The Neutro-Sigma Algebras and Anti-Sigma Algebras

Abstract

Neutro-algebra structures play a significant role in the neutrosophic theory. Especially, with the help of neutro-algebraic structures; neutrosophic theory makes a valuable addition to the classical theory. In this article, neutro-sigma algebras and anti-sigma algebras are obtained. Furthermore, basic properties and examples for neutro-sigma algebras and anti-sigma algebras are obtained and proved. Also, classical sigma algebra, neutro-sigma algebra and anti-sigma algebra are compared to each other. Neutro-sigma algebra is shown to have a more general structure with respect to classical sigma algebra and anti-sigma algebra. Thus, (T, I, F) components that constitute the neutrosophic theory are added into classical sigma algebra (without using neutrosophic sets) and a new structure is obtained. In addition, we show that a neutro-sigma algebra can be obtained from every classical sigma algebra and a neutro-sigma algebra can be obtained from every anti-sigma algebra.