Author: S. Suryoto
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 7
Book Description
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.
The algebraic structure on the neutrosophic triplet set
Author: S. Suryoto
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 7
Book Description
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.
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 7
Book Description
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
ISBN: 3038974757
Category : Mathematics
Languages : en
Pages : 450
Book Description
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.
Publisher: MDPI
ISBN: 3038974757
Category : Mathematics
Languages : en
Pages : 450
Book Description
Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (,
Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets, Volume II
Author: Florentin Smarandache
Publisher: Infinite Study
ISBN: 3038974765
Category : Mathematics
Languages : en
Pages : 450
Book Description
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.
Publisher: Infinite Study
ISBN: 3038974765
Category : Mathematics
Languages : en
Pages : 450
Book Description
Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (,
Study on the Development of Neutrosophic Triplet Ring and Neutrosophic Triplet Field
Author: Mumtaz Ali
Publisher: Infinite Study
ISBN:
Category :
Languages : en
Pages : 10
Book Description
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.
Publisher: Infinite Study
ISBN:
Category :
Languages : en
Pages : 10
Book Description
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.
Study on the Algebraic Structure of Refined Neutrosophic Numbers
Author: Qiaoyan Li
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 13
Book Description
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.
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 13
Book Description
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.
Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets, Volume I
Author: Florentin Smarandache
Publisher: Infinite Study
ISBN: 3038973858
Category : Mathematics
Languages : en
Pages : 480
Book Description
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.
Publisher: Infinite Study
ISBN: 3038973858
Category : Mathematics
Languages : en
Pages : 480
Book Description
Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (,
Neutrosophic Triplets in Neutrosophic Rings
Author: Vasantha Kandasamy W. B.
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 9
Book Description
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.
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 9
Book Description
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.
NeutroAlgebra of Neutrosophic Triplets
Author: Vasantha Kandasamy
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 15
Book Description
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.
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 15
Book Description
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.
Neutrosophic Triplet Non-Associative Semihypergroups with Application
Author: Muhammad Gulistan
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 12
Book Description
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.
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 12
Book Description
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.
Some Results on Neutrosophic Triplet Group and Their Applications
Author: TèmĂtĂłpĂ© GbĂłláhĂ n JaĂyĂ©olá
Publisher: Infinite Study
ISBN:
Category :
Languages : en
Pages : 14
Book Description
Unified gauge theory has the algebraic structure of a generalized group abstrusely, in its physical background. It has been a challenge for physicists and mathematicians to find a desirable unified theory for twistor theory, isotopies theory, and so on.
Publisher: Infinite Study
ISBN:
Category :
Languages : en
Pages : 14
Book Description
Unified gauge theory has the algebraic structure of a generalized group abstrusely, in its physical background. It has been a challenge for physicists and mathematicians to find a desirable unified theory for twistor theory, isotopies theory, and so on.