Some Neutrosophic Algebraic Structures And Neutrosophic N Algebraic Structures

Author : W. B. Vasantha Kandasamy,Florentin Smarandache
Publisher : Infinite Study
Page : 220 pages
File Size : 55,6 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 : W. B. Vasantha Kandasamy
Publisher : Unknown
Page : 220 pages
File Size : 42,9 Mb
Release : 2014-05-14
Category : MATHEMATICS
ISBN : 1461929997

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

Author : S. Suryoto,Harjito,T. Udjiani
Publisher : Infinite Study
Page : 7 pages
File Size : 48,7 Mb
Release : 2024-06-30
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 : Mumtaz Ali,Florentin Smarandache,Muhammad Shabir
Publisher : Infinite Study
Page : 128 pages
File Size : 55,8 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 9781599733135

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New Research on Neutrosophic Algebraic Structures by Mumtaz Ali,Florentin Smarandache,Muhammad Shabir Pdf

In this book, we define several new neutrosophic algebraic structures and their related properties. The main focus of this book is to study the important class of neutrosophic rings such as neutrosophic LA-semigroup ring, neutrosophic loop ring, neutrosophic groupoid ring and so on. We also construct their generalization in each case to study these neutrosophic algebraic structures in a broader sense. The indeterminacy element “I“ gives rise to a bigger algebraic structure than the classical algebraic structures. It mainly classifies the algebraic structures in three categories such as: neutrosophic algebraic structures, strong neutrosophic algebraic structures, and classical algebraic structures respectively. This reveals the fact that a classic algebraic structure is a part of the neutrosophic algebraic structures. This opens a new way for the researcher to think in a broader way to visualize these vast neutrosophic algebraic structures.

Author : Mumtaz Ali,Florentin Smarandache,Muhammad Shabir
Publisher : Infinite Study
Page : 128 pages
File Size : 40,9 Mb
Release : 2024-06-30
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 : W. B. Vasantha Kandasamy
Publisher : Infinite Study
Page : 203 pages
File Size : 45,7 Mb
Release : 2006-01-01
Category : Mathematics
ISBN : 9781931233163

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Smarandache Neutrosophic Algebraic Structures by W. B. Vasantha Kandasamy Pdf

Smarandache algebraic structures that inter-relates two distinct algebraic structures and analyzes them relatively can be considered a paradigm shift in the study of algebraic structures. For instance, the algebraic structure Smarandache semigroup simultaneously involves both group and semigroup.Recently, Neutrosophic Algebraic Structures were introduced. This book ventures to define Smarandache Neutrosophic Algebraic Structures.Here, Smarandache neutrosophic structures of groups, semigroups, loops and groupoids and their N-ary structures are introduced and analyzed. There is a lot of scope for interested researchers to develop these concepts.

Author : Mohammad Abobala
Publisher : Infinite Study
Page : 8 pages
File Size : 54,5 Mb
Release : 2024-06-30
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.

Author : Phattharaphon Rangsuk,Pattarin Huana, Aiyared Iampan
Publisher : Infinite Study
Page : 41 pages
File Size : 46,7 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 8210379456XXX

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Neutrosophic N-structures over UP-algebras by Phattharaphon Rangsuk,Pattarin Huana, Aiyared Iampan Pdf

Among many algebraic structures, algebras of logic form important class of algebras. Examples of these are BCK-algebras, BCI-algebras, BCH-algebras, KU-algebras [28], SU-algebras and others.

Author : Adel Mohammad Al-Odhari
Publisher : Infinite Study
Page : 12 pages
File Size : 47,8 Mb
Release : 2024-01-01
Category : Mathematics
ISBN : 8210379456XXX

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The Computations of Algebraic Structure of Neutrosophic Determinants by Adel Mohammad Al-Odhari Pdf

This paper aims to make a valuable contribution to the field of neutrosophic determinants and their properties. By utilizing neutrosophic real numbers in the form of a+bI, we provide an alternative approach to recent research on determinants conducted between 2020 and 2023. Our goal is to expand the scope of academic content being developed in the theory of neutrosophic linear algebra. Additionally, we seek to complement our work on some algebraic structures of neutrosophic matrices.

Author : Florentin Smarandache,Xiaohong Zhang,Mumtaz Ali
Publisher : MDPI
Page : 450 pages
File Size : 40,7 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 : 50,9 Mb
Release : 2024-06-30
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 : V.S. Subha,G. Rajasekar, S. Soundaravalli
Publisher : Infinite Study
Page : 8 pages
File Size : 48,9 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 8210379456XXX

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Algebraic Structures of Semigroup by Rough Neutrosophic Ideals by V.S. Subha,G. Rajasekar, S. Soundaravalli Pdf

In this article, we will look at the definition of rough neutrosophic set in semigroups and investigate their properties. We also introduce the concept of rough Neutrosophic (right,left,two-sided,bi-) ideals in a semigroup and study some properties of the ideals of semigroup.

Author : Florentin Smarandache,Memet Şahin,Derya Bakbak,Vakkas Uluçay,Abdullah Kargın
Publisher : Infinite Study
Page : 269 pages
File Size : 55,5 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 : T. Chalapathi,R. V. M. S. S. Kiran Kumar
Publisher : Infinite Study
Page : 8 pages
File Size : 47,7 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 8210379456XXX

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Neutrosophic Units of Neutrosophic Rings and Fields by T. Chalapathi,R. V. M. S. S. Kiran Kumar Pdf

In recent years, the inter connection between classical structures and Neutrosophic structures is studied by few researchers. For such kind of study, researchers defined new algebraic structures whose elements are generated by elements in classical algebraic set and indeterminate of the real world problem with respect to algebraic operations on the well defined Neutrosophic elements.

Author : W. B. Vasantha Kandasamy,Florentin Smarandache
Publisher : Infinite Study
Page : 209 pages
File Size : 54,5 Mb
Release : 2005-01-01
Category : Mathematics
ISBN : 9781931233057

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

In this book, for the first time we introduce the notions of N-groups, N-semigroups, N-loops and N-groupoids. We also define a mixed N-algebraic structure. The book is organized into six chapters. The first chapter gives the basic notions of S-semigroups, S-groupoids and S-loops thereby making the book self-contained. Chapter two introduces N-groups and their Smarandache analogues. In chapter three, N-loops and Smarandache N-loops are introduced and analyzed. Chapter four defines N-groupoids and S-N-groupoids. Since the N-semigroup structures are sandwiched between groups and groupoids, the study can be carried out without any difficulty. Mixed N-algebraic structures and S-mixed algebraic structures are given in chapter five. Some problems are suggested in chapter six. It is pertinent to mention that several exercises and problems (Some in the form of proof to the theorems are given in all the chapters.) A reader who attempts to solve them will certainly gain a sound knowledge about these concepts. We have given 50 problems for the reader to solve in chapter 6. The main aim of this book is to introduce new concepts and explain them with examples there by encouraging young mathematics to pursue research in this direction. Several theorems based on the definition can be easily proved with simple modification. Innovative readers can take up that job. Also these notions find their applications in automaton theory and coloring problems. The N-semigroups and N-automaton can be applied to construct finite machines, which can perform multitasks, so their capability would be much higher than the usual automaton of finite machines constructed. We have suggested a list of references for further reading.