Download or read book A note on AntiGeometry and NeutroGeometry and their application to real life written by Carlos Granados and published by Infinite Study. This book was released on 2022-04-27 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Applications of NeutroGeometry and AntiGeometry in Real World written by Erick Gonzalez-Caballero and published by Infinite Study. This book was released on 2023-01-01 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 ,

Download or read book Applications of NeutroGeometry and AntiGeometry in Real World written by Erick González-Caballero and published by Infinite Study. This book was released on 2023-01-01 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 , , and .

Download or read book Real Examples of NeutroGeometry AntiGeometry written by Florentin Smarandache and published by Infinite Study. This book was released on 2023-01-01 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book NeutroGeometry AntiGeometry are alternatives and generalizations of the Non Euclidean Geometries revisited written by Florentin Smarandache and published by Infinite Study. This book was released on 2021-10-01 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we extend the NeutroAlgebra & AntiAlgebra to the geometric spaces, by founding the NeutroGeometry & AntiGeometry. While the Non-Euclidean Geometries resulted from the total negation of one specific axiom (Euclid’s Fifth Postulate), the AntiGeometry results from the total negation of any axiom or even of more axioms from any geometric axiomatic system (Euclid’s, Hilbert’s, etc.) and from any type of geometry such as (Euclidean, Projective, Finite, Affine, Differential, Algebraic, Complex, Discrete, Computational, Molecular, Convex, etc.) Geometry, and the NeutroGeometry results from the partial negation of one or more axioms [and no total negation of no axiom] from any geometric axiomatic system and from any type of geometry. Generally, instead of a classical geometric Axiom, one may take any classical geometric Theorem from any axiomatic system and from any type of geometry, and transform it by NeutroSophication or AntiSophication into a NeutroTheorem or AntiTheorem respectively in order to construct a NeutroGeometry or AntiGeometry. Therefore, the NeutroGeometry and AntiGeometry are respectively alternatives and generalizations of the Non-Euclidean Geometries. In the second part, we recall the evolution from Paradoxism to Neutrosophy, then to NeutroAlgebra & AntiAlgebra, afterwards to NeutroGeometry & AntiGeometry, and in general to NeutroStructure & AntiStructure that naturally arise in any field of knowledge. At the end, we present applications of many NeutroStructures in our real world.

Download or read book NeutroGeometry NeutroAlgebra and SuperHyperAlgebra in Today s World written by Smarandache, Florentin and published by IGI Global. This book was released on 2023-05-15 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book NeutroGeometry AntiGeometry are alternatives and generalizations of the Non Euclidean Geometries written by Florentin Smarandache and published by Infinite Study. This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we extend the NeutroAlgebra & AntiAlgebra to the geometric space, by founding the NeutroGeometry & AntiGeometry. While the Non-Euclidean 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 even of more axioms from any geometric axiomatic system (Euclid’s, Hilbert’s, etc.), and the NeutroAxiom results from the partial negation of one or more axioms [and no total negation of no axiom] from any geometric axiomatic system. Therefore, the NeutroGeometry and AntiGeometry are respectively alternatives and generalizations of the Non-Euclidean Geometries. In the second part, we recall the evolution from Paradoxism to Neutrosophy, then to NeutroAlgebra & AntiAlgebra, afterwards to NeutroGeometry & AntiGeometry, and in general to NeutroStructure & AntiStructure that naturally arise in any field of knowledge. At the end, we present applications of many NeutroStructures in our real world.

Download or read book Theory of Distances in NeutroGeometry written by and published by Infinite Study. This book was released on 2024-01-01 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Neutrosophic Sets and Systems vol 49 2022 written by Florentin Smarandache and published by Infinite Study. This book was released on 2022-04-01 with total page 611 pages. Available in PDF, EPUB and Kindle. Book excerpt: “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 and with their spectrum of neutralities in between them (i.e. notions or ideas supporting neither nor ). The and ideas together are referred to as . Neutrosophy is a generalization of Hegel's dialectics (the last one is based on and only). According to this theory every idea tends to be neutralized and balanced by and ideas - as a state of equilibrium. In a classical way , , are disjoint two by two. But, since in many cases the borders between notions are vague, imprecise, Sorites, it is possible that , , (and of course) have common parts two by two, or even all three of them as well. Neutrosophic Set and Neutrosophic Logic are generalizations of the fuzzy set and respectively fuzzy logic (especially of intuitionistic fuzzy set and respectively intuitionistic fuzzy logic).

