Download or read book Algebraic Structures of Semigroup by Rough Neutrosophic Ideals written by V.S. Subha and published by Infinite Study. This book was released on with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Fuzzy and Neutrosophic Sets in Semigroups written by Young Bae Jun and published by Infinite Study. This book was released on 2018-01-01 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topics discussed in this book are Int-soft semigroup, Int-soft left (right) ideal, Int-soft (generalized) bi-ideal, Int-soft quasi-ideal, Int-soft interior ideal, Int-soft left (right) duo semigroup, starshaped (∈, ∈∨ qk)-fuzzy set, quasi-starshaped (∈, ∈∨ qk)-fuzzy set, semidetached mapping, semidetached semigroup, (∈, ∈ ∨qk)-fuzzy subsemi-group, (qk, ∈ ∨qk)-fuzzy subsemigroup, (∈, ∈ ∨ qk)-fuzzy subsemigroup, (qk, ∈ ∨ qk)-fuzzy subsemigroup, (∈ ∨ qk, ∈ ∨ qk)-fuzzy subsemigroup, (∈, ∈∨ qkδ)-fuzzy subsemigroup, ∈∨ qkδ -level subsemigroup/bi-ideal, (∈, ∈∨ qkδ )-fuzzy (generalized) bi-ideal, δ-lower (δ-upper) approximation of fuzzy set, δ-lower (δ-upper) rough fuzzy subsemigroup, δ-rough fuzzy subsemigroup, Neutrosophic N -structure, neutrosophic N -subsemigroup, ε-neutrosophic N -subsemigroup, and neutrosophic N -product.

Download or read book Algebraic Structures of Neutrosophic Triplets Neutrosophic Duplets or Neutrosophic Multisets Volume II written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Algebraic Structures of Neutrosophic Triplets Neutrosophic Duplets or Neutrosophic Multisets written by Florentin Smarandache and published by MDPI. This book was released on 2019-04-04 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Smarandache Neutrosophic Algebraic Structures written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2006-01-01 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Algebraic Structures on Fuzzy Unit Square and Neutrosophic Unit Square written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2014 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book authors build algebraic structures on fuzzy unit semi-open square UF = {(a,b), with a, b in [0, 1)} and on neutrosophic unit semi-open square UN = {a+bI, with a, b in [0, 1)}. As distributive laws are not true, we are not in a position to develop several properties of rings, semirigs and linear algebras. Seven open conjectures are proposed.

Download or read book Neutrosophic Set Approach to Algebraic Structures written by Madad Khan and published by Infinite Study. This book was released on with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of seven chapters. In chapter one we introduced neutrosophic ideals (bi, quasi, interior, (m,n) ideals) and discussed the properties of these ideals. Moreover, we characterized regular and intra-regular AG-groupoids using these ideals. In chapter two we introduced neutrosophic minimal ideals in AG-groupoids and discussed several properties. In chapter three, we introduced different neutrosophic regularities of AG-groupoids. Further we discussed several condition where these classes are equivalent. In chapter four, we introduced neutrosophic M-systems and neutrosophic p-systems in non-associative algebraic structure and discussed their relations with neutrosophic ideals. In chapter five, we introduced neutrosophic strongly regular AG-groupoids and characterized this structure using neutrosophic ideals. In chapter six, we introduced the concept of neutrosophic ideal, neutrosophic prime ideal, neutrosophic bi-ideal and neutrosophic quasi ideal of a neutrosophic semigroup. With counter example we have shown that the union and product of two neutrosophic quasi-ideals of a neutrosophic semigroup need not be a neutrosophic quasi-ideal of neutrosophic semigroup. We have also shown that every neutrosophic bi-ideal of a neutrosophic semigroup need not be a neutrosophic quasi-ideal of a neutrosophic semigroup. We have also characterized the regularity and intra-regularity of a neutrosophic semigroup. In chapter seven, we introduced neutrosophic left almost rings and discussed several properties using their neutrosophic ideals. Keywords: neutrosophic set, algebraic structure, neutrosophic ideal, AG-groupoids, neutrosophic minimal ideals, neutrosophic regularities, neutrosophic M-systems, neutrosophic p-systems, neutrosophic strongly regular AG-groupoids neutrosophic prime ideal, neutrosophic bi-ideal, neutrosophic quasi ideal, neutrosophic semigroup, neutrosophic left almost rings

