The extreme points of the set of belief measures

• Autores: Martin Brüning, Dieter Denneberg
• Localización: International journal of approximate reasoning, ISSN 0888-613X, Vol. 48, Nº 3, 2008, págs. 670-675
• Idioma: inglés
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• Resumen

  • It is known that the s-additive Möbius transform of a belief function (we prefer to call it belief measure) can be derived from Choquet�s Theorem. One has to show that the extreme points of the compact convex set of belief measures are the {0, 1}-valued belief measures, which are called filter games as well. A proof is implicit in the famous 1953/54 paper of Choquet but it is hard to read it. We present a direct proof and � for the sake of completeness � derive the Möbius transform.