Some Aspects of Neutrosophic Set Theory

Abstract

This article aims to introduce my work on constructing neutrosophic set theory. Neutrosophy is a new branch of mathematical systems proposed by Smarandache in 1995 as an extension of an intuitionistic fuzzy set according to three-degree membership functions. The new perspective of neutrosophic sets consists of two paths, the first path depends on the three degrees including the degree of truth-membership, degree of indeterminacy-membership, and degree of false-non-membership respectively, while the second path depends on the generated classical set by three types of neutrosophic sets and study the concepts of neutrosophic theory. In previous work, I Presented the concepts of neutrosophic sets including universal, empty, compliment, and subsets. I also explored neutrosophic operations and their properties, such as neutrosophic unions and neutrosophic intersections. In this article, I shall delve into additional materials and theorems related to these concepts and discuss neutrosophic and symmetric differences, including their properties. Furthermore, I shall present a generalization of De Morgan's theorem.