Hyperplane Aggregation of Dominance Decision Rules

In this paper we consider multiple criteria decision aid systems based on decision rules generated from examples. A common problem in such systems is the over-abundance of decision rules, as in many situations the rule generation algorithms produce very large sets of rules. This prolific representation of knowledge provides a great deal of detailed information about the described objects, but is appropriately difficult to interpret and use. One way of solving this problem is to aggregate the created rules into more general ones, e.g. by forming rules of enriched syntax. The paper presents a generalization of elementary rule conditions into linear combinations. This corresponds to partitioning the preference-ordered condition space of criteria with non-orthogonal hyperplanes. The objective of this paper is to introduce the generalized rules into the multiple criteria classification problems and to demonstrate that these problems can be successfully solved using the introduced rules. The usefulness of the introduced solution is finally demonstrated in computational experiments with real-life data sets.