Time-dependent differential inclusions, cocycle attractors and fuzzy differential equations

Traditional formulations of fuzzy differential equations do not reproduce the rich and varied behavior of crisp differential equations (DEs). A recent interpretation in terms of differential inclusions, expressed level setwise, overcomes this deficiency and opens up for profitable investigation such properties as stability, attraction, periodicity, and the like. This is especially important for investigating continuous systems which are uncertain or incompletely specified. This paper studies attractors of fuzzy DEs in terms of cocycles and encompasses both the time-dependent and autonomous cases