Deriving Consensus for Hierarchical Incomplete Ordered Partitions and Coverings

A method for determining consensus of hierarchical incomplete ordered partitions and coverings of sets is presented in this chapter. Incomplete ordered partitions and coverings are often used in expert information analysis. These structures should be useful when an expert has to classify elements of a set into given classes, but referring to several elements he does not know to which classes they should belong. The hierarchical ordered partition is a more general structure than incomplete ordered partition. In this chapter we present definitions of the notion of hierarchical incomplete ordered partitions and coverings of sets. The distance functions between hierarchical incomplete ordered partitions and coverings are defined. We present also algorithms of consensus determining for a finite set of hierarchical incomplete ordered partitions and coverings.