{"id":"W1994621692","doi":"10.1016/s0024-3795(03)00476-2","title":"Max-algebra and pairwise comparison matrices","year":2003,"lang":"en","type":"article","venue":"Linear Algebra and its Applications","topic":"Multi-Criteria Decision Making","field":"Decision Sciences","cited_by":54,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Victoria","funders":"University of Victoria","keywords":"Mathematics; Eigenvalues and eigenvectors; Transitive relation; Reciprocal; Ranking (information retrieval); Matrix (chemical analysis); Pairwise comparison; Linear algebra; Measure (data warehouse); Combinatorics; Generalized eigenvector; Symmetric matrix; Statistics; Computer science; Geometry","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.009579922,0.001381863,0.002418865,0.002521364,0.001490763,0.003172654,0.00238284,0.001188767,0.008920721],"category_scores_gemma":[0.02471311,0.0007648217,0.001744472,0.00599313,0.003346806,0.007497902,0.002466988,0.003067415,0.001533182],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001592493,"about_ca_system_score_gemma":0.001801847,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001311582,"about_ca_topic_score_gemma":0.001142686,"domain_scores_codex":[0.9898038,0.007012182,0.0004047608,0.001021898,0.001499281,0.0002581302],"domain_scores_gemma":[0.9784546,0.01657582,0.001545322,0.001255476,0.001743819,0.0004249827],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00006061533,0.00007807487,0.0001676064,0.0002048966,0.00007149067,0.00004247125,0.000151951,0.02250281,0.0003814146,0.9214889,0.00269742,0.05215234],"study_design_scores_gemma":[0.00000621694,0.00002715797,0.00007274216,0.00001870237,0.00001039735,0.00003049908,0.00002040695,0.03270214,0.0001678458,0.9651856,0.001742896,0.00001530357],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.005815665,0.002089661,0.9840052,0.0005484243,0.0001385535,0.00004319079,0.0001921956,0.0001240404,0.007043186],"genre_scores_gemma":[0.3505339,0.004386831,0.6290144,0.0006647274,0.001120821,0.0007388061,0.0007630598,0.0002058338,0.01257165],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.009579922,"threshold_uncertainty_score":0.05066413,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1147421302884672,"score_gpt":0.4074115333315407,"score_spread":0.2926694030430735,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}