The fuzzy stability model: an interactive framework for measuring robustness and resiliency under uncertainty

The increasing complexity in workflow management systems (WMSs) has led to greater vulnerability due to system failure. Although system vulnerabilities cannot be completely eliminated, the accidental or anticipated failures have to be thoroughly understood and guarded. Traditionally, the failure in military command and control (C2) systems has been studied with robustness, the concept of self-protecting systems and resiliency, the concept of self-healing systems. Robustness and resiliency in C2 systems are generally measured with precise repair-recovery costs and repair-recovery times. However, the repair-recovery costs and repair-recovery times in real-world problems are often imprecise or uncertain. Fuzzy logic and fuzzy sets can represent imprecise or uncertain information formalising inaccuracy in human decision-making. We develop a stability model for simultaneous consideration of robustness and resiliency in fuzzy C2 systems. We measure robustness and resiliency with fuzzy repair-recovery times and fuzzy repair-recovery costs. The interactive method plots the fuzzy robustness and fuzzy resiliency measures in a Cartesian coordinate system and derives an overall fuzzy stability index for various processes in the C2 system based on the theory of displaced ideals.