Download or read book Introduction to NeutroAlgebraic Structures and AntiAlgebraic Structures revisited written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: In all classical algebraic structures, the Laws of Compositions on a given set are well-defined. But this is a restrictive case, because there are many more situations in science and in any domain of knowledge when a law of composition defined on a set may be only partially-defined (or partially true) and partially-undefined (or partially false), that we call NeutroDefined, or totally undefined (totally false) that we call AntiDefined.

Download or read book Neutrosophy written by Florentin Smarandache and published by . This book was released on 1998 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Introduction to the Division by Zero Calculus written by SABUROU SAITOH and published by Scientific Research Publishing, Inc. USA. This book was released on 2021-02-04 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: The common sense on the division by zero with the long and mysterious history is wrong and our basic idea on the space around the point at infinity is also wrong since Euclid. On the gradient or on differential coefficients we have a great missing since tan(π/2) = 0. Our mathematics is also wrong in elementary mathematics on the division by zero. In this book in a new and definite sense, we will show and give various applications of the division by zero 0/0 = 1/0 = z/0 = 0. In particular, we will introduce several fundamental concepts in calculus, Euclidean geometry, analytic geometry, complex analysis and differential equations. We will see new properties on the Laurent expansion, singularity, derivative, extension of solutions of differential equations beyond analytical and isolated singularities, and reduction problems of differential equations. On Euclidean geometry and analytic geometry, we will find new fields by the concept of the division by zero. We will collect many concrete properties in mathematical sciences from the viewpoint of the division by zero. We will know that the division by zero is our elementary and fundamental mathematics.

Download or read book Neutrosophic Sets and Systems vol 19 2018 written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: “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.

Download or read book Neutrosophic Set A Generalization of The Intuitionistic Fuzzy Set written by Florentin Smarandache and published by Infinite Study. This book was released on 2010-08-23 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper one generalizes the intuitionistic fuzzy set (IFS), paraconsistent set, and intuitionistic set to the neutrosophic set (NS). Many examples are presented. Distinctions between NS and IFS are underlined.

Download or read book Advances in Type 2 Fuzzy Sets and Systems written by Alireza Sadeghian and published by Springer. This book was released on 2013-06-25 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores recent developments in the theoretical foundations and novel applications of general and interval type-2 fuzzy sets and systems, including: algebraic properties of type-2 fuzzy sets, geometric-based definition of type-2 fuzzy set operators, generalizations of the continuous KM algorithm, adaptiveness and novelty of interval type-2 fuzzy logic controllers, relations between conceptual spaces and type-2 fuzzy sets, type-2 fuzzy logic systems versus perceptual computers; modeling human perception of real world concepts with type-2 fuzzy sets, different methods for generating membership functions of interval and general type-2 fuzzy sets, and applications of interval type-2 fuzzy sets to control, machine tooling, image processing and diet. The applications demonstrate the appropriateness of using type-2 fuzzy sets and systems in real world problems that are characterized by different degrees of uncertainty.

Download or read book Multi Criteria Decision Making Models and Techniques Neutrosophic Approaches written by Abdel-Basset, Mohamed and published by IGI Global. This book was released on 2024-09-12 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the rising information technology trends, cost, time, delivery, space, quality, durability, and price are all paramount in addressing managerial decision-making complexities within the supply chain, transportation, and inventory control. The intensifying competition within imprecise environments further complicates these challenges. Customer demand, influenced by multifaceted factors such as production price and income levels, often remains elusive or unpredictable in the real-world market. Fuzzy sets, while useful, need to catch up in directly capturing such uncertainties due to their numeric membership functions. Multi-Criteria Decision Making Models and Techniques: Neutrosophic Approaches explores the neutrosophic sets as a solution, uniquely poised to accommodate inherent uncertainties. Neutrosophic sets and logic are evolutionary extensions of fuzzy and intuitionistic fuzzy sets and logic. In real-world problems, these diverse uncertain systems demonstrate a capability to manage heightened levels of uncertainty. This book delves into the burgeoning field of neutrosophic theory, elucidating its application in operations research. Neutrosophic sets and logic have emerged as pivotal tools in grappling with uncertainty, impreciseness, vagueness, incompleteness, inconsistency, and indeterminacy.

Download or read book Euclidean and Non Euclidean Geometries written by Marvin J. Greenberg and published by . This book was released on 1993 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: