an:06840595
Zbl 1383.62060
Coletti, Giulianella; Petturiti, Davide
Finitely maxitive conditional possibilities, Bayesian-like inference, disintegrability and conglomerability
EN
Fuzzy Sets Syst. 284, 31-55 (2016).
00374229
2016
j
62F15 60A05 62F86
Bayesian-like inference; disintegrability; conglomerability; finite maxitivity; \(T\)-conditional possibility; possibilistic likelihood function; coherence
Summary: 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.