A categorical approach to probability theory (Q965910)

The authors continue their studies of categorical aspects of fuzzification of probability theory. They demonstrate that the category \(ID\) of \(D\)-posets of fuzzy sets and sequentially continuous \(D\)-homomorphisms is a suitable category to model classical and fuzzy probability theory and their mutual relationship. E.g. they show that fuzzy probability theory is a minimal categorical generalization of classical probability theory. Further they describe a model of probability theory which generalizes the two (classical and fuzzy) probability theories in a natural way. Finally, they present a modification in which the closed unit interval as domain of traditional states is replaced by a simplex.