Pythagorean Neutrosophic Triplet Groups

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Pythagorean Neutrosophic Triplet Groups

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Author : Madad Khan
language : en
Publisher: Infinite Study
Release Date : 2024-01-01

Pythagorean Neutrosophic Triplet Groups written by Madad Khan and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-01 with Mathematics categories.

It is a well-known fact that groups are the only algebraic structures having a single binary operation that is mathematically so perfect that it is impossible to introduce a richer structure within it. The main purpose of this study is to introduce the notion of the Pythagorean neutrosophic triplet (PNT) which is the generalization of neutrosophic triplet (NT). The PNT is an algebraic structure of three ordered pairs that satisfy several properties under the binary operation (B-Operation) “*” . Furthermore, we used the PNTs to introduce the novel concept of a Pythagorean neutrosophic triplet group (PNTG). The algebraic structure (AS) of PNTG is different from the neutrosophic triplet group (NTG). We discussed some properties, related results, and particular examples of these novel concepts. We further studied Pythagorean neutro-homomorphism, Pythagorean neutro-isomorphism, etc., for PNTGs. Moreover, we discussed the main distinctions between the neutrosophic triplet group (NTG) and the PNTG.

Neutrosophic Sets And Systems Vol 67 2024

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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date : 2024-05-01

Neutrosophic Sets And Systems Vol 67 2024 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 2024-05-01 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.

Algebraic Structures Of Neutrosophic Triplets Neutrosophic Duplets Or Neutrosophic Multisets Volume Ii

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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date :

Algebraic Structures Of Neutrosophic Triplets Neutrosophic Duplets Or Neutrosophic Multisets Volume Ii 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 with Mathematics categories.

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

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Author : Florentin Smarandache
language : en
Publisher: MDPI
Release Date : 2019-04-04

Algebraic Structures Of Neutrosophic Triplets Neutrosophic Duplets Or Neutrosophic Multisets written by Florentin Smarandache and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-04 with Mathematics categories.

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 54 2023 Special Issue On Neutrosophic Algebraic Structures Neutroalgebra Antialgebra And Superhyperalgebra Neutrosophic Superhyperalgebra Contributions Of Researchers From The Arab World

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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date : 2024-02-01

Neutrosophic Sets And Systems Vol 54 2023 Special Issue On Neutrosophic Algebraic Structures Neutroalgebra Antialgebra And Superhyperalgebra Neutrosophic Superhyperalgebra Contributions Of Researchers From The Arab World 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 2024-02-01 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). In neutrosophic logic a proposition has a degree of truth (T), a degree of indeterminacy (I), and a degree of falsity (F), where T, I, F are standard or non-standard subsets of ]-0, 1+[. Neutrosophic Probability is a generalization of the classical probability and imprecise probability. Neutrosophic Statistics is a generalization of the classical statistics. What distinguishes the neutrosophics from other fields is the , which means neither nor . , which of course depends on , can be indeterminacy, neutrality, tie game, unknown, contradiction, ignorance, imprecision, etc.

Neutrosophic Sets And Systems Vol 30 2019

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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date :

Neutrosophic Sets And Systems Vol 30 2019 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 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.

Algebraic Structures Of Neutrosophic Triplets Neutrosophic Duplets Or Neutrosophic Multisets Volume I

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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date :

Algebraic Structures Of Neutrosophic Triplets Neutrosophic Duplets Or Neutrosophic Multisets Volume I 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 with Mathematics categories.

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 Book Series Vol 30 2019

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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date :

Neutrosophic Sets And Systems Book Series Vol 30 2019 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 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.

Neutrosophic Sets And Systems Vol 46 2021

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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date : 2021-10-19

Neutrosophic Sets And Systems Vol 46 2021 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 2021-10-19 with Antiques & Collectibles categories.

Papers on neutrosophic programming, neutrosophic hypersoft set, neutrosophic topological spaces, NeutroAlgebra, NeutroGeometry, AntiGeometry, NeutroNearRings, neutrosophic differential equations, etc.

Neutrosophic Set Is A Generalization Of Intuitionistic Fuzzy Set Inconsistent Intuitionistic Fuzzy Set Picture Fuzzy Set Ternary Fuzzy Set Pythagorean Fuzzy Set Spherical Fuzzy Set And Q Rung Orthopair Fuzzy Set While Neutrosophication Is A Generalization Of Regret Theory Grey System Theory And Three Ways Decision Revisited

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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date :

Neutrosophic Set Is A Generalization Of Intuitionistic Fuzzy Set Inconsistent Intuitionistic Fuzzy Set Picture Fuzzy Set Ternary Fuzzy Set Pythagorean Fuzzy Set Spherical Fuzzy Set And Q Rung Orthopair Fuzzy Set While Neutrosophication Is A Generalization Of Regret Theory Grey System Theory And Three Ways Decision Revisited 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 with Mathematics categories.

In this paper, we prove that Neutrosophic Set (NS) is an extension of Intuitionistic Fuzzy Set (IFS) no matter if the sum of neutrosophic components is <1, or >1, or =1. For the case when the sum of components is 1 (as in IFS), after applying the neutrosophic aggregation operators, one gets a different result than applying the intuitionistic fuzzy operators, since the intuitionistic fuzzy operators ignore the indeterminacy, while the neutrosophic aggregation operators take into consideration the indeterminacy at the same level as truth-membership and falsehood-nonmembership are taken.