› › Neutrosophic Triplet Normed Space

Neutrosophic Triplet m-Banach Spaces

Author : Abdullah Kargın

Publisher : Infinite Study

Page : 16 pages

File Size : 12,6 MB

Release : 2020-12-01

Category : Mathematics

ISBN :

Get eBook

Book Description

Neutrosophic triplet theory has an important place in neutrosophic theory. Since the neutrosophic triplet set (Nts), which have the feature of having multiple unit elements, have different units than the classical unit, they have more features than the classical set. Also, Banach spaces are complete normed vector space defined by real and complex numbers that are studied historically in functional analysis. Thus, normed space and Banach space have an important place in functional analysis. In this article, neutrosophic triplet m-Banach spaces (NtmBs) are firstly obtained. Then, some definitions and examples are given for NtmBs. Based on these definitions, new theorems are given and proved. In addition, it is shown that NtmBs is different from neutrosophic triplet Banach space (NtBs). Furthermore, it is shown that relationship between NtmBs and NtBs. So, we added a new structure to functional analysis and neutrosophic triplet theory.



NEUTROSOPHIC TRIPLET STRUCTURES, Volume I

Author : Florentin Smarandache

Publisher : Infinite Study

Page : 199 pages

File Size : 36,79 MB

Release : 2019

Category : Mathematics

ISBN : 1599735954

Get eBook

Book Description

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 Triplet Partial v-Generalized Metric Space

Author : Memet Şahin

Publisher : Infinite Study

Page : 20 pages

File Size : 45,92 MB

Release :

Category : Mathematics

ISBN :

Get eBook

Book Description

In this chapter, study the notion of neutrosophic triplet partial v-generalized metric space. Then, we give some definitions and examples for neutrosophic triplet partial v-generalized metric space and obtain some properties and prove these properties. Furthermore, we show that neutrosophic triplet partial v-generalized metric space is different from neutrosophic triplet v-generalized metric space and neutrosophic triplet partial metric space.



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

Author : Florentin Smarandache

Publisher : Infinite Study

Page : 480 pages

File Size : 22,36 MB

Release :

Category : Mathematics

ISBN : 3038973858

Get eBook

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.



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

Author : Florentin Smarandache

Publisher : Infinite Study

Page : 452 pages

File Size : 41,4 MB

Release :

Category : Mathematics

ISBN : 3038974765

Get eBook

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.



Neutrosophic Sets and Systems, Vol. 38, 2020

Author : Florentin Smarandache

Publisher : Infinite Study

Page : 662 pages

File Size : 15,85 MB

Release :

Category : Mathematics

ISBN :

Get eBook

Book Description

“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.



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

Author : Florentin Smarandache

Publisher : MDPI

Page : 450 pages

File Size : 15,85 MB

Release : 2019-04-04

Category : Mathematics

ISBN : 3038974757

Get eBook

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.



Neutrosophic Sets and Systems, Vol. 33, 2020

Author : Florentin Smarandache

Publisher : Infinite Study

Page : 353 pages

File Size : 34,75 MB

Release :

Category : Mathematics

ISBN :

Get eBook

Book Description

“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. Some articles in this issue: Extension of HyperGraph to n-SuperHyperGraph and to Plithogenic n-SuperHyperGraph, and Extension of HyperAlgebra to n-ary (Classical-/Neutro-/Anti-)HyperAlgebra, Neutrosophic Triplet Partial Bipolar Metric Spaces, The Neutrosophic Triplet of BI-algebras.



Neutrosophic Triplet Cosets and Quotient Groups

Author : Mikail Bal

Publisher : Infinite Study

Page : 13 pages

File Size : 17,23 MB

Release :

Category : Mathematics

ISBN :

Get eBook

Book Description

In this paper, by utilizing the concept of a neutrosophic extended triplet (NET), we define the neutrosophic image, neutrosophic inverse-image, neutrosophic kernel, and the NET subgroup. The notion of the neutrosophic triplet coset and its relation with the classical coset are defined and the properties of the neutrosophic triplet cosets are given. Furthermore, the neutrosophic triplet normal subgroups, and neutrosophic triplet quotient groups are studied.



Neutrosophic Sets and Systems: An International Book Series in Information Science and Engineering, vol. 21 / 2018

Author : Florentin Smarandache

Publisher : Infinite Study

Page : 168 pages

File Size : 42,90 MB

Release : 2018

Category : Mathematics

ISBN : 1599735814

Get eBook

Book Description

“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.