Publisher's Synopsis
This work was based on the development of an analytical study of the Neutrosophic crisp set in terms of its algebraic structures. Since Florentin and the salama developed types of algebraic processes such as union, intersection, belonging and subsets as well as for the complement leading to overlap and clash between them, from which the idea of classification into families crystallized with a definition of a special type of topology that we called stable neutrosophic topological space and in special cases it is topological but not topological in the general sense, where the thesis was fragmented into four main ideas with its main axes: The first stage: We presented a classification to the neutrosophic crisp sets, which was represented by three families within specific conditions for them and the algebraic operations that correspond to them (union, intersection, belonging, partial group, complement) and in more than one form. With the presentation of the form of neutrosophic crisp points, in addition to providing various examples that shed light on some important contradictions and correcting the path of some results and theories so that these sets have coherent algebraic structure.
