear and conflicting information, and they do not apply in the same degree to each element. Therefore, these partial, hybrid, and mixed structures are necessary. NeutroGeometry, NeutroAlgebra, and SuperHyperAlgebra in Today's World presents applications of many NeutroStructures in our real world and considers NeutroGeometry and AntiGeometry as new fields of research that resemble everyday life. Covering key topics such as hyperbolic geometry, elliptic geometry, and AntiGeometry, this reference work is ideal for mathematicians, industry professionals, researchers, scholars, academicians, practitioners, instructors, and students.
Real Examples Of Neutrogeometry Antigeometry
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Author : Florentin Smarandache
language : un
Publisher: Infinite Study
Release Date : 2023-01-01
Real Examples Of Neutrogeometry Antigeometry written by Florentin Smarandache and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-01 with Mathematics categories.
For the classical Geometry, in a geometrical space, all items (concepts, axioms, theorems, etc.) are totally (100%) true. But, in the real world, many items are not totally true. The NeutroGeometry is a geometrical space that has some items that are only partially true (and partially indeterminate, and partially false), and no item that is totally false. The AntiGeometry is a geometrical space that has some item that are totally (100%) false. While the Non-Euclidean Geometries [hyperbolic and elliptic geometries] resulted from the total negation of only one specific axiom (Euclid’s Fifth Postulate), the AntiGeometry results from the total negation of any axiom [and in general: theorem, concept, idea etc.] and even of more axioms [theorem, concept, idea, etc.] and in general from any geometric axiomatic system (Euclid’s five postulates, Hilbert’s 20 axioms, etc.), and the NeutroAxiom results from the partial negation of any axiom (or concept, theorem, idea, etc.). Clearly, the AntiGeometry is a generalization of Non-Euclidean Geometries.
Neutrosophic Sets And Systems Vol 49 2022
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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date : 2022-04-01
Neutrosophic Sets And Systems Vol 49 2022 written by Florentin Smarandache and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-01 with Mathematics categories.
“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc. Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. This theory considers every notion or idea together with its opposite or negation
Advancing Uncertain Combinatorics Through Graphization Hyperization And Uncertainization Fuzzy Neutrosophic Soft Rough And Beyond
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Author : Takaaki Fujita
language : en
Publisher: Infinite Study
Release Date : 2025-01-20
Advancing Uncertain Combinatorics Through Graphization Hyperization And Uncertainization Fuzzy Neutrosophic Soft Rough And Beyond written by Takaaki Fujita and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-20 with Mathematics categories.
This book is the fifth volume in the series of Collected Papers on Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond. This volume specifically delves into the concept of Various SuperHyperConcepts, building on the foundational advancements introduced in previous volumes. The series aims to explore the ongoing evolution of uncertain combinatorics through innovative methodologies such as graphization, hyperization, and uncertainization. These approaches integrate and extend core concepts from fuzzy, neutrosophic, soft, and rough set theories, providing robust frameworks to model and analyze the inherent complexity of real-world uncertainties. At the heart of this series lies combinatorics and set theory—cornerstones of mathematics that address the study of counting, arrangements, and the relationships between collections under defined rules. Traditionally, combinatorics has excelled in solving problems involving uncertainty, while advancements in set theory have expanded its scope to include powerful constructs like fuzzy and neutrosophic sets. These advanced sets bring new dimensions to uncertainty modeling by capturing not just binary truth but also indeterminacy and falsity. In this fifth volume, the exploration of Various SuperHyperConcepts provides an innovative lens to address uncertainty, complexity, and hierarchical relationships. It synthesizes key methodologies introduced in earlier volumes, such as hyperization and neutrosophic extensions, while advancing new theories and applications. From pioneering hyperstructures to applications in advanced decision-making, language modeling, and neural networks, this book represents a significant leap forward in uncertain combinatorics and its practical implications across disciplines. The book is structured into 17 chapters, each contributing unique perspectives and advancements in the realm of Various SuperHyperConcepts and their related frameworks: Chapter 1 introduces the concept of Body-Mind-Soul-Spirit Fluidity within psychology and phenomenology, while examining established social science frameworks like PDCA and DMAIC. It extends these frameworks using Neutrosophic Sets, a flexible extension of Fuzzy Sets, to improve their adaptability for mathematical and programming applications. The chapter emphasizes the potential of Neutrosophic theory to address multi-dimensional challenges in social sciences. Chapter 2 delves into the theoretical foundation of Hyperfunctions and their generalizations, such as Hyperrandomness and Hyperdecision-Making. It explores higher-order frameworks like Weak Hyperstructures, Hypergraphs, and Cognitive Hypermaps, aiming to establish their versatility in addressing multi-layered problems and setting a foundation for further studies. Chapter 3 extends traditional decision-making methodologies into HyperDecision-Making and n-SuperHyperDecision-Making. By building on approaches like MCDM and TOPSIS, this chapter develops frameworks capable of addressing complex decision-making scenarios, emphasizing their applicability in dynamic, multi-objective contexts. Chapter 4 explores integrating uncertainty frameworks, including Fuzzy, Neutrosophic, and Plithogenic Sets, into Large Language Models (LLMs). It proposes innovative models like Large Uncertain Language Models and Natural Uncertain Language Processing, integrating hierarchical and generalized structures to advance the handling of uncertainty in linguistic representation and processing. Chapter 5 introduces the Natural n-Superhyper Plithogenic Language by synthesizing natural language, plithogenic frameworks, and superhyperstructures. This innovative construct seeks to address challenges in advanced linguistic and structural modeling, blending attributes of uncertainty, complexity, and hierarchical abstraction. Chapter 6 defines mathematical extensions such as NeutroHyperstructures and AntiHyperstructures using the Neutrosophic Triplet framework. It formalizes structures like neutro-superhyperstructures, advancing classical frameworks into higher-dimensional realms. Chapter 7 explores the extension of Binary Code, Gray Code, and Floorplans through hyperstructures and superhyperstructures. It highlights their iterative and hierarchical applications, demonstrating their adaptability for complex data encoding and geometric arrangement challenges. Chapter 8 investigates the Neutrosophic TwoFold SuperhyperAlgebra, combining classical algebraic operations with neutrosophic components. This chapter expands upon existing algebraic structures like Hyperalgebra and AntiAlgebra, exploring hybrid frameworks for advanced mathematical modeling. Chapter 9 introduces Hyper Z-Numbers and SuperHyper Z-Numbers by extending the traditional Z-Number framework with hyperstructures. These extensions aim to represent uncertain information in more complex and multidimensional contexts. Chapter 10 revisits category theory through the lens of hypercategories and superhypercategories. By incorporating hierarchical and iterative abstractions, this chapter extends the foundational principles of category theory to more complex and layered structures. Chapter 11 formalizes the concept of n-SuperHyperBranch-width and its theoretical properties. By extending hypergraphs into superhypergraphs, the chapter explores recursive structures and their potential for representing intricate hierarchical relationships. Chapter 12 examines superhyperstructures of partitions, integrals, and spaces, proposing a framework for advancing mathematical abstraction. It highlights the potential applications of these generalizations in addressing hierarchical and multi-layered problems. Chapter 13 revisits Rough, HyperRough, and SuperHyperRough Sets, introducing new concepts like Tree-HyperRough Sets. The chapter connects these frameworks to advanced approaches for modeling uncertainty and complex relationships. Chapter 14 explores Plithogenic SuperHyperStructures and their applications in decision-making, control, and neuro systems. By integrating these advanced frameworks, the chapter proposes innovative directions for extending existing systems to handle multi-attribute and contradictory properties. Chapter 15 focuses on superhypergraphs, expanding hypergraph concepts to model complex structural types like arboreal and molecular superhypergraphs. It introduces Generalized n-th Powersets as a unifying framework for broader mathematical applications, while also touching on hyperlanguage processing. Chapter 16 defines NeutroHypergeometry and AntiHypergeometry as extensions of classical geometric structures. Using the Geometric Neutrosophic Triplet, the chapter demonstrates the flexibility of these frameworks in representing multi-dimensional and uncertain relationships. Chapter 17 establishes the theoretical groundwork for SuperHyperGraph Neural Networks and Plithogenic Graph Neural Networks. By integrating advanced graph structures, this chapter opens pathways for applying neural networks to more intricate and uncertain data representations.
