Neutrosophic Algebraic Structures And Their Applications

Author : Florentin Smarandache,Memet Şahin,Derya Bakbak,Vakkas Uluçay,Abdullah Kargın
Publisher : Infinite Study
Page : 269 pages
File Size : 44,9 Mb
Release : 2022-08-01
Category : Mathematics
ISBN : 8210379456XXX

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Neutrosophic Algebraic Structures and Their Applications by Florentin Smarandache,Memet Şahin,Derya Bakbak,Vakkas Uluçay,Abdullah Kargın Pdf

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.

Author : Florentin Smarandache
Publisher : Unknown
Page : 0 pages
File Size : 42,8 Mb
Release : 2022
Category : Electronic
ISBN : OCLC:1404016901

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Neutrosophic Algebraic Structures and Their Applications by Florentin Smarandache Pdf

Author : S. Suryoto,Harjito,T. Udjiani
Publisher : Infinite Study
Page : 7 pages
File Size : 41,8 Mb
Release : 2024-06-27
Category : Mathematics
ISBN : 8210379456XXX

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The algebraic structure on the neutrosophic triplet set by S. Suryoto,Harjito,T. Udjiani Pdf

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.

Author : W. B. Vasantha Kandasamy,Florentin Smarandache
Publisher : Infinite Study
Page : 149 pages
File Size : 46,7 Mb
Release : 2004-01-01
Category : Mathematics
ISBN : 9781931233873

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Basic Neutrosophic Algebraic Structures and Their Application to Fuzzy and Neutrosophic Models by W. B. Vasantha Kandasamy,Florentin Smarandache Pdf

For the involvement of uncertainty of varying degrees, when the total of the membership degree exceeds one or less than one, then the newer mathematical paradigm shift, Fuzzy Theory proves appropriate.For the past two or three decades, Fuzzy Theory has become the potent tool to study and analyze uncertainty involved in all problems. But, many real world problems also abound with the concept of indeterminacy.In this book, the new, powerful tool of neutrosophy that deals with indeterminacy is utilized. Innovative neutrosophic models are described.The theory of neutrosophic graphs is introduced and applied to fuzzy and neutrosophic models.Neutrosophic Logic and Neutrosophic Set (generalizations of Intuitionistic Fuzzy Logic and Intuitionistic Fuzzy Set respectively) became strong tools for applications.

Author : W. B. Vasantha Kandasamy
Publisher : Hexis
Page : 150 pages
File Size : 51,8 Mb
Release : 2014-05-14
Category : MATHEMATICS
ISBN : 1461929733

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Basic Neutrosophic Algebraic Structures and Their Application to Fuzzy and Neutrosophic Models by W. B. Vasantha Kandasamy Pdf

Author : Florentin Smarandache,Xiaohong Zhang,Mumtaz Ali
Publisher : MDPI
Page : 478 pages
File Size : 44,7 Mb
Release : 2019-04-04
Category : Mathematics
ISBN : 9783038973843

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Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets by Florentin Smarandache,Xiaohong Zhang,Mumtaz Ali Pdf

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.

Author : Mamika Ujianita Romdhini,Ashraf Al-Quran,Faisal Al-Sharqi,Mohammad K. Tahat,Abdalwali Lutfi
Publisher : Infinite Study
Page : 14 pages
File Size : 42,7 Mb
Release : 2023-01-01
Category : Mathematics
ISBN : 8210379456XXX

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Exploring the Algebraic Structures of Q-Complex Neutrosophic Soft Fields by Mamika Ujianita Romdhini,Ashraf Al-Quran,Faisal Al-Sharqi,Mohammad K. Tahat,Abdalwali Lutfi Pdf

A field is a fundamental algebraic structure that finds extensive applications in algebra and various mathematical domains. On the other hand, a Q-complex neutrosophic soft set (Q-CNSS) is a unique hybrid model that combines the characteristics of soft sets and neutrosophic sets within a complex number framework. It utilizes the effectiveness of Q-set as a powerful tool in the domain of this particular model. In this article, we leverage this model to define fields under uncertainty. We present the Q-complex neutrosophic soft field (Q-CNSF) and examine the unique algebraic properties associated with this model. Additionally, we explore the relationships between Q-CNSF and Q-neutrosophic soft field (Q-NSF). Furthermore, we define the Cartesian product of QCNSFs and delve into the relevant properties. Through this comprehensive exploration, our aim is to enhance the understanding of Q-CNSFs and their properties, ultimately contributing to the field of algebraic analysis and its practical applications in handling uncertainty and vagueness.

Author : Vakkas Uluçay,Memet Sahin
Publisher : Infinite Study
Page : 17 pages
File Size : 50,6 Mb
Release : 2024-06-27
Category : Mathematics
ISBN : 8210379456XXX

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Neutrosophic Multigroups and Applications by Vakkas Uluçay,Memet Sahin Pdf

In recent years, fuzzy multisets and neutrosophic sets have become a subject of great interest for researchers and have been widely applied to algebraic structures include groups, rings, fields and lattices. Neutrosophic multiset is a generalization of multisets and neutrosophic sets. In this paper, we proposed a algebraic structure on neutrosophic multisets is called neutrosophic multigroups which allow the truth-membership, indeterminacy-membership and falsity-membership sequence have a set of real values between zero and one.

