A distance metric for a space of linguistic summaries

Producing linguistic summaries of large databases or temporal sequences of measurements is an endeavor that is receiving increasing attention. These summaries can be used in a continuous monitoring situation, like eldercare, where it is important to ascertain if the current summaries represent an abnormal condition. It is therefore necessary to compute the distance between summaries as a basis for such a determination. In this paper, we propose a dissimilarity measure between summaries based on fuzzy protoforms, and prove that this measure is a metric. We take into account not only the linguistic meaning of the summaries, but also two quality evaluations, namely the truth values and the degrees of focus. We present examples of how the distance metric behaves and show that it corresponds with intuition.