Finitely maxitive conditional possibilities, Bayesian-like inference, disintegrability and conglomerability

The aim of the paper is to study Bayesian-like inference processes involving coherent finitely maxitive T-conditional possibilities assessed on infinite sets of conditional events. Coherence of an assessment consisting of an arbitrary possibilistic prior and an arbitrary possibilistic likelihood function is proved, thus a closed form expression for the envelopes of the relevant joint and posterior possibilities is given when T is the minimum or a strict t-norm. The notions of disintegrability and conglomerability are also studied and their relevance in the infinite version of the possibilistic Bayes formula is highlighted.