Proper decision-making is one of the most important capabilities of an organization. Therefore, it is important to have a clear understanding and overview of the decisions an organization makes. A means to understanding and modeling decisions is the Decision Model and Notation (DMN) standard published by the Object Management Group in 2015. In this standard, it is possible to design and specify how a decision should be taken. However, DMN lacks elements to specify the actors that fulfil different roles in the decision-making process as well as not taking into account the autonomy of machines. In this paper, we re-address and-present our earlier work [1] that focuses on the construction of a framework that takes into account different roles in the decision-making process, and also includes the extent of the autonomy when machines are involved in the decision-making processes. Yet, we extended our previous research with more detailed discussion of the related literature, running cases, and results, which provides a grounded basis from which further research on the governance of (semi) automated decision-making can be conducted. The contributions of this paper are twofold; 1) a framework that combines both autonomy and separation of concerns aspects for decision-making in practice while 2) the proposed theory forms a grounded argument to enrich the current DMN standard.