Abstract
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.
Highlights
The notion of a neutrosophic set is proposed by F
We will show that the algebra system ( NQ, ∗)(or ( NQ, ?)) is a neutrosophic extended triplet group (NETG)
We explore the algebra structure properties of neutrosophic quadruple numbers
Summary
The notion of a neutrosophic set is proposed by F. As a new algebraic structure, NTG (NETG) immediately attracted the attention of scholars and conducted in-depth research. These studies are mainly carried out by the following three aspects. In paper [9], the notion of the neutrosophic triplet coset and its relation with the classical coset are proposed and the properties of the neutrosophic triplet cosets are given. The generalized neutrosophic extended triplet group (GNETG) is proposed in [11] and verify that for each n ∈ Z + , n ≥ 2, ( Zn , ⊗) is a commutative GNETG It is the application research on the algebraic system NET.
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