Many different formal techniques, both numerical and symbolic, have been developed over the past two decades for dealing with uncertain and vague information.

In the first part of this talk, the most important of these formalisms are briefly reviewed, describing how they work, and in what ways they differ from one another. We also consider heterogeneous approaches which incorporate two or more approximate reasoning mechanisms within a single reasoning system. These have been proposed to address limitations in the use of individual formalisms.

In the second part of this talk, Bayesian networks are presented in more detail. Bayesian networks are used to structure uncertain knowledge about high-dimensional domains, and efficient propagation methods have been developed. In our research group a variety of additional knowledge-based operations on graphical models have been developed, where revision, updating, the fusion of networks with relational rule systems, network approximation, and learning from data samples are some of the most important ones. Using real world examples (e.g. item planning at Volkswagen), the power of these concepts is demonstrated.