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New Results On Neutrosophic Extended Triplet Groups Equipped With A Partial Order
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Book Synopsis New Results on Neutrosophic Extended Triplet Groups Equipped with a Partial Order by : Xin Zhou
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.
Book Synopsis NeutroAlgebra of Neutrosophic Triplets by : Vasantha Kandasamy
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.
Book Synopsis New Development of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, and Neutrosophic Plithogenic Optimizations by : Florentin Smarandache
Download or read book New Development of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, and Neutrosophic Plithogenic Optimizations written by Florentin Smarandache and published by Infinite Study. This book was released on 2022-09-01 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents state-of-the-art papers on new topics related to neutrosophic theories, such as neutrosophic algebraic structures, neutrosophic triplet algebraic structures, neutrosophic extended triplet algebraic structures, neutrosophic algebraic hyperstructures, neutrosophic triplet algebraic hyperstructures, neutrosophic n-ary algebraic structures, neutrosophic n-ary algebraic hyperstructures, refined neutrosophic algebraic structures, refined neutrosophic algebraic hyperstructures, quadruple neutrosophic algebraic structures, refined quadruple neutrosophic algebraic structures, neutrosophic image processing, neutrosophic image classification, neutrosophic computer vision, neutrosophic machine learning, neutrosophic artificial intelligence, neutrosophic data analytics, neutrosophic deep learning, and neutrosophic symmetry, as well as their applications in the real world.
Book Synopsis Generalized Neutrosophic Extended Triplet Group by : Yingcang Ma
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.
Book Synopsis Generalized Neutrosophic Extended Triplet Group by : Yingcang Ma
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.
Book Synopsis Neutrosophic Extended Triplet Group Based on Neutrosophic Quadruple Numbers by : Qiaoyan Li
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.
Book Synopsis ON NEUTROSOPHIC EXTENDED TRIPLET GROUP ACTION by : Moges Mekonnen Shalla
Download or read book ON NEUTROSOPHIC EXTENDED TRIPLET GROUP ACTION written by Moges Mekonnen Shalla and published by Infinite Study. This book was released on with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis discusses neutrosophic extended triplet (NET) direct product, semi-direct product and NET group actions. The aim is to give a clear introduction that provides a solid foundation for further studies into the subject. We introduce NET internal and external direct and semi-direct products for NET group by utilizing the notion of NET set theory of Smarandache. We also give examples and discuss their difference with the classical one.
Book Synopsis Collected Papers. Volume IX by : Florentin Smarandache
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.
Book Synopsis On neutrosophic extended triplet groups (loops) and Abel-Grassmann’s groupoids (AG-groupoids) by : Xiaohong Zhang
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.
Book Synopsis COMMUTATIVE NEUTROSOPHIC TRIPLET GROUP AND NEUTRO-HOMOMORPHISM BASIC THEOREM by : Xiaohong Zhang
Download or read book COMMUTATIVE NEUTROSOPHIC TRIPLET GROUP AND NEUTRO-HOMOMORPHISM BASIC THEOREM written by Xiaohong Zhang and published by Infinite Study. This book was released on with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we further study neutrosophic triplet group. First, to avoid confusion, some new symbols are introduced, and several basic properties of neutrosophic triplet group are rigorously proved (because the original proof is awed), and a result about neutrosophic triplet subgroup is revised. Second, some new properties of commutative neutrosophic triplet group are funded, and a new equivalent relation is established. Third, based on the previous results, the following important propositions are proved: from any commutative neutrosophic triplet group, an Abel group can be constructed; from any commutative neutrosophic triplet group, a BCI-algebra can be constructed. Moreover, some important examples are given. Finally, by using any neutrosophic triplet subgroup of a commutative neutrosophic triplet group, a new congruence relation is established, and then the quotient structure induced by neutrosophic triplet subgroup is constructed and the neutro-homomorphism basic theorem is proved.
