Abstract
In Shafer evidence theory some belief functions, called separable belief functions, can be decomposed in terms of simple support functions. Moreover this decomposition is unique. Recently, a qualitative counterpart to Shafer evidence theory has been proposed. The mass functions in Shafer (addition-based) evidence theory are replaced by basic possibilistic assignments. The sum of weights is no longer 1, but their maximum is equal to 1. In such a context, a maxitive counterpart to belief functions, called possibilistic belief functions can be defined, replacing the addition by the maximum. The possibilistic evidence framework provides a general setting for describing imprecise possibility and necessity measures. This paper investigates a qualitative counterpart of the result about the decomposition of belief functions. Considering the qualitative Möbius transform, conditions for the existence of a decomposition of possibilistic belief functions into simple support functions are presented. Moreover the paper studies the unicity of such a decomposition.
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Chemin, M., Rico, A., Prade, H. (2011). Decomposition of Possibilistic Belief Functions into Simple Support Functions. In: Melo-Pinto, P., Couto, P., Serôdio, C., Fodor, J., De Baets, B. (eds) Eurofuse 2011. Advances in Intelligent and Soft Computing, vol 107. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24001-0_5
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