Clustering and isolation in the consensus problem for partitions
We examine the problem of aggregating several partitions of a finite set into a single consensus partition. We note that the dual concepts of clustering and isolation are especially significant in this connection. The hypothesis that a consensus partition should respect unanimity with respect to either concept leads us to stress a consensus interval rather than a single partition. The extremes of this inverval are characterized axiomatically. If a sufficient totality of traits has been measured, and if measurement errors are independent, then a ``true'' classifying partition can be expected to lie in the consensus interval. The structure of the partitions in the interval lends itself to partial solutions of the consensus problem. Conditional entropy may be used to quantify the uncertainty inherent in the interval as a whole.
scientific article; zbMATH DE number 4013784