The main subject of this paper is the embedding of fuzzy set theory-and related concepts-in a coherent conditional probability scenario. This allows to deal with perception-based information-in the sense of Zadeh-and 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|.) 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.
Conditional probability and fuzzy information.
COLETTI, Giulianella;
2006
Abstract
The main subject of this paper is the embedding of fuzzy set theory-and related concepts-in a coherent conditional probability scenario. This allows to deal with perception-based information-in the sense of Zadeh-and 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|.) 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
