Towards Fast Algorithms for the Preference Consistency Problem Based on Hierarchical Models

Such order relations can be, e.g., comparing alternatives by the values of the evaluation functions In this paper, we construct and compare algorithmic approaches lexicographically [15], by Pareto order, weighted sums [6], to solve the Preference Consistency Problem for based on hierarchical models [16] or by conditional preferences preference statements based on hierarchical models. Instances structures as CP-nets [2] and partial lexicographic preference of this problem contain a set of preference statements that are trees [11]. Here, the choice of the order relation can direct comparisons (strict and non-strict) between some alternatives, lead to stronger or weaker inferences and can make solving and a set of evaluation functions by which all alternatives PDP computationally more or less challenging. In a recommender can be rated. An instance is consistent based on hierarchical system or in a multi-objective decision making scenario, preference models, if there exists an hierarchical model the user should only be presented with a relatively small on the evaluation functions that induces an order relation on number of solutions, hence, a strong order relation is required.