Extendibility of Choquet rational preferences on generalized lotteries

Given a finite set of generalized lotteries, that is random quantities equipped with a belief function, and a partial preference relation on them, a necessary and sufficient condition (Choquet rationality) has been provided for its representation as a Choquet expected utility of a strictly increasing utility function. Here we prove that this condition assures the extension of the preference relation and it actually guides the decision maker in this process.