Abstract
The Dempster-Shafer theory of belief functions has proved to be a powerful formalism for uncertain reasoning. However, belief functions on a finite frame of discernment \({\it \Omega}\) are usually defined in the power set 2Ω , resulting in exponential complexity of the operations involved in this framework, such as combination rules. When \({\it \Omega}\) is linearly ordered, a usual trick is to work only with intervals, which drastically reduces the complexity of calculations. In this paper, we show that this trick can be extrapolated to frames endowed with an arbitrary lattice structure, not necessarily a linear order. This principle makes it possible to apply the Dempster-Shafer framework to very large frames such as, for instance, the power set of a finite set \({\it \Omega}\), or the set of partitions of a finite set. Applications to multi-label classification and ensemble clustering are demonstrated.
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Denœux, T., Masson, MH. (2010). Dempster-Shafer Reasoning in Large Partially Ordered Sets: Applications in Machine Learning. In: Huynh, VN., Nakamori, Y., Lawry, J., Inuiguchi, M. (eds) Integrated Uncertainty Management and Applications. Advances in Intelligent and Soft Computing, vol 68. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11960-6_5
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DOI: https://doi.org/10.1007/978-3-642-11960-6_5
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