What's in a Fuzzy Set?

A modified version of the first-order logic of probability presented in (Halpern 1990) – with probability on possible worlds – makes it possible to formulate an alternative characterisation of fuzzy sets. In this approach, fuzzy sets are no longer seen as primitive entities with an intuitive justification, but rather as structured entities emerging in a suitable logical framework. Some fuzzy techniques of practical relevance are shown to be encodable in this way. In addition, the resulting approach leads to a clearer epistemological analysis in that it clarifies the purposive nature of the kind of uncertainty that can be modelled by fuzziness.