TitleReasoning about Uncertainty of Fuzzy Events: an Overview
Publication TypeBook Chapter
Year of Publication2011
AuthorsFlaminio T, Godo L, Marchioni E
EditorCintula P, Fermueller C., Godo L, Hájek P
Book TitleUnderstanding Vagueness - Logical, Philosophical, and Linguistic Perspectives
EditionP. Cintula, C. G.. Fermüller, L. Godo and P. Hájek
Series Volume36
Pagination367 - 401
PublisherCollege Publications
CityLondon
ISBN Number978-1-84890-037-0
Abstract

Our aim, in this overview paper, is to give a comprehensive logical treatment of several generalizations of main classes of measures of uncertainty over fuzzy events. In particular, we will show how it is possible to represent and logically formalize reasoning about classes of measures such as probabilities, plausibility, possibilities and necessities over several classes of many-valued events. Fuzzy logics provide a powerful framework to handle and combine fuzziness and uncertainty. Indeed, in such logics the operations associated to the evaluation of the connectives are functions defined over the real unit interval [0, 1], that correspond, directly or up to some combinations, to operations used to compute degrees of uncertainty. Then, such algebraic operations can be embedded in the connectives of the many-valued logical framework, resulting in clear and elegant formalizations.