The set theory is one of the important mathematical topics on which the rest of the branches of mathematics are based and is considered the basic foundation for it. Among this importance, scientists began to find a different formula for sets, whether on a one – dimensional, two – dimension) or three – dimensional level. Behind all this, is to finding optimal solutions to some open problems in the natural sciences as well as engineering and other sciences. There are many types of them, fuzzy sets [1], soft fuzzy sets [2], fuzzy soft sets [3 ], double sets [4] and neutresoploic sets [4]. If  is the non – empty universal set, the fuzzy set are constructed on the  plane , but the soft sets are constructed on , where  be the set of all parameters for . Similarly for double sets, they are constructed in the plane  . But the neutrosophic crisp set are constructed on the plane space . The reason for the diversity of the creation of these sets, as well as the diversity and difference of the binary operations that the identified, came as a result of the diversity and difference of problems that scientists face in the natural and engineering sciences, as well as the difference, whether in the two – dimensional or three – dimensional.

   Through sharing simple and intensive study of some of the concepts presented by Salama and Florentin [5] on the topic of the Neutrosophic crisp and which are important in the process of algebraic construction of these aggregates: