Type-2 fuzzy conceptual spaces

We show how Type-2 fuzzy set modeling strengthens the theory of conceptual spaces first presented by Gärdenfors and developed by various authors. In fuzzy conceptual spaces, domains are defined as sets with a measure, properties as Type-2 fuzzy sets on domains, contexts as sets of properties, and concepts as Type-2 fuzzy sets on pairs of properties in a context. An observation is a family of fuzzy sets on the domains that are relevant to a context. Membership of an observation in a property is a Type-2 fuzzy set on the collection of observations. A geographical application illustrates how improved modeling of imprecision can affect decisions.