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Common part of preference relations

Levin M. S.

Foundations of Computing and Decision Sciences

2003

Vol. 28, No. 4

223-246

The paper addresses a problem to build a common part for a set of preference relations (digraphs, posets) which are defined over the same set of vertices (e.g., alternatives). A special new contradiction is proposed for the vertices which are included into the common subgraph. A new problem formulation is: find the largest (by vertices and by arcs) common subgraph or its the ''best" approximation, while taking into account a contradiction. Thus the model is oriented to Pareto-effective solutions. The common subgraph can be considered as a structural measure for proximity of initial preference relations. The case of many initial digraphs allows various kinds of the aggregation for arc information. Our solving scheme is based on a combinatorial model (morphological clique problem). The following situations are described: (a) a general description for the two digraphs case and (b) the n digraph case. Numerical examples illustrate the problems and solving processes.