Axiomatic of Neutrosophic Groups

Abstract

The aim of this article is to; present a neutrosophic group according to axioms such as classical group theory and the neutrosophic set, and to study some properties and theorems related to the neutrosophic group. The new concept of the neutrosophic set is a new approach that is suitable for mathematical problems related to philosophical concepts, such as uncertainty and indeterminacy, in which human knowledge and human evaluation are necessary. Neutrosophic algebra is a branch of neutrosophic set theory, and in 2004, Kandasamy and Smarandache introduced basic neutrosophic algebraic structures and their applications to fuzzy and neutrosophic models; in 2006, Kandasamy and Smarandache presented neutrosophic algebraic structures and neutrosophic N-algebraic structures; in 2019, Smarandache introduced new fields of research in Neutrosophy, which he called Neutro-Structures and Anti-Structures. In 2020, Agboola presented an Introduction to the neutrosophic group by a different presentation.