NeutroGeometry, NeutroAlgebra, and SuperHyperAlgebra in Today's World

NeutroGeometry, NeutroAlgebra, and SuperHyperAlgebra in Today's World

Florentin Smarandache, Madeline Al Tahan
Indexed In: SCOPUS
Release Date: May, 2023|Copyright: © 2023 |Pages: 264
DOI: 10.4018/978-1-6684-4740-6
ISBN13: 9781668447406|ISBN10: 1668447401|ISBN13 Softcover: 9781668447413|EISBN13: 9781668447420
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Description & Coverage
Description:

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.

Coverage:

The many academic areas covered in this publication include, but are not limited to:

  • AntiGeometry
  • Elliptic Geometry
  • Geometry
  • Hyperbolic Geometry
  • Mixed Projective-Affine Geometry
  • NeutroAlgebra
  • NeutroGeometries
  • NeutroTopological Spaces
  • Non-Euclidean Geometries
  • SuperHyperAlgebra
Reviews & Statements

“New developments included applications of neutrosophic statistics for indeterminate data and statistical procedure, new algebraic structures such as NeutroAlgebra and AntiAlgebra, that are algebras with partially true or respectively totally false axioms, as well as NeutroGeometry and AntiGeometry as generalizations and alternatives of Euclidean and Non-Euclidean Geometries.

The SuperHyperAlgebra, SuperHyperFunction, SuperHyper Topology and SuperHyperGraph as the most general forms of algebras and graphs built on the n-th PowerSet of a set as in our world where a system is formed by sub-systems, then each sub-system by sub-sub-systems etc. and their multiple applications. And the extension of the Soft Set to HyperSoft Set, then to IndetermSoft Set and respectively to IndetermHyperSoft Set, and TreeSoft Set as extension of the MultiSoft Set and their practical applications.”

– Florentin Smarandache, University of New Mexico
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Editor/Author Biographies

Florentin Smarandache is the founder of neutrosophy (a new branch of philosophy - generalization of dialectics), neutrosophic set, logic, probability statistics and published hundreds of papers and books on neutrosophic physics, superluminal and instantaneous physics, unmatter, quantum paradoxes, absolute theory of relativity, redshift and blueshift due to the medium gradient and refraction index besides the Doppler effect, paradoxism, oUTER-aRT, Law of Included Multiple-Middle, multispace and multistructure, HyperSoft set, TreeSoft Set, IndetermSoft Set and IndetermHyperSoft Set, SuperHyperGraph, SuperHyperTopology, SuperHyperAlgebra, SuperHyperFunction, Neutrosophic SuperHyperAlgebra, Refined Neutrosophic Set, neutrosophic over-under-off-set, plithogenic set / logic / probability / statistics, symbolic plithogenic algebraic structures, neutrosophic triplet and duplet structures, quadruple neutrosophic structures, extension of algebraic structures to NeutroAlgebra and AntiAlgebra, NeutroGeometry and AntiGeometry, NeutroTopology and AntiTopology, He also published books of poetry, dramas, children stories, translations, essays, novel, folklore, art albums: https://fs.unm.edu/FlorentinSmarandache.htm.

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