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The algebraic structure on the neutrosophic triplet set

Author: S. Suryoto

Publisher: Infinite Study

Published:

Total Pages: 7

ISBN-13:

The notion of the neutrosophic triplet was introduced by Smarandache and Ali. This notion is based on the fundamental law of neutrosophy that for an idea X, we have neutral of X denoted as neut(X) and anti of X denoted as anti(X). This paper studied a neutrosophic triplet set which is a collection of all triple of three elements that satisfy certain properties with some binary operation. Also given some interesting properties related to them. Further, in this paper investigated that from the neutrosophic triplet group can construct a classical group under multiplicative operation for ℤ𝑛 , for some specific n. These neutrosophic triplet groups are built using only modulo integer 2p, with p is an odd prime or Cayley table.

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

Author: Florentin Smarandache

Publisher: MDPI

Published: 2019-04-04

Total Pages: 478

ISBN-13: 303897384X

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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

Author: Florentin Smarandache

Publisher: Infinite Study

Published:

Total Pages: 450

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.

Study on the Development of Neutrosophic Triplet Ring and Neutrosophic Triplet Field

Author: Mumtaz Ali

Publisher: Infinite Study

Published:

Total Pages: 10

ISBN-13:

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Rings and fields are significant algebraic structures in algebra and both of them are based on the group structure. In this paper, we attempt to extend the notion of a neutrosophic triplet group to a neutrosophic triplet ring and a neutrosophic triplet field.

The Neutrosophic Triplet of BI-algebras

Author: Akbar Rezaei

Publisher: Infinite Study

Published: 2020-10-01

Total Pages: 9

ISBN-13:

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In this paper, the concepts of a Neutro-𝐵𝐼-algebra and Anti-𝐵𝐼-algebra are introduced, and some related properties are investigated. We show that the class of Neutro-𝐵𝐼-algebra is an alternative of the class of 𝐵𝐼-algebras.

The Neutrosophic Triplet of 𝑩𝑰-algebras

Author: Akbar Rezaei

Publisher: Infinite Study

Published: 2020-05-12

Total Pages: 9

ISBN-13:

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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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Neutrosophic Triplets in Neutrosophic Rings

Author: Vasantha Kandasamy W. B.

Publisher: Infinite Study

Published:

Total Pages: 9

ISBN-13:

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It is proved that these rings can contain only three types of neutrosophic triplets, these collections are distinct, and these collections form a torsion free abelian group as triplets under component wise product. However, these collections are not even closed under component wise addition.

NEUTROSOPHIC TRIPLET STRUCTURES, Volume I

Author: Florentin Smarandache

Publisher: Infinite Study

Published:

Total Pages: 21

ISBN-13:

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In this chapter, we introduce neutrosophic triplet cosets for neutrosophic triplet G-module and neutrosophic triplet quotient G-module. Then, we give some definitions and examples for neutrosophic triplet quotient G-module and neutrosophic triplet cosets. Also, we obtain isomorphism theorems for neutrosophic triplet G-modules and we prove isomorphism theorems for neutrosophic triplet G-modules.

Study on the Algebraic Structure of Refined Neutrosophic Numbers

Author: Qiaoyan Li

Publisher: Infinite Study

Published:

Total Pages: 13

ISBN-13:

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This paper aims to explore the algebra structure of refined neutrosophic numbers. Firstly, the algebra structure of neutrosophic quadruple numbers on a general field is studied. Secondly, The addition operator and multiplication operator on refined neutrosophic numbers are proposed and the algebra structure is discussed. We reveal that the set of neutrosophic refined numbers with an additive operation is an abelian group and the set of neutrosophic refined numbers with a multiplication operation is a neutrosophic extended triplet group. Moreover, algorithms for solving the neutral element and opposite elements of each refined neutrosophic number are given.