{"id":"https://openalex.org/W2044912531","doi":"https://doi.org/10.2478/forma-2013-0024","title":"Introduction to Formal Preference Spaces","display_name":"Introduction to Formal Preference Spaces","publication_year":2013,"publication_date":"2013-10-01","ids":{"openalex":"https://openalex.org/W2044912531","doi":"https://doi.org/10.2478/forma-2013-0024","mag":"2044912531"},"language":"en","primary_location":{"id":"doi:10.2478/forma-2013-0024","is_oa":true,"landing_page_url":"https://doi.org/10.2478/forma-2013-0024","pdf_url":"https://sciendo.com/pdf/10.2478/forma-2013-0024","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://sciendo.com/pdf/10.2478/forma-2013-0024","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060883252","display_name":"Eliza Niewiadomska","orcid":null},"institutions":[{"id":"https://openalex.org/I245364917","display_name":"University of Bia\u0142ystok","ror":"https://ror.org/01qaqcf60","country_code":"PL","type":"education","lineage":["https://openalex.org/I245364917"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Eliza Niewiadomska","raw_affiliation_strings":["Institute of Mathematics University of Biaystok Akademicka 2, 15-267 Biaystok Poland","Institute of Mathematics University of Bia\u0142ystok Akademicka 2 15\u2013267 Bia\u0142ystok, Poland"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics University of Biaystok Akademicka 2, 15-267 Biaystok Poland","institution_ids":["https://openalex.org/I245364917"]},{"raw_affiliation_string":"Institute of Mathematics University of Bia\u0142ystok Akademicka 2 15\u2013267 Bia\u0142ystok, Poland","institution_ids":["https://openalex.org/I245364917"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073856205","display_name":"Adam Grabowski","orcid":"https://orcid.org/0000-0001-5026-3990"},"institutions":[{"id":"https://openalex.org/I245364917","display_name":"University of Bia\u0142ystok","ror":"https://ror.org/01qaqcf60","country_code":"PL","type":"education","lineage":["https://openalex.org/I245364917"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Adam Grabowski","raw_affiliation_strings":["Institute of Informatics University of Biaystok Akademicka 2, 15-267 Biaystok Poland","Institute of Informatics University of Bia\u0142ystok Akademicka 2, 15-267 Bia\u0142ystok Poland"],"affiliations":[{"raw_affiliation_string":"Institute of Informatics University of Biaystok Akademicka 2, 15-267 Biaystok Poland","institution_ids":["https://openalex.org/I245364917"]},{"raw_affiliation_string":"Institute of Informatics University of Bia\u0142ystok Akademicka 2, 15-267 Bia\u0142ystok Poland","institution_ids":["https://openalex.org/I245364917"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5060883252"],"corresponding_institution_ids":["https://openalex.org/I245364917"],"apc_list":null,"apc_paid":null,"fwci":1.9042,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.90390295,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"21","issue":"3","first_page":"223","last_page":"233"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.9944999814033508,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.9944999814033508,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12137","display_name":"Economic theories and models","score":0.9854999780654907,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9768000245094299,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/preference","display_name":"Preference","score":0.7403494715690613},{"id":"https://openalex.org/keywords/binary-relation","display_name":"Binary relation","score":0.7217251658439636},{"id":"https://openalex.org/keywords/preference-relation","display_name":"Preference relation","score":0.6989511251449585},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6815711259841919},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.624357283115387},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.6216810941696167},{"id":"https://openalex.org/keywords/completeness","display_name":"Completeness (order theory)","score":0.5754561424255371},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.5552482604980469},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.5245340466499329},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.48823311924934387},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.47756725549697876},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3413114547729492},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3233477473258972},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2995392084121704},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22623607516288757},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.19979804754257202}],"concepts":[{"id":"https://openalex.org/C2781249084","wikidata":"https://www.wikidata.org/wiki/Q908656","display_name":"Preference","level":2,"score":0.7403494715690613},{"id":"https://openalex.org/C65180967","wikidata":"https://www.wikidata.org/wiki/Q130901","display_name":"Binary