Approximation of Incoherent Probabilities

In order to explore making incoherent probabilistic knowledge more applicable, we considered the approach of using mathematically precise probability to approximate set functions that represent incoherent subjective knowledge. The approximation approach has the advantage of being applicable to any kind of set function whereas other transformation methods are mainly restricted to a certain subclass. The projection method was developed for approximation using Euclidean distance. We analyze its advantages and disadvantages in comparison with normalization for additive set functions. Here, we present novel properties of both, the projection method and normalization. Thus, in the context of additive set functions, the question of which method is superior remains open, but with further arguments on both sides