*Article* **Designing Possibilistic Information Fusion—The Importance of Associativity, Consistency, and Redundancy**

**Christoph-Alexander Holst \* and Volker Lohweg**

inIT—Institute Industrial IT, Technische Hochschule Ostwestfalen-Lippe, Campusallee 6, 32657 Lemgo, Germany; volker.lohweg@th-owl.de

**\*** Correspondence: christoph-alexander.holst@th-owl.de

**Abstract:** One of the main challenges in designing information fusion systems is to decide on the structure and order in which information is aggregated. The key criteria by which topologies are constructed include the associativity of fusion rules as well as the consistency and redundancy of information sources. Fusion topologies regarding these criteria are flexible in design, produce maximal specific information, and are robust against unreliable or defective sources. In this article, an automated data-driven design approach for possibilistic information fusion topologies is detailed that explicitly considers associativity, consistency, and redundancy. The proposed design is intended to handle epistemic uncertainty—that is, to result in robust topologies even in the case of lacking training data. The fusion design approach is evaluated on selected publicly available real-world datasets obtained from technical systems. Epistemic uncertainty is simulated by withholding parts of the training data. It is shown that, in this context, consistency as the sole design criterion results in topologies that are not robust. Including a redundancy metric leads to an improved robustness in the case of epistemic uncertainty.

**Keywords:** information fusion; possibility theory; information fusion system design
