{"paper":{"title":"Notes on the existence of solutions in the pairwise comparisons method using the Heuristic Rating Estimation approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Konrad Ku{\\l}akowski","submitted_at":"2014-02-17T17:11:55Z","abstract_excerpt":"Pairwise comparisons are a well-known method for modelling of the subjective preferences of a decision maker. A popular implementation of the method is based on solving an eigenvalue problem for M - the matrix of pairwise comparisons. This does not take into account the actual values of preference. The Heuristic Rating Estimation (HRE) approach is a modification of this method in which allows modelling of the reference values. To determine the relative order of preferences is to solve a certain linear equation system defined by the matrix A and the constant term vector b (both derived from M)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.4064","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}