{"id":"W2131088269","doi":"10.1016/s0165-0114(03)00260-4","title":"Duality in linear programming with fuzzy parameters and matrix games with fuzzy pay-offs","year":2003,"lang":"en","type":"article","venue":"Fuzzy Sets and Systems","topic":"Optimization and Mathematical Programming","field":"Engineering","cited_by":126,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Manitoba","funders":"","keywords":"Mathematics; Duality (order theory); Fuzzy logic; Dual (grammatical number); Linear programming; Mathematical optimization; Matrix (chemical analysis); Fuzzy number; Fuzzy set operations; Fuzzy classification; Fuzzy associative matrix; Fuzzy set; Algebra over a field; Discrete mathematics; Artificial intelligence; Computer science; Pure mathematics","routes":{"ca_aff":true,"ca_fund":false,"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":[0.006831389,0.002079098,0.003399345,0.001985999,0.00134983,0.006130717,0.002296644,0.003051606,0.005351895],"category_scores_gemma":[0.01914989,0.001400383,0.001706429,0.002739807,0.005445255,0.008766442,0.003074354,0.005821872,0.0004846259],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.004422716,"about_ca_system_score_gemma":0.00260305,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.003233602,"about_ca_topic_score_gemma":0.002474325,"domain_scores_codex":[0.995972,0.002781375,0.0001207328,0.0003205732,0.0005219201,0.0002833804],"domain_scores_gemma":[0.9899718,0.008137229,0.0006257272,0.0002832884,0.0005926773,0.0003893157],"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":[0.00003856427,0.00003505853,0.0000759733,0.00007202102,0.00002175538,0.0000402505,0.00008720339,0.04312256,0.0001355601,0.9522811,0.0008617931,0.003228154],"study_design_scores_gemma":[0.00001657306,0.00001834307,0.00004193684,0.00002236836,0.000007992618,0.00002285223,0.00004020898,0.1210857,0.00005403439,0.8778716,0.0008060496,0.00001243271],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.02755404,0.003228003,0.926239,0.002968194,0.0003792193,0.00008443906,0.0001702039,0.00006248314,0.03931461],"genre_scores_gemma":[0.8217454,0.004922266,0.1373143,0.0007505988,0.001121406,0.0005493626,0.0002145462,0.0001597199,0.0332222],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.006831389,"threshold_uncertainty_score":0.03612828,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0162352130909944,"score_gpt":0.2447732079311289,"score_spread":0.2285379948401345,"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."}}