Multi-level state evaluation in complex systems: information granules and evidence theory approach

Real-world systems often exhibit intricate complexity. Navigating and examining the conditions under which these systems operate present various challenges. These systems are characterized by a web of interconnected inputs and subsystems organized in hierarchical way. The status of each subsystem depends on multiple inputs and the conditions of other interconnected subsystems. Additionally, articulating precise definitions for the states of these subsystems is a complex task, usually fraught with uncertainties. Experts frequently employ information granules to encapsulate imprecise quantities, basing these granules on specialized domain knowledge. These granules may manifest as linguistic terms or intervals, resulting in approximate state definitions. To the best of our knowledge, no methodology currently accommodates multiple uncertainties—including those tied to state definitions—while also offering an evaluation of the varying states of different subsystems. In this study, we present a novel technique for identifying local and global states in hierarchical, multi-component systems under conditions of uncertainty. Utilizing principles of Evidence Theory, we incorporate a recently devised method to evaluate how well uncertain objectives are met. These uncertain objectives correspond to state definitions formulated using information granules of a specific context. By measuring the extent to which the inputs to a given subsystem align with these imprecise state definitions, we can identify the most probable state the subsystem will likely be in. Our proposed method addresses various types of uncertainty when ascertaining system states. The specific areas of imprecision tackled by our approach include: (1) the vagueness and ambiguity inherent in the measurements serving as subsystem inputs, (2) the levels of uncertainty involved in defining subsystem states based on the conditions of other interconnected subsystems, and (3) the indistinct and incomplete knowledge incorporated into the definitions describing individual subsystems’ states. In summary, this paper introduces a method for determining the most likely state of complex systems. Its novelty lies in the application of a technique for satisfying uncertain targets. We have developed a methodology suitable for hierarchical systems. We elaborate on the intricacies of our method and include a case study to demonstrate how system states can be identified when faced with ambiguous definitions of subsystem states and uncertain values of inputs.