Abstract: This research informs new types of weakly α-open sets via. ideals which generalize a usual notion for α-g-open sets which is finer than α-open set. The relationship between this notion and previously defined concepts was studied. Some properties are studied like compactness by using this notion. Some examples have been shown that the opposite is not true for many propositions and various types of ideals were used in these examples. The relationship between different types of compactness has been clarified in a flowchart. As a result, we obtained many propositions and remarks of knowledge sets, including that the existence of two different ideals on the same set such that one of them subset of the other does not necessarily indicate that there is a relationships between the two sets defined on these ideals. It is also by using different types of topologies and ideals to know the form of new knowledge sets.