Fuzzy Dynamics: Methodological Framework and Applications to Compartmental Modeling

摘要

We propose a method for modeling uncertainty in dynamical systems which is based on the theory of fuzzy sets. Corresponding models appear in the form of fuzzy differential equations. Such models are interpreted from a probabilistic point of view as generalized models of bounded uncertainty. Fuzzy reachable sets are introduced for characterizing the class of system behaviors compatible with the specification of a model. Thus, it becomes possible to anticipate future system states, and to compare these states according to their level of plausibility. The usefulness of the approach is exemplified in connection with the modeling of compartmental systems. For this type of system, we also present results which provide the basis of efficient numerical methods.