Author : Florentin Smarandache
Publisher : Infinite Study
Page : 11 pages
File Size : 54,5 Mb
Release : 2020-03-12
Category : Mathematics
ISBN : 8210379456XXX

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NeutroAlgebra is a Generalization of Partial Algebra by Florentin Smarandache Pdf

In this paper we recall, improve, and extend several definitions, properties and applications of our previous 2019 research referred to NeutroAlgebras and AntiAlgebras (also called NeutroAlgebraic Structures and respectively AntiAlgebraic Structures). Let be an item (concept, attribute, idea, proposition, theory, etc.). Through the process of neutrosphication, we split the nonempty space we work on into three regions {two opposite ones corresponding to and , and one corresponding to neutral (indeterminate) (also denoted ) between the opposites}, which may or may not be disjoint – depending on the application, but they are exhaustive (their union equals the whole space). A NeutroAlgebra is an algebra which has at least one NeutroOperation or one NeutroAxiom (axiom that is true for some elements, indeterminate for other elements, and false for the other elements). A Partial Algebra is an algebra that has at least one Partial Operation, and all its Axioms are classical (i.e. axioms true for all elements). Through a theorem we prove that NeutroAlgebra is a generalization of Partial Algebra, and we give examples of NeutroAlgebras that are not Partial Algebras. We also introduce the NeutroFunction (and NeutroOperation).

Author : Florentin Smarandache,Xiaohong Zhang,Mumtaz Ali
Publisher : MDPI
Page : 450 pages
File Size : 50,6 Mb
Release : 2019-04-04
Category : Mathematics
ISBN : 9783038974758

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Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets by Florentin Smarandache,Xiaohong Zhang,Mumtaz Ali Pdf

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.

Author : Florentin Smarandache,Xiaohong Zhang,Mumtaz Ali
Publisher : Infinite Study
Page : 450 pages
File Size : 44,6 Mb
Release : 2024-06-27
Category : Mathematics
ISBN : 9783038974765

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Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets, Volume II by Florentin Smarandache,Xiaohong Zhang,Mumtaz Ali Pdf

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.

Author : Mumtaz Ali,Florentin Smarandache,Muhammad Shabir
Publisher : Infinite Study
Page : 128 pages
File Size : 50,8 Mb
Release : 2024-06-27
Category : Electronic
ISBN : 9781599733067

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Soft Neutrosophic Algebraic Structures and Their Generalization, Vol. 2 by Mumtaz Ali,Florentin Smarandache,Muhammad Shabir Pdf

In this book, the authors define several new types of soft neutrosophic algebraic structures over neutrosophic algebraic structures and we study their generalizations. These soft neutrosophic algebraic structures are basically parameterized collections of neutrosophic sub-algebraic structures of the neutrosophic algebraic structure. An important feature of this book is that the authors introduce the soft neutrosophic group ring, soft neutrosophic semigroup ring with its generalization, and soft mixed neutrosophic N-algebraic structure over neutrosophic group ring, then the neutrosophic semigroup ring and mixed neutrosophic N-algebraic structure respectively.

Author : Florentin Smarandache
Publisher : Infinite Study
Page : 16 pages
File Size : 45,5 Mb
Release : 2024-06-27
Category : Mathematics
ISBN : 8210379456XXX

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Introduction to NeutroAlgebraic Structures and AntiAlgebraic Structures (revisited) by Florentin Smarandache Pdf

In all classical algebraic structures, the Laws of Compositions on a given set are well-defined. But this is a restrictive case, because there are many more situations in science and in any domain of knowledge when a law of composition defined on a set may be only partially-defined (or partially true) and partially-undefined (or partially false), that we call NeutroDefined, or totally undefined (totally false) that we call AntiDefined.

Author : W. B. Vasantha Kandasamy,Florentin Smarandache
Publisher : Infinite Study
Page : 220 pages
File Size : 48,8 Mb
Release : 2006-01-01
Category : Mathematics
ISBN : 9781931233156

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Some Neutrosophic Algebraic Structures and Neutrosophic N-Algebraic Structures by W. B. Vasantha Kandasamy,Florentin Smarandache Pdf

This book for the first time introduces neutrosophic groups, neutrosophic semigroups, neutrosophic loops and neutrosophic groupoids and their neutrosophic N-structures.The special feature of this book is that it tries to analyze when the general neutrosophic algebraic structures like loops, semigroups and groupoids satisfy some of the classical theorems for finite groups viz. Lagrange, Sylow, and Cauchy.This is mainly carried out to know more about these neutrosophic algebraic structures and their neutrosophic N-algebraic structures.

Author : Mohammad Abobala
Publisher : Infinite Study
Page : 8 pages
File Size : 49,8 Mb
Release : 2024-06-27
Category : Mathematics
ISBN : 8210379456XXX

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n-Refined Neutrosophic Groups I by Mohammad Abobala Pdf

The aim of this paper is to define for the first time the concept of n-refined neutrosophic group. This work is devoted to study some elementary properties of n-refined neutrosophic groups and to establish the algebraic basis of this structure such as n-refined neutrosophic subgroups, n-refined neutrosophic homomorphisms, and n-refined neutrosophic isomorphisms.