Int N-Soft Substructures of Semigroups

The N-soft sets are newly defined structures with many applications in the real world. We aim for combining the semigroup theory and N-soft sets to provide a comprehensive account of the hybrid framework of N-soft Semigroups. In this paper, we define the gamma-inclusive set, int N-soft subsemigroups, int N-soft left [right] ideals of S, int N-soft product and int N-soft characteristic function, theta-Generalized int N-soft subsemigroups and theta-Generalized int N-soft left [right] ideals of S. We also discuss some examples and theorems based on the restricted (extended) union, restricted (extended) intersection, and gamma-inclusive set.