Study of Two Kinds of Quasi AG-Neutrosophic Extended Triplet Loops

Xiaogang An,Mingming Chen,Parimala Mani

doi:10.1155/2021/6649751

Xiaogang An, Mingming Chen + Show 1 more

Open Access

https://doi.org/10.1155/2021/6649751

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Abstract

Abel-Grassmann’s groupoid and neutrosophic extended triplet loop are two important algebraic structures that describe two kinds of generalized symmetries. In this paper, we investigate quasi AG-neutrosophic extended triplet loop, which is a fusion structure of the two kinds of algebraic structures mentioned above. We propose new notions of AG-(l,r)-Loop and AG-(r,l)-Loop, deeply study their basic properties and structural characteristics, and prove strictly the following statements: (1) each strong AG-(l,r)-Loop can be represented as the union of its disjoint sub-AG-groups, (2) the concepts of strong AG-(l,r)-Loop, strong AG-(l,l)-Loop, and AG-(l,lr)-Loop are equivalent, and (3) the concepts of strong AG-(r,l)-Loop and strong AG-(r,r)-Loop are equivalent.

Highlights

The so-called left almost semigroup (LA-semigroup) was the concept of an Abel-Grassmann’s groupoid (AGgroupoid), which was put forward by Kazim and Naseeruddin [1] at the first time in 1972
Neutrosophic set (NS) theory is widely used in a couple of sectors such as professional selection [7], integrated speech and text sentiment analysis [8], finite automata [9], clustering methods [10], and deep learning [11]
The concept of Abel-Grassmann’s neutrosophic extended triplet loop (AG-NET-Loop), which plays a significant role in neutrosophic triplet algebraic structures, was proposed in [18], that is, an AG-NET-Loop is both an AGgroupoid and a neutrosophic extended triplet loop (NETLoop)

Summary

Introduction

The so-called left almost semigroup (LA-semigroup) was the concept of an Abel-Grassmann’s groupoid (AGgroupoid), which was put forward by Kazim and Naseeruddin [1] at the first time in 1972. The concept of Abel-Grassmann’s neutrosophic extended triplet loop (AG-NET-Loop), which plays a significant role in neutrosophic triplet algebraic structures, was proposed in [18], that is, an AG-NET-Loop is both an AGgroupoid and a neutrosophic extended triplet loop (NETLoop). In [20], two kinds of quasi AG-NET-Loops (AG-(l,l)-Loop and AG-(r,r)-Loop) were proposed and their basic properties were investigated. As a continuation of [20], we propose two other kinds of quasi AG-NET-Loops, which are the AG-(l,r)-Loop and the AG-(r,l)-Loop. We study their properties and analyze their relationship.

Preliminaries

Alternative Quasi AG-NET-Loop

Conclusion