Weight Intervals Conservatively adding quantified uncertainty to similarity

Numeric-valued similarity measures are the traditional means used in Case-Based Reasoning (CBR) systems for case retrieval, and for procedures such as clustering analysis and case classification. Similarity measures are customarily combined using the technique of taking the weighted sum of a vector of similarity values, each determined by the application of a single component measure. Osborne, Ferguson, and Bridge’s framework of similarity metrics generalises this treatment, allowing similarity values to be from any partially ordered set. As a consequence of this, however, the usual weighted sum combining form is not generally usable, and alternatives must be (and have been) devised. Presented here is a partial reconciliation of these notions: using weight-intervals, some of the desirable features of the more general metric approach may be retained, while obtaining results that are a strict generalisation of those possible with conventional weighting.