Modelling inoperability propagation mechanism in interdependent systems

This communication considers the issue of deriving a model to describ how the inoperating level of a particular system (a production unit, a transportation system, an energy supply plant, etc.) of interconnected or interdependent systems(neworking and interdependency are interchangeable in this communication) will impact the operating level of other systems for the purpose of analysis, simulation, prediction, risk assessment, etc. The mechanism of such impacting process may be very complex; for instance to impact the operating level of a system the inoperability of another system may need to reach a certain level (threshold), to combine (synergy) with other events or situations; there may exist some preemptivity condition (that is to destabilize a given system some particular conditions must be satisfied). The main purpose of this communication is therefore to establish a model of inoperability propagation in a networked systems when taking into account as much as possible phenomena such as thresholding, synergy, resilience, etc. Necessity of synergy appeals for a synergetic aggregation operator; to this end, we propose to consider using Choquet integral associeted with a weighted cardinal fuzzy meaure (wcfm) as the appropriate aggregation operator. Furthermore this association leads to a straightforward formula to compute the integral