topkcriteria

Topkcriteria is a generic framework used to describe the criteria and methods for selecting the top-k items from a set of alternatives. It is not a single algorithm, but a concept used across information retrieval, decision making, and optimization to formalize how multiple criteria influence the ranking of candidates.

Formalization: Given a set A of alternatives and a finite set of criteria C1,...,Ck, each alternative a in A has values c_j(a) for each criterion j. The top-k items are chosen by applying a decision rule that aggregates the criteria or compares alternatives via a dominance relation. Aggregation can be a scalar scoring function S(a)=∑ w_j c_j(a) with weights w_j≥0, or non-aggregated methods such as Pareto dominance or lexicographic ordering. The result is a subset T of A with |T|=k.

Common methods: Weighted sums, multi-criteria decision analysis (MCDA) methods like Analytic Hierarchy Process (AHP), Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), or ELECTRE; Pareto front approaches that present non-dominated alternatives; and lexicographic ranking that uses criteria in fixed priority order.

Applications: Top-k criteria are used to rank search results, products, or recommendations; in databases for top-k queries; in portfolio selection and resource allocation; in operations research and logistics.

Considerations: criteria normalization, handling missing data, trade-offs among criteria, and fairness and bias in the selection rule.