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New Results on Neutrosophic Extended Triplet Groups Equipped with a Partial Order

1
School of Science, Xi’an Polytechnic University, Xi’an 710048, China
2
Departmet of Mathematics, University of New Mexico, 705 Gurley Ave., Gallup, NM 87301, USA
3
College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, China
4
Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(12), 1514; https://doi.org/10.3390/sym11121514
Received: 13 November 2019 / Revised: 9 December 2019 / Accepted: 10 December 2019 / Published: 13 December 2019
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. Firstly, in a po-NETG, we propose the concepts of the positive cone and negative cone, and investigate the structure features of them. Secondly, we study the specificity of the positive cone in a partially ordered weak commutative neutrosophic extended triplet group (po-WCNETG). Finally, we introduce the concept of a po-NETG homomorphism between two po-NETGs, construct a po-NETG on a quotient set by providing a multiplication and a partial order, then we discuss some fundamental properties of them. View Full-Text
Keywords: partially ordered neutrosophic extended triplet group; positive cone; homomorphism; quotient set partially ordered neutrosophic extended triplet group; positive cone; homomorphism; quotient set
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MDPI and ACS Style

Zhou, X.; Li, P.; Smarandache, F.; Khalil, A.M. New Results on Neutrosophic Extended Triplet Groups Equipped with a Partial Order. Symmetry 2019, 11, 1514. https://doi.org/10.3390/sym11121514

AMA Style

Zhou X, Li P, Smarandache F, Khalil AM. New Results on Neutrosophic Extended Triplet Groups Equipped with a Partial Order. Symmetry. 2019; 11(12):1514. https://doi.org/10.3390/sym11121514

Chicago/Turabian Style

Zhou, Xin; Li, Ping; Smarandache, Florentin; Khalil, Ahmed M. 2019. "New Results on Neutrosophic Extended Triplet Groups Equipped with a Partial Order" Symmetry 11, no. 12: 1514. https://doi.org/10.3390/sym11121514

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