Book Synopsis Neutrosophic Triplet Cosets and Quotient Groups by : Mikail Bal
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.
Book Synopsis Some Results on Neutrosophic Triplet Group and Their Applications by : Tèmítópé Gbóláhàn Jaíyéolá
Download or read book Some Results on Neutrosophic Triplet Group and Their Applications written by Tèmítópé Gbóláhàn Jaíyéolá and published by Infinite Study. This book was released on 2018-11-01 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: This article is based on new developments on a neutrosophic triplet group (NTG) and applications earlier introduced in 2016 by Smarandache and Ali. NTG sprang up from neutrosophic triplet set X: a collection of triplets (b, neut(b), anti(b)) for an b ∈ X that obeys certain axioms (existence of neutral(s) and opposite(s)). Some results that are true in classical groups were investigated in NTG and were shown to be either universally true in NTG or true in some peculiar types of NTG. Distinguishing features between an NTG and some other algebraic structures such as: generalized group (GG), quasigroup, loop and group were investigated. Some neutrosophic triplet subgroups (NTSGs) of a neutrosophic triplet group were studied. Applications of the neutrosophic triplet set, and our results on NTG in relation to management and sports, are highlighted and discussed.
Book Synopsis Direct and Semi-Direct Product of Neutrosophic Extended Triplet Group by : Moges Mekonnen Shalla
Download or read book Direct and Semi-Direct Product of Neutrosophic Extended Triplet Group written by Moges Mekonnen Shalla and published by Infinite Study. This book was released on with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: The object of this article is mainly to discuss the notion of neutrosophic extended triplet direct product (NETDP) and neutrosophic extended triplet semi-direct product (NETS-DP) of NET group. The purpose is to give a clear introduction that allows a solid foundation for additional studies into the field. We introduce neutrosophic extended triplet internal direct product (NETIDP) and neutrosophic extended triplet external direct products (NETEDP) of NET group. Then, we define NET internal and external semi-direct products for NET group by utilizing the notion of NET set theory of Smarandache. Moreover, some results related to NETDP and NETS-DPs are obtained.
Book Synopsis Neutrosophic Extended Triplet Group Action and Burnside’s Lemma by : Moges Mekonnen Shalla
Download or read book Neutrosophic Extended Triplet Group Action and Burnside’s Lemma written by Moges Mekonnen Shalla and published by Infinite Study. This book was released on with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this article is mainly to discuss the neutrosophic extended triplet (NET) group actions and Burnside’s lemma of NET group. We introduce NET orbits, stabilizers, conjugates and NET group action. Then, we give and proof the Orbit stabilizer formula for NET group by utilizing the notion of NET set theory. Moreover, some results related to NET group action, and Burnside’s lemma are obtained.
Book Synopsis Neutrosophic Duplet Semi-Group and Cancellable Neutrosophic Triplet Groups by : Xiaohong Zhang
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.
Book Synopsis The Decomposition Theorems of AG-Neutrosophic Extended Triplet Loops and Strong AG-(l, l)-Loops by : Xiaoying Wu
Download or read book The Decomposition Theorems of AG-Neutrosophic Extended Triplet Loops and Strong AG-(l, l)-Loops written by Xiaoying Wu and published by Infinite Study. This book was released on with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, some new properties of Abel Grassmann‘s Neutrosophic Extended Triplet Loop (AG-NET-Loop) were further studied. The following important results were proved: (1) an AG-NET-Loop is weakly commutative if, and only if, it is a commutative neutrosophic extended triplet (NETG); (2) every AG-NET-Loop is the disjoint union of its maximal subgroups. At the same time, the new notion of Abel Grassmann’s (l, l)-Loop (AG-(l, l)-Loop), which is the Abel-Grassmann’s groupoid with the local left identity and local left inverse, were introduced. The strong AG-(l, l)-Loops were systematically analyzed, and the following decomposition theorem was proved: every strong AG-(l, l)-Loop is the disjoint union of its maximal sub-AG-groups.
