Introduction To Superhyperalgebra And Neutrosophic Superhyperalgebra

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Introduction To Superhyperalgebra And Neutrosophic Superhyperalgebra

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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date : 2022-10-23

Introduction To Superhyperalgebra And Neutrosophic Superhyperalgebra 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 2022-10-23 with Antiques & Collectibles categories.

In this paper we recall our concepts of n th-Power Set of a Set, SuperHyperOperation, SuperHyperAxiom, SuperHyperAlgebra, and their corresponding Neutrosophic SuperHyperOperation, Neutrosophic SuperHyperAxiom and Neutrosophic SuperHyperAlgebra. In general, in any field of knowledge, one actually encounters SuperHyperStructures (or more accurately (m, n)- SuperHyperStructures).

Neutrosophic Superhyperalgebra And New Types Of Topologies

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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date : 2023-09-01

Neutrosophic Superhyperalgebra And New Types Of Topologies 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 2023-09-01 with Mathematics categories.

In general, a system S (that may be a company, association, institution, society, country, etc.) is formed by sub-systems Si { or P(S), the powerset of S }, and each sub-system Si is formed by sub-sub-systems Sij { or P(P(S)) = P2(S) } and so on. That’s why the n-th PowerSet of a Set S { defined recursively and denoted by Pn(S) = P(Pn-1(S) } was introduced, to better describes the organization of people, beings, objects etc. in our real world. The n-th PowerSet was used in defining the SuperHyperOperation, SuperHyperAxiom, and their corresponding Neutrosophic SuperHyperOperation, Neutrosophic SuperHyperAxiom in order to build the SuperHyperAlgebra and Neutrosophic SuperHyperAlgebra. In general, in any field of knowledge, one in fact encounters SuperHyperStructures. Also, six new types of topologies have been introduced in the last years (2019-2022), such as: Refined Neutrosophic Topology, Refined Neutrosophic Crisp Topology, NeutroTopology, AntiTopology, SuperHyperTopology, and Neutrosophic SuperHyperTopology.

Neutrosophic Twofold Superhyperalgebra And Anti Superhyperalgebra

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Author : Takaaki Fujita
language : en
Publisher: Infinite Study
Release Date : 2025-01-01

Neutrosophic Twofold Superhyperalgebra And Anti Superhyperalgebra 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 2025-01-01 with Mathematics categories.

Neutrosophic Sets are conceptual frameworks designed to address uncertainty. A Neutrosophic TwoFold Algebra is a hybrid algebraic structure defined over a neutrosophic set, combining classical algebraic operations with neutrosophic components. Concepts such as Hyperalgebra and Superhyperalgebra extend classical Algebra using Power Sets and 𝑛-th powersets. Additionally, structures such as NeutroAlgebra and AntiAlgebra have been defined in recent y ears. This paper explores several related concepts, including TwoFold SuperhyperAlgebra and Anti SuperhyperAlgebra.

The Superhyperfunction And The Neutrosophic Superhyperfunction

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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date : 2022-04-27

The Superhyperfunction And The Neutrosophic Superhyperfunction 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 2022-04-27 with Antiques & Collectibles categories.

In this paper, one recalls the general definition of the SuperHyperAlgebra with its SuperHyperOperations and SuperHyperAxioms. Then one introduces for the first time the SuperHyperTopology and especially the SuperHyperFunction and Neutrosophic SuperHyperFunction. One gives a numerical example of a SuperHyperGroup.

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.

Neutrosophic Sets And Systems Vol 55 2023

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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date : 2024-02-15

Neutrosophic Sets And Systems Vol 55 2023 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 2024-02-15 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 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 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 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).

Neutrosophic Algebraic Structures And Their Applications

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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date : 2022-08-01

Neutrosophic Algebraic Structures And Their Applications 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 2022-08-01 with Mathematics categories.

Neutrosophic theory and its applications have been expanding in all directions at an astonishing rate especially after of the introduction the journal entitled “Neutrosophic Sets and Systems”. New theories, techniques, algorithms have been rapidly developed. One of the most striking trends in the neutrosophic theory is the hybridization of neutrosophic set with other potential sets such as rough set, bipolar set, soft set, hesitant fuzzy set, etc. The different hybrid structures such as rough neutrosophic set, single valued neutrosophic rough set, bipolar neutrosophic set, single valued neutrosophic hesitant fuzzy set, etc. are proposed in the literature in a short period of time. Neutrosophic set has been an important tool in the application of various areas such as data mining, decision making, e-learning, engineering, medicine, social science, and some more.

Neutrosophic Sets And Systems Vol 61 2023

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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date : 2023-11-15

Neutrosophic Sets And Systems Vol 61 2023 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 2023-11-15 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 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.

Introduction To Upside Down Logic Its Deep Relation To Neutrosophic Logic And Applications

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Author : Takaaki Fujita
language : en
Publisher: Infinite Study
Release Date :

Introduction To Upside Down Logic Its Deep Relation To Neutrosophic Logic And Applications 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 with Mathematics categories.

In the study of uncertainty, concepts such as fuzzy sets [113], fuzzy graphs [79], and neutrosophic sets [88] have been extensively investigated. This paper focuses on a novel logical framework known as Upside-Down Logic, which systematically transforms truths into falsehoods and vice versa by altering contexts, meanings, or perspectives. The concept was first introduced by F. Smarandache in [99]. To contribute to the growing interest in this area, this paper presents a mathematical definition of Upside-Down Logic, supported by illustrative examples, including applications related to the Japanese language. Additionally, it introduces and explores Contextual Upside-Down Logic, an advanced extension that incorporates a contextual transformation function, enabling the adjustment of logical connectives in conjunction with flipping truth values based on contextual shifts. Furthermore, the paper introduces Indeterm-Upside-Down Logic and Certain Upside-Down Logic, both of which expand Upside-Down Logic to better accommodate indeterminate values. Finally, a simple algorithm leveraging Upside-Down Logic is proposed and analyzed, providing insights into its computational characteristics and potential applications.