109 urn:lsid:arphahub.com:pub:3dc5f44e-8666-58db-bc76-a455210e8891 JUCS - Journal of Universal Computer Science jucs 0948-695X 0948-6968 Journal of Universal Computer Science 10.3217/jucs-013-02-0317 28744 Research Article E.1 - DATA STRUCTURES H.2.1 - Logical Design I.2.11 - Distributed Artificial Intelligence I.2.4 - Knowledge Representation Formalisms and Methods Deriving Consensus for Hierarchical Incomplete Ordered Partitions and Coverings Hernes Marcin mhernes@interia.pl 1 Nguyen Ngoc Thanh 1 Wroclaw University of Technology, , Poland Wroclaw University of Technology Poland

Corresponding author: Marcin Hernes (mhernes@interia.pl).

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2007 28 02 2007 13 2 317 328 175E639E-2988-546E-A6FE-82B2E0125705 6999778 Marcin Hernes, Ngoc Thanh Nguyen This article is freely available under the J.UCS Open Content License.

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.