Download or read book Neutrosophic Sets and Systems Vol VII written by Florentin Smarandache, Mumtaz Ali and published by Infinite Study. This book was released on 2015-02-01 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: Twelve papers on soft interval-valued neutrosophic rough sets, fuzzy neutosophic relation equations with geometric programming, rough neutrosophic multi-attribute decision-making, classes of neutrosophic crisp nearly open sets and possible application to GIS topology, neutrosophic probability in physics, and similar topics. Contributors: H. E. Khalid, K. Mondal, S. Pramanik, A. A. Salama, S. Broumi, F. Smarandache, F. Yuhua, M. Ali, M. Shabir, V. Patrascu, S. Ye, J. Fu, J. Ye, A. Hussain, and L. Vladareanu.

Download or read book Neutrosophic Sets and Systems vol 3 2014 written by Fu Yuhua and published by Infinite Study. This book was released on with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: “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.

Download or read book Neutrosophic Sets and Systems vol 7 2015 written by H. E. Khalid and published by Infinite Study. This book was released on with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: “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.

Download or read book N Algebraic Structures written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2005-01-01 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Applications of Neutrosophic N Structures In Ternary Semigroups written by Amornrat Rattana and published by Infinite Study. This book was released on with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, the notions of neutrosophic N -ternary subsemigroups of ternary semigroups are introduced and several properties are investigated.

Download or read book Basic Neutrosophic Algebraic Structures and Their Application to Fuzzy and Neutrosophic Models written by W. B. Vasantha Kandasamy and published by Hexis. This book was released on 2014-05-14 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Algebraic Structures of Neutrosophic Triplets Neutrosophic Duplets or Neutrosophic Multisets Volume I written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Algebraic Structures on Real and Neutrosophic Semi Open Squares written by W. B. Vasantha Kandasamy and published by . This book was released on 2014 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Neutrosophic Sets and Systems Vol III written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of ten papers, written by different authors and co-authors (listed in the order of the papers): F. Yuhua, A. A. Salama, F. Smarandache, S. A. Alblowi, M. Ali, M. Shabir, M. Naz, A. A. A. Agboola, S. A. Akinleye, M. Dhar, S. Broumi, P. Biswas, S. Pramanik, B. C. Giri, H. A. El-Ghareeb, A. M. Maine, V. Kandasamy, P. Sekar and J. Vidhyalakshmi. In first paper, the author proposed Expanding Newton Mechanics with Neutrosophy and Quad-stage Method-New Newton Mechanics Taking Law of Conservation of Energy as Unique Source Law. The Characteristic Function of a Neutrosophic Set is proposed in the second paper. Neutrosophic Left Almost Semigroup is studied in third paper. In fourth paper Neutrosophic Hypercompositional Structures defined by Binary Relations are introduced. Similarly in fifth paper A Note on Square Neutrosophic Fuzzy Matrices are discussed. In paper six A New Methodology for Neutrosophic Multi-Attribute Decision-Making with Unknown Weight Information is presented by the authors. Introduction to Develop Some Software Programs for dealing with Neutrosophic Sets is given in seventh paper. Paper eight is about to Soft Neutrosophic Ring and Soft Neutrosophic Field. In the next paper Rough Neutrosophic Sets are discussed. The authors introduced new type of Fuzzy Relational Equations and Neutrosophic Relational Equations-To Analyze Customer Preference to street shops in the last paper.

Download or read book The Algebraic Theory of Semigroups Volume I written by Alfred Hoblitzelle Clifford and published by American Mathematical Soc.. This book was released on 1961-12-31 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: The material in this volume was presented in a second-year graduate course at Tulane University, during the academic year 1958-1959. The book aims at being largely self-contained, but it is assumed that the reader has some familiarity with sets, mappings, groups, and lattices. Only in Chapter 5 will more preliminary knowledge be required, and even there the classical definitions and theorems on the matrix representations of algebras and groups are summarized.