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Open AccessArticle

Symmetry in Hyperstructure: Neutrosophic Extended Triplet Semihypergroups and Regular Hypergroups

1
Department of Mathematics, Shaanxi University of Science & Technology, Xi’an 710021, China
2
Department of Mathematics, University of New Mexico, 705 Gurley Avenue, Gallup, NM 87301, USA
3
School of Science, Xi’an Polytechnic University, Xi’an 710048, China
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(10), 1217; https://doi.org/10.3390/sym11101217
Received: 28 August 2019 / Revised: 22 September 2019 / Accepted: 25 September 2019 / Published: 1 October 2019
The symmetry of hyperoperation is expressed by hypergroup, more extensive hyperalgebraic structures than hypergroups are studied in this paper. The new concepts of neutrosophic extended triplet semihypergroup (NET- semihypergroup) and neutrosophic extended triplet hypergroup (NET-hypergroup) are firstly introduced, some basic properties are obtained, and the relationships among NET- semihypergroups, regular semihypergroups, NET-hypergroups and regular hypergroups are systematically are investigated. Moreover, pure NET-semihypergroup and pure NET-hypergroup are investigated, and a strucuture theorem of commutative pure NET-semihypergroup is established. Finally, a new notion of weak commutative NET-semihypergroup is proposed, some important examples are obtained by software MATLAB, and the following important result is proved: every pure and weak commutative NET-semihypergroup is a disjoint union of some regular hypergroups which are its subhypergroups.
Keywords: hypergroup; semihypergroup; neutrosophic extended triplet group; neutrosophic extended triplet semihypergroup (NET-semihypergroup); NET-hypergroup hypergroup; semihypergroup; neutrosophic extended triplet group; neutrosophic extended triplet semihypergroup (NET-semihypergroup); NET-hypergroup
MDPI and ACS Style

Zhang, X.; Smarandache, F.; Ma, Y. Symmetry in Hyperstructure: Neutrosophic Extended Triplet Semihypergroups and Regular Hypergroups. Symmetry 2019, 11, 1217.

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