Innovative Generalized Classes of Operators Inspired by Upper Soft Open Sets

The generalization of soft open sets (so-sets) plays an important vital role in applications of topological spaces. In this paper, we generalize nearly all the introduced weaker forms of so-sets. Specially, we define a new class of so-sets named upper soft open sets (upper-so-sets) and discuss its essential features. Specifically, we prove that upper-so-sets in soft topological space (STS) and their soft subspaces typically have no relationship. With providing examples, we study the mutual relationships among our new approach and the preceding generalizations of so-sets. It is also critical to illustrate the relationships between our innovative approach and its counterpart in the parametric topology. Also, the finite product of upper-so-sets is an upper-so-set. Inspired by upper-so-sets, we construct novel kinds of soft operators called upper soft interior (closure, limit, boundary, and exterior) operator, respectively. Moreover, we present the differences among these novel operators and their corresponding classical operators. In addition to their relationships with earlier related concepts, we also establish connections between them. Finally, we provide multiple crucial examples to support our study and elucidate the significance of our new results.