{"id":"https://openalex.org/W1857574948","doi":"https://doi.org/10.1109/fskd.2015.7381933","title":"Rating alternatives from pairwise comparisons by solving tropical optimization problems","display_name":"Rating alternatives from pairwise comparisons by solving tropical optimization problems","publication_year":2015,"publication_date":"2015-08-01","ids":{"openalex":"https://openalex.org/W1857574948","doi":"https://doi.org/10.1109/fskd.2015.7381933","mag":"1857574948"},"language":"en","primary_location":{"id":"doi:10.1109/fskd.2015.7381933","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fskd.2015.7381933","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 12th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD)","raw_type":"proceedings-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1504.00800","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Nikolai Krivulin","orcid":null},"institutions":[{"id":"https://openalex.org/I172901346","display_name":"St Petersburg University","ror":"https://ror.org/023znxa73","country_code":"RU","type":"education","lineage":["https://openalex.org/I172901346"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Nikolai Krivulin","raw_affiliation_strings":["Faculty of Mathematics and Mechanics, Saint Petersburg State University, St. Petersburg, Russia"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Mechanics, Saint Petersburg State University, St. Petersburg, Russia","institution_ids":["https://openalex.org/I172901346"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I172901346"],"apc_list":null,"apc_paid":null,"fwci":1.4595,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.82613633,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"41","issue":null,"first_page":"162","last_page":"167"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9918000102043152,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.907800018787384},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.7684999704360962},{"id":"https://openalex.org/keywords/reciprocal","display_name":"Reciprocal","score":0.5108000040054321},{"id":"https://openalex.org/keywords/ordinal-optimization","display_name":"Ordinal optimization","score":0.47780001163482666},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.40220001339912415}],"concepts":[{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.907800018787384},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.7684999704360962},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6904000043869019},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5770000219345093},{"id":"https://openalex.org/C2777742833","wikidata":"https://www.wikidata.org/wiki/Q1964083","display_name":"Reciprocal","level":2,"score":0.5108000040054321},{"id":"https://openalex.org/C81386100","wikidata":"https://www.wikidata.org/wiki/Q7100792","display_name":"Ordinal optimization","level":3,"score":0.47780001163482666},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.40220001339912415},{"id":"https://openalex.org/C202652594","wikidata":"https://www.wikidata.org/wiki/Q2982669","display_name":"Tropical geometry","level":2,"score":0.32420000433921814},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.2676999866962433},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2451999932527542}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/fskd.2015.7381933","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fskd.2015.7381933","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 12th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1504.00800","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1504.00800","pdf_url":"https://arxiv.org/pdf/1504.00800","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1504.00800","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1504.00800","pdf_url":"https://arxiv.org/pdf/1504.00800","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W341186930","https://openalex.org/W586948577","https://openalex.org/W616288317","https://openalex.org/W1604659615","https://openalex.org/W1970216276","https://openalex.org/W1994621692","https://openalex.org/W1995006674","https://openalex.org/W2001758413","https://openalex.org/W2033442452","https://openalex.org/W2083026665","https://openalex.org/W2124790506","https://openalex.org/W2141654299","https://openalex.org/W2962878765","https://openalex.org/W2963722849","https://openalex.org/W4206269833","https://openalex.org/W4232542481","https://openalex.org/W4232837771","https://openalex.org/W6639192726","https://openalex.org/W6723822716"],"related_works":[],"abstract_inverted_index":{"We":[0],"consider":[1],"problems":[2,23],"of":[3,20,29,40,98],"rating":[4,99],"alternatives":[5,100],"based":[6],"on":[7,16],"their":[8],"pairwise":[9,34],"comparison":[10,35,54],"under":[11],"various":[12],"assumptions,":[13],"including":[14],"constraints":[15],"the":[17,27,58],"final":[18],"scores":[19],"alternatives.":[21],"The":[22],"are":[24,101],"formulated":[25],"in":[26,45,68,78],"framework":[28],"tropical":[30,69],"mathematics":[31],"to":[32],"approximate":[33],"matrices":[36,39],"by":[37],"reciprocal":[38],"unit":[41],"rank,":[42],"and":[43,52,60,88],"written":[44],"a":[46,79],"common":[47],"form":[48],"for":[49],"both":[50],"multiplicative":[51],"additive":[53],"scales.":[55],"To":[56],"solve":[57],"unconstrained":[59],"constrained":[61],"approximation":[62],"problems,":[63],"we":[64],"apply":[65],"recent":[66],"results":[67,87],"optimization,":[70],"which":[71],"provide":[72],"new":[73],"complete":[74],"direct":[75],"solutions":[76,84],"given":[77],"compact":[80],"vector":[81],"form.":[82],"These":[83],"extend":[85],"known":[86],"involve":[89],"less":[90],"computational":[91],"effort.":[92],"As":[93],"an":[94],"illustration,":[95],"numerical":[96],"examples":[97],"presented.":[102]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2016-06-24T00:00:00"}
