Composite decisions consist of interconnected parts or subdecisions and correspond to a composite (composable, modular, decomposable) system. The composite decision approach extends the traditional paradigm of decision making of Herbert A. Simon, i.e. choice of the best alternative(s), and realizes a two-stage solving scheme: (a) the selection of alternatives as the best subdecisions or local decisions and (b) composition of the selected local decisions into a composite global decision while taking into account the quality of the local decisions and their compatibility.