The Comparison of Multi-objective Preference Inference Based on Lexicographic and Weighted Average Models

Preference Inference Based on Pareto Models

“…For many order relations like lexicographic orders, hierarchical models and weighted sums, PDP and PCP are mutually expressive [13,4]. More specifically, for M being the set of all feasible preference models due to one of the aforementioned order relations, Γ M ϕ if and only if Γ ∪ {ϕ} is M-inconsistent (i.e., there exists no model in M that satisfies all statements in Γ ∪ {ϕ}).…”

“…Then Opt(S, ≺) represents the alternatives that could be optimal for a user under the assumption that the users preference model is an order relation of the form ≺. In [4] the following relations were established between weighted average (WA) and lexicographic (LEX) models. Here, ⊆ signifies that the set relation ⊆ dos not necessarily hold for every S ⊆ A and Γ ⊆ L A (but might hold for some).…”

“…In applications like recommender systems or multiobjective optimisation it can be very helpful to use inferences that keep the number of undominated alternatives small, so that the user is not overwhelmed when she is presented with them. First, we define HCLP models, lexicographic models and weighted average models as in [4,13].…”

“…The Preference Consistency Problem (PCP) decides if a set of given user preference statements is consistent, i.e., the statements do not contradict each other. PDP and PCP have been studied under different order relations such as lexicographic orders [11,9,12], hierarchical orders [13,5] and weighted sums [3,8,4]. Under these order relations PDP and PCP are mutually expressive, i.e., PDP can be solved using algorithms for PCP and vice versa.…”