We introduce the H(Θ)-open sets modification given by a hereditary class and a generalized topology μ and investigate some properties and characterizations. With the help of H(Θ)-open sets, we define new classes of sets H(Θ) -- preopen, H(Θ) -- semiopen, H(Θ) -- α -- open, H(Θ) -- β -- open in hereditary generalized topological spaces and study the relation between such sets and Θ -- open sets on generalized topologies.