Fuzzy sets as conditional probabilities: which meaningful operations can be defined?

Conditional events and coherent conditional probability theory can be a proper framework for dealing with fuzzy theory, both from a semantic and a syntactic point of view: the former aspect has been emphasized in a previous NAFIPS conference, while here we discuss the latter by embedding our approach in a formal logic framework. We introduce suitable operations between fuzzy sets, looked on as corresponding operations between conditional events endowed with the relevant conditional probability.