Some Results on Neutrosophic Triplet Group and Their Applications
Some Results on Neutrosophic Triplet Group and Their Applications

Author: Tèmítópé Gbóláhàn Jaíyéolá

Publisher: Infinite Study

Published: 2018-11-01

Total Pages: 14

ISBN-13:

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This article is based on new developments on a neutrosophic triplet group (NTG) and applications earlier introduced in 2016 by Smarandache and Ali. NTG sprang up from neutrosophic triplet set X: a collection of triplets (b, neut(b), anti(b)) for an b ∈ X that obeys certain axioms (existence of neutral(s) and opposite(s)). Some results that are true in classical groups were investigated in NTG and were shown to be either universally true in NTG or true in some peculiar types of NTG. Distinguishing features between an NTG and some other algebraic structures such as: generalized group (GG), quasigroup, loop and group were investigated. Some neutrosophic triplet subgroups (NTSGs) of a neutrosophic triplet group were studied. Applications of the neutrosophic triplet set, and our results on NTG in relation to management and sports, are highlighted and discussed.

NeutroAlgebra of Neutrosophic Triplets
NeutroAlgebra of Neutrosophic Triplets

Author: Vasantha Kandasamy

Publisher: Infinite Study

Published: 2020-12-01

Total Pages: 15

ISBN-13:

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In this paper, authors define the NeutroAlgebra of neutrosophic triplets groups. We prove the existence theorem for NeutroAlgebra of neutrosophic triplet groups. Several open problems are proposed. Further, the NeutroAlgebras of extended neutrosophic triplet groups have been obtained.

Further Theory of Neutrosophic Triplet Topology and Applications
Further Theory of Neutrosophic Triplet Topology and Applications

Author: Mohammed A. Al Shumrani

Publisher: Infinite Study

Published:

Total Pages: 12

ISBN-13:

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In this paper we study and develop the Neutrosophic Triplet Topology (NTT) that was recently introduced by Sahin et al. Like classical topology, the NTT tells how the elements of a set relate spatially to each other in a more comprehensive way using the idea of Neutrosophic Triplet Sets.

Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets, Volume I
Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets, Volume I

Author: Florentin Smarandache

Publisher: Infinite Study

Published:

Total Pages: 480

ISBN-13: 3038973858

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Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (, , ), where is an entity (i.e., element, concept, idea, theory, logical proposition, etc.), is the opposite of , while is the neutral (or indeterminate) between them, i.e., neither nor . Based on neutrosophy, the neutrosophic triplets were founded; they have a similar form: (x, neut(x), anti(x), that satisfy some axioms, for each element x in a given set. This book contains the successful invited submissions to a special issue of Symmetry, reporting on state-of-the-art and recent advancements of neutrosophic triplets, neutrosophic duplets, neutrosophic multisets, and their algebraic structures—that have been defined recently in 2016, but have gained interest from world researchers, and several papers have been published in first rank international journals.

Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets
Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets

Author: Florentin Smarandache

Publisher: MDPI

Published: 2019-04-04

Total Pages: 450

ISBN-13: 3038974757

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Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (, , ), where is an entity {i.e. element, concept, idea, theory, logical proposition, etc.}, is the opposite of , while is the neutral (or indeterminate) between them, i.e., neither nor . Based on neutrosophy, the neutrosophic triplets were founded, which have a similar form (x, neut(x), anti(x)), that satisfy several axioms, for each element x in a given set. This collective book presents original research papers by many neutrosophic researchers from around the world, that report on the state-of-the-art and recent advancements of neutrosophic triplets, neutrosophic duplets, neutrosophic multisets and their algebraic structures – that have been defined recently in 2016 but have gained interest from world researchers. Connections between classical algebraic structures and neutrosophic triplet / duplet / multiset structures are also studied. And numerous neutrosophic applications in various fields, such as: multi-criteria decision making, image segmentation, medical diagnosis, fault diagnosis, clustering data, neutrosophic probability, human resource management, strategic planning, forecasting model, multi-granulation, supplier selection problems, typhoon disaster evaluation, skin lesson detection, mining algorithm for big data analysis, etc.

Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets, Volume II
Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets, Volume II

Author: Florentin Smarandache

Publisher: Infinite Study

Published:

Total Pages: 452

ISBN-13: 3038974765

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Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (, , ), where is an entity (i.e., element, concept, idea, theory, logical proposition, etc.), is the opposite of , while is the neutral (or indeterminate) between them, i.e., neither nor . Based on neutrosophy, the neutrosophic triplets were founded; they have a similar form: (x, neut(x), anti(x), that satisfy some axioms, for each element x in a given set. This book contains the successful invited submissions to a special issue of Symmetry, reporting on state-of-the-art and recent advancements of neutrosophic triplets, neutrosophic duplets, neutrosophic multisets, and their algebraic structures—that have been defined recently in 2016, but have gained interest from world researchers, and several papers have been published in first rank international journals.

Neutrosophic Triplet Non-Associative Semihypergroups with Application
Neutrosophic Triplet Non-Associative Semihypergroups with Application

Author: Muhammad Gulistan

Publisher: Infinite Study

Published:

Total Pages: 12

ISBN-13:

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In this paper, we extended the idea of a neutrosophic triplet set to non-associative semihypergroups and define neutrosophic triplet LA-semihypergroup.We discuss some basic results and properties. At the end, we provide an application of the proposed structure in Football.

The Encyclopedia of Neutrosophic Researchers, 2nd volume
The Encyclopedia of Neutrosophic Researchers, 2nd volume

Author: Florentin Smarandache

Publisher: Infinite Study

Published:

Total Pages: 111

ISBN-13:

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This is the second volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to my invitation. The introduction contains a short history of neutrosophics, together with links to the main papers and books.

Generalized Neutrosophic Extended Triplet Group
Generalized Neutrosophic Extended Triplet Group

Author: Yingcang Ma

Publisher: Infinite Study

Published:

Total Pages: 16

ISBN-13:

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Neutrosophic extended triplet group is a new algebra structure and is different from the classical group. In this paper, the notion of generalized neutrosophic extended triplet group is proposed and some properties are discussed.

Neutrosophic Sets and Systems, Book Series, Vol. 31, 2020. An International Book Series in Information Science and Engineering
Neutrosophic Sets and Systems, Book Series, Vol. 31, 2020. An International Book Series in Information Science and Engineering

Author: Florentin Smarandache

Publisher: Infinite Study

Published:

Total Pages: 318

ISBN-13:

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“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.