On the Structuration and Composition of Decision Problems: A Systemic Approach to Rollbacks

Following Maier principles, system of systems are composed of constituent systems that exhibit together emergent behaviors which cannot be exposed using individually the constituent systems. All constituent systems chosen to realize emergent behaviors are themselves composed of thousands of system elements, which were selected also as a result of decision processes. However, decision making based on specific criteria and decision gates in ISO/IEC 15288:2023 is based on management assumptions rather than formal mathematical formulations. The present paper proposes a mathematical formulation of decision aid composition in systems of systems. Based on the observation that state-of-the-art in decision aid applied mathematics domain could be tackled with system engineering process. Using decision aid, we expose the big picture in architecture selection as a composition of decisions. Through a simple example of a choice to introduce a new technology in an existing air-defence system-ofsystem, a sketch of a decision algebra in system-of-system design holds keys to validation of GO/No GO with quantifyable interests of multiple external stakeholders. Our definitions and axioms are presented as a solid foundation for shaping design spaces in systems with respect to dedicated large industrial consortiums.