Neutrosophic Extended Triplet Group Based on Neutrosophic Quadruple Numbers

• Main Authors: Qiaoyan Li, Yingcang Ma, Xiaohong Zhang, Juanjuan Zhang
• Format: Article
• Language: English
• Published: MDPI AG 2019-05-01
• Series: Symmetry
• Subjects: neutrosophic extended triplet group; neutrosophic quadruple numbers; neutrosophic set
• Online Access: https://www.mdpi.com/2073-8994/11/5/696

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.