Conditional probability and fuzzy information
The main subject of this paper is the embedding of fuzzy set theoryand related conceptsin a coherent conditional probability scenario. This allows to deal with perception-based informationin the sense of Zadehand with a rigorous treatment of the concept of likelihood, dealing also with its role in statistical inference. A coherent conditional probability is looked on as a general non-additive uncertainty measure m()=P(E|) m (  ) = P ( E |  ) of the conditioning events. This gives rise to a clear, precise and rigorous mathematical frame, which allows to define fuzzy subsets and to introduce in a very natural way the counterparts of the basic continuous T-norms and the corresponding dual T-conorms, bound to the former by coherence. Also the ensuing connections of this approach to possibility theory and to information measures are recalled.
coherent conditional probability likelihood function fuzzy theory perception-based information