Bioperators on soft topological spaces

To contribute to soft topology, we originate the notion of soft bioperators (gamma) over tilde and (gamma) over tilde'. Then, we apply them to analyze soft ((gamma) over tilde, (gamma) over tilde')-open sets and study main properties. We also prove that every soft ((gamma) over tilde, (gamma) over tilde')-open set is soft open; however, the converse is true only when the soft topological space is soft ((gamma) over tilde, (gamma) over tilde')-regular. After that, we define and study two classes of soft closures namely Cl-((gamma) over tilde,Cl- (gamma) over tilde') and (tau) over tilde (((gamma) over tilde, (gamma) over tilde'))-Cl operators, and two classes of soft interior namely Int(((gamma) over tilde, (gamma) over tilde')) and (tau) over tilde (((gamma) over tilde, (gamma) over tilde'))-Int operators. Moreover, we introduce the notions of soft ((gamma) over tilde, (gamma) over tilde')-g.closed sets and soft ((gamma) over tilde, (gamma) over tilde')-T-1/2 spaces, and explore their fundamental properties. In general, we explain the relationships between these notions, and give some counterexamples.