On the scoring approach to admissibility of uncertainty measures in expert systems (Q807063)

DeFinetti considered coherence of uncertainties as a two-person zero-sum game with squared loss function, played by the ``nature'' on the one hand and the ``decision-maker'' on the other hand. Later Lindley reconsidered this game theoretic approach by replacing the squared loss function by a more general score function and he arrived at the conclusion that an admissible uncertainty measure is necessarily a probability measure. What contradicts some results commonly taken for granted in the fuzzy mathematics community. In the present paper, one recasts Lindley's concepts within a game theoretic setting, one shows that there are admissible uncertainty measures which are not probability measures, and one studies the effects of the assumption of additive score functions.