Neutrosophic Sets And Systems Vol 75 2025
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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date : 2025-01-06
Neutrosophic Sets And Systems Vol 75 2025 written by Florentin Smarandache and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-06 with Mathematics categories.
“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc. Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. This theory considers every notion or idea together with its opposite or negation
Smarandache Geometries Or Hybrids
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Author : Ion Pătrașcu
language : un
Publisher: Infinite Study
Release Date : 2023-01-01
Smarandache Geometries Or Hybrids written by Ion Pătrașcu and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-01 with Mathematics categories.
An axiom is said to be smarandachely negated if in the same space the axiom behaves differently (ie, validated and invalidated; or only invalidated, but in at least two distinct ways). Therefore, we say that an axiom is partially negated or there is a degree of negation of an axiom. A Smarandache geometry (or hybrid geometry) is a geometry that has at least one axiom negated in two different ways (1969). Thus, as a particular case, the Euclidean, Lobachevsky-Bolyai-Gaussian and Riemannian geometries can be joined altogether, in the same space, by some Smarandache geometries. These latter geometries can be partly Euclidean and partly non-Euclidean. A (classical) Geometry structure has all axioms completely (100%) true. A NeutroGeometry structure has some axioms that are only partially true, partially indeterminate, and partially false (and no axiom is totally (100%) false to distinguish it from AntiGeometry). Whereas an AntiGeometry structure has at least one axiom that is totally (100%) false.
Aut Viam Inveniam Aut Faciam
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Author : Dan Florin Lazăr
language : ro
Publisher: Infinite Study
Release Date : 2023-12-10
Aut Viam Inveniam Aut Faciam written by Dan Florin Lazăr and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-10 with Literary Criticism categories.
Acest volum adună articole și consemnări despre activitatea științifică și literară a prof. dr. univ. Florentin Smarandache din ultimii cinci ani, în diverse limbi (română, engleză, spaniolă, franceză, greacă, turcă, arabă, albaneză). Volumul este structurat în mai multe părți: A. fișe de dicționar; B. articole și cronici; C. interviuri; D. mențiuni risipite; E. reacții (la seria monumentală de folclor umoristic românesc); F. mesaje aniversare colectate de pe pagina de facebook a lui Florentin Smarandache; G. mesaje de la cercetători în neutrosofie, disciplina fondată de Florentin Smarandache; H. alte mesaje destinate prof. Smarandache pe diverse canale online; I. fotografii și capturi de ecran. Intenția volumului este de a adăuga o tușă de culoare la un posibil portret “Florentin Smarandache”, care să reflecte via și bogata activitate a profesorului româno-american care predă matematică de peste două decenii la University of New Mexico (Statele Unite ale Americii), care, pe lângă activitatea didactică și științifică, se manifestă energic și în diverse domenii literar-artistice. Prin natura muncii și eforturilor sale pluridisciplinare, Florentin Smarandache susține și promovează dialogul onest și direct, dincolo de orice constrângeri legate de ideologii, iar această opțiune este cât se poate de transparentă în mesajele pe care le-am colectat în acest volum.
Theory Of Distances In Neutrogeometry
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Author :
language : en
Publisher: Infinite Study
Release Date : 2024-01-01
Theory Of Distances In Neutrogeometry written by and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-01 with Mathematics categories.
NeutroGeometry is one of the most recent approaches to geometry. In NeutroGeometry mod-els, the main condition is to satisfy an axiom, definition, property, operator and so on, that is neither entirely true nor entirely false. When one of these concepts is not satisfied at all it is called AntiGeometry. One of the problems that this new theory has had is the scarcity of models. Another open problem is the definition of angle and distance measurements within the framework of NeutroGeometry. This paper aims to introduce a general theory of distance measures in any NeutroGeometry. We also present an algorithm for distance measurement in real-life problems.