Download or read book A Classical Group of Neutrosophic Triplet Groups written by Vasantha KandasamyW.B. and published by Infinite Study. This book was released on with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fuzzy set theory was introduced by Zadeh and was generalized to the Intuitionistic Fuzzy Set (IFS) by Atanassov. Real-world, uncertain, incomplete, indeterminate, and inconsistent data were presented philosophically as a neutrosophic set by Smarandache, who also studied the notion of neutralities that exist in all problems.

Download or read book Neutrosophic Triplet Groups and their Applications to Mathematical Modelling written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2017 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book we define new operations mainly to construct mathematical models akin to Fuzzy Cognitive Maps (FCMs) model, Neutrosophic Cognitive Maps (NCMs) model and Fuzzy Relational Maps (FRMs) model. These new models are defined in chapter four of this book. These new models can find applications in discrete Artificial Neural Networks, soft computing, and social network analysis whenever the concept of indeterminate is involved.

Download or read book Neutrosophic Triplet Cosets and Quotient Groups written by Mikail Bal and published by Infinite Study. This book was released on with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book The algebraic structure on the neutrosophic triplet set written by S. Suryoto and published by Infinite Study. This book was released on with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Generalized Neutrosophic Extended Triplet Group written by Yingcang Ma and published by Infinite Study. This book was released on with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: Neutrosophic extended triplet group is a new algebra structure and is different from the classical group. In this paper, the notion of generalized neutrosophic extended triplet group is proposed and some properties are discussed.

Download or read book Neutrosophic Duplet Semi Group and Cancellable Neutrosophic Triplet Groups written by Xiaohong Zhang and published by Infinite Study. This book was released on with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: The notions of the neutrosophic triplet and neutrosophic duplet were introduced by Florentin Smarandache. From the existing research results, the neutrosophic triplets and neutrosophic duplets are completely different from the classical algebra structures.

Download or read book Generalized Neutrosophic Extended Triplet Group written by Yingcang Ma and published by Infinite Study. This book was released on with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: Neutrosophic extended triplet group is a new algebra structure and is different from the classical group. In this paper, the notion of generalized neutrosophic extended triplet group is proposed and some properties are discussed.

Download or read book NeutroAlgebra of Neutrosophic Triplets written by Vasantha Kandasamy and published by Infinite Study. This book was released on 2020-12-01 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, authors define the NeutroAlgebra of neutrosophic triplets groups. We prove the existence theorem for NeutroAlgebra of neutrosophic triplet groups. Several open problems are proposed. Further, the NeutroAlgebras of extended neutrosophic triplet groups have been obtained.

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 478 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 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 Neutrosophic Extended Triplet Group Based on Neutrosophic Quadruple Numbers written by Qiaoyan Li and published by Infinite Study. This book was released on with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we explore the algebra structure based on neutrosophic quadruple numbers. Moreover, two kinds of degradation algebra systems of neutrosophic quadruple numbers are introduced. In particular, the following results are strictly proved: (1) the set of neutrosophic quadruple numbers with a multiplication operation is a neutrosophic extended triplet group; (2) the neutral element of each neutrosophic quadruple number is unique and there are only sixteen different neutral elements in all of neutrosophic quadruple numbers; (3) the set which has same neutral element is closed with respect to the multiplication operator; (4) the union of the set which has same neutral element is a partition of four-dimensional space.

Download or read book New Results on Neutrosophic Extended Triplet Groups Equipped with a Partial Order written by Xin Zhou and published by Infinite Study. This book was released on with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: Neutrosophic extended triplet group (NETG) is a novel algebra structure and it is different from the classical group. The major concern of this paper is to present the concept of a partially ordered neutrosophic extended triplet group (po-NETG), which is a NETG equipped with a partial order that relates to its multiplicative operation, and consider properties and structure features of po-NETGs.

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 Left Right Quasi Neutrosophic Triplet Loops Groups and Generalized BE Algebras written by Xiaohong Zhang and published by Infinite Study. This book was released on with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: The new notion of a neutrosophic triplet group (NTG) is proposed by Florentin Smarandache; it is a new algebraic structure different from the classical group.

Download or read book On neutrosophic extended triplet groups loops and Abel Grassmann s groupoids AG groupoids written by Xiaohong Zhang and published by Infinite Study. This book was released on with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the perspective of semigroup theory, the characterizations of a neutrosophic extended triplet group (NETG) and AG-NET-loop (which is both an Abel-Grassmann groupoid and a neutrosophic extended triplet loop) are systematically analyzed and some important results are obtained. In particular, the following conclusions are strictly proved: (1) an algebraic system is neutrosophic extended triplet group if and only if it is a completely regular semigroup; (2) an algebraic system is weak commutative neutrosophic extended triplet group if and only if it is a Clifford semigroup; (3) for any element in an AG-NET-loop, its neutral element is unique and idempotent; (4) every AG-NET-loop is a completely regular and fully regular Abel-Grassmann groupoid (AG-groupoid), but the inverse is not true. Moreover, the constructing methods of NETGs (completely regular semigroups) are investigated, and the lists of some finite NETGs and AG-NET-loops are given.

Download or read book Neutrosophic Triplet Cosets and Quotient Groups written by Mikail Bal and published by Infinite Study. This book was released on with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Collected Papers Volume IX written by Florentin Smarandache and published by Infinite Study. This book was released on 2022-05-10 with total page 1008 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ninth volume of Collected Papers includes 87 papers comprising 982 pages on Neutrosophic Theory and its applications in Algebra, written between 2014-2022 by the author alone or in collaboration with the following 81 co-authors (alphabetically ordered) from 19 countries: E.O. Adeleke, A.A.A. Agboola, Ahmed B. Al-Nafee, Ahmed Mostafa Khalil, Akbar Rezaei, S.A. Akinleye, Ali Hassan, Mumtaz Ali, Rajab Ali Borzooei , Assia Bakali, Cenap Özel, Victor Christianto, Chunxin Bo, Rakhal Das, Bijan Davvaz, R. Dhavaseelan, B. Elavarasan, Fahad Alsharari, T. Gharibah, Hina Gulzar, Hashem Bordbar, Le Hoang Son, Emmanuel Ilojide, Tèmítópé Gbóláhàn Jaíyéolá, M. Karthika, Ilanthenral Kandasamy, W.B. Vasantha Kandasamy, Huma Khan, Madad Khan, Mohsin Khan, Hee Sik Kim, Seon Jeong Kim, Valeri Kromov, R. M. Latif, Madeleine Al-Tahan, Mehmat Ali Ozturk, Minghao Hu, S. Mirvakili, Mohammad Abobala, Mohammad Hamidi, Mohammed Abdel-Sattar, Mohammed A. Al Shumrani, Mohamed Talea, Muhammad Akram, Muhammad Aslam, Muhammad Aslam Malik, Muhammad Gulistan, Muhammad Shabir, G. Muhiuddin, Memudu Olaposi Olatinwo, Osman Anis, Choonkil Park, M. Parimala, Ping Li, K. Porselvi, D. Preethi, S. Rajareega, N. Rajesh, Udhayakumar Ramalingam, Riad K. Al-Hamido, Yaser Saber, Arsham Borumand Saeid, Saeid Jafari, Said Broumi, A.A. Salama, Ganeshsree Selvachandran, Songtao Shao, Seok-Zun Song, Tahsin Oner, M. Mohseni Takallo, Binod Chandra Tripathy, Tugce Katican, J. Vimala, Xiaohong Zhang, Xiaoyan Mao, Xiaoying Wu, Xingliang Liang, Xin Zhou, Yingcang Ma, Young Bae Jun, Juanjuan Zhang.