Soft Sets with Atoms

The theory of finitely supported structures is used for dealing with very large sets having a certain degree symmetry. This framework generalizes the classical set Zermelo-Fraenkel by allowing infinitely many basic elements no internal structure (atoms) and equipping group actions permutation over these elements. On other hand, soft represent generalization fuzzy to deal uncertainty in parametric manner. In this paper, we study new structures, associating any crisp family atoms describing it. We prove some finiteness properties infinite sets, order Tarski-like fixed point results mappings between atoms.