A concept geometry for conceptual spaces

This paper generalizes and extends the theory of conceptual spaces as originally proposed by Gardenförs (Conceptual spaces. Cambridge, MA: MIT Press) to provide further geometric representations of both concepts and object observations within a multi-dimensional fuzzy space corresponding to a subset of a unit hypercube. With these representations, we are able directly to calculate normalized scalar measures both of the similarity of two different concepts and of the degree to which an observation satisfies a concept description, and thus to perform inferences with respect to situational assessments and predictions. This capability is directly relevant to the implementation of Levels 2 and 3 data fusion functions using our approach.