Abstract
This article aims to present more facts about neutrosophic set theory such as classical set theory. It includes; more connection between operations on the neutrosophic set theory of three types such as union, intersection, difference, and their generalization. further, the generalization of union, intersection, and complement with DE-Morgan's theorem. In addition, we studied the Cartesian Products and their properties. This work opens a new parallel path of a new neutrosophic structure of degree of membership functions that does not depend on intuitionistic fuzzy set and fuzzy set respectively.
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