Conditional probability and fuzzy information

• Published in: Computational statistics & data analysis Vol. 51; no. 1; pp. 115 - 132
• Main Authors: Coletti, Giulianella, Scozzafava, Romano
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.11.2006; Elsevier
• Series: Computational Statistics & Data Analysis
• Subjects: Coherent conditional probability; Fuzzy theory; Likelihood function; Perception-based information; Coherent conditional probability; Perception-based information; Fuzzy theory; Likelihood function
• ISSN: 0167-9473; 1872-7352
• DOI: 10.1016/j.csda.2006.04.028

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.