A mathematical model for formulating interdependence of autonomy and belonging in systems of systems

Among different proposed characteristics of a system of systems, autonomy and belonging are widely accepted as definitive. Since these two characteristics were perceived as independent from one another, their underlying relationship has not been explicitly explored by scholars. This paper proposes that autonomy and belonging are interdependent characteristics according to the purpose of a system of systems and its constituent elements. The coherence between the purposes of the constituent elements and the system of systems defines the level of belonging, and the independence of these purposes is conceptualized as autonomy. The mathematical formulation of this interdependence is presented to analyze the correlation between these two characteristics.