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Open AccessArticle

Neutrosophic Duplet Semi-Group and Cancellable Neutrosophic Triplet Groups

1
Department of Mathematics, Shaanxi University of Science &Technology, Xi’an 710021, China
2
Department of Mathematics, Shanghai Maritime University, Shanghai 201306, China
3
Department of Mathematics, University of New Mexico, Gallup, NM 87301, USA
*
Author to whom correspondence should be addressed.
Symmetry 2017, 9(11), 275; https://doi.org/10.3390/sym9110275
Received: 14 October 2017 / Revised: 9 November 2017 / Accepted: 10 November 2017 / Published: 14 November 2017
(This article belongs to the Special Issue Neutrosophic Theories Applied in Engineering)
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. In this paper, we further study neutrosophic duplet sets, neutrosophic duplet semi-groups, and cancellable neutrosophic triplet groups. First, some new properties of neutrosophic duplet semi-groups are funded, and the following important result is proven: there is no finite neutrosophic duplet semi-group. Second, the new concepts of weak neutrosophic duplet, weak neutrosophic duplet set, and weak neutrosophic duplet semi-group are introduced, some examples are given by using the mathematical software MATLAB (MathWorks, Inc., Natick, MA, USA), and the characterizations of cancellable weak neutrosophic duplet semi-groups are established. Third, the cancellable neutrosophic triplet groups are investigated, and the following important result is proven: the concept of cancellable neutrosophic triplet group and group coincide. Finally, the neutrosophic triplets and weak neutrosophic duplets in BCI-algebras are discussed. View Full-Text
Keywords: neutrosophic duplet; neutrosophic triplet; weak neutrosophic duplet; semi-group; BCI-algebra neutrosophic duplet; neutrosophic triplet; weak neutrosophic duplet; semi-group; BCI-algebra
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Zhang, X.; Smarandache, F.; Liang, X. Neutrosophic Duplet Semi-Group and Cancellable Neutrosophic Triplet Groups. Symmetry 2017, 9, 275.

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