relation","level":2,"score":0.7217251658439636},{"id":"https://openalex.org/C2777062324","wikidata":"https://www.wikidata.org/wiki/Q25036211","display_name":"Preference relation","level":3,"score":0.6989511251449585},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6815711259841919},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.624357283115387},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.6216810941696167},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.5754561424255371},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.5552482604980469},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5245340466499329},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.48823311924934387},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.47756725549697876},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3413114547729492},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3233477473258972},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2995392084121704},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22623607516288757},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.19979804754257202},{"id":"https://openalex.org/C171250308","wikidata":"https://www.wikidata.org/wiki/Q11468","display_name":"Nanotechnology","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2478/forma-2013-0024","is_oa":true,"landing_page_url":"https://doi.org/10.2478/forma-2013-0024","pdf_url":"https://sciendo.com/pdf/10.2478/forma-2013-0024","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:74b87c557d9b4cddba3666ab77800e0e","is_oa":true,"landing_page_url":"https://doaj.org/article/74b87c557d9b4cddba3666ab77800e0e","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Formalized Mathematics, Vol 21, Iss 3, Pp 223-233 (2013)","raw_type":"article"},{"id":"pmh:oai:repozytorium.uwb.edu.pl:11320/3691","is_oa":false,"landing_page_url":"http://hdl.handle.net/11320/3691","pdf_url":null,"source":{"id":"https://openalex.org/S4306400933","display_name":"The Repository of University in Bialystok (University in Bialystok)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210094198","host_organization_name":"University Clinical Hospital In Bialystok","host_organization_lineage":["https://openalex.org/I4210094198"],"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":"Article"}],"best_oa_location":{"id":"doi:10.2478/forma-2013-0024","is_oa":true,"landing_page_url":"https://doi.org/10.2478/forma-2013-0024","pdf_url":"https://sciendo.com/pdf/10.2478/forma-2013-0024","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2044912531.pdf","grobid_xml":"https://content.openalex.org/works/W2044912531.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W22141270","https://openalex.org/W180239714","https://openalex.org/W192809544","https://openalex.org/W1527353349","https://openalex.org/W1979930662","https://openalex.org/W2014447778","https://openalex.org/W2017527449","https://openalex.org/W2036910311","https://openalex.org/W2112898323","https://openalex.org/W2115474581","https://openalex.org/W2137081715","https://openalex.org/W2163641194","https://openalex.org/W2168483961","https://openalex.org/W2296232473","https://openalex.org/W2330150951","https://openalex.org/W4235956817","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W4205262062","https://openalex.org/W2096290915","https://openalex.org/W2022533988","https://openalex.org/W2790208073","https://openalex.org/W2016410556","https://openalex.org/W1595663582","https://openalex.org/W3122913338","https://openalex.org/W2141137858","https://openalex.org/W2949156599","https://openalex.org/W237677924"],"abstract_inverted_index":{"Summary":[0],"In":[1],"the":[2,4,14,20,90,109,120,174,178,184,203,205,218,229],"article":[3,179],"formal":[5],"characterization":[6,185],"of":[7,19,24,37,99,108,126,162,171,177,186,192,228],"preference":[8,15,172,188],"spaces":[9,224],"[1]":[10],"is":[11,17,142,181],"given.":[12],"As":[13],"relation":[16,198],"one":[18],"very":[21],"basic":[22],"notions":[23],"mathematical":[25],"economics":[26],"[9],":[27],"it":[28],"prepares":[29],"some":[30,41,166],"ground":[31],"for":[32],"a":[33,79,159,193],"more":[34,143],"thorough":[35],"formalization":[36],"consumer":[38,91,187],"theory":[39],"(although":[40],"work":[42,62],"has":[43],"already":[44],"been":[45],"done":[46],"-":[47],"see":[48],"[17]).":[49],"There":[50,67],"was":[51],"an":[52,94],"attempt":[53],"to":[54,71,182,201],"formalize":[55],"similar":[56],"results":[57],"in":[58,73,78,87,190],"Mizar,":[59],"but":[60],"this":[61,213],"seems":[63],"still":[64],"unfinished":[65],"[18].":[66],"are":[68,98,114,152],"many":[69],"approaches":[70],"preferences":[72],"literature.":[74],"We":[75,164],"modelled":[76],"them":[77],"rather":[80,138],"illustrative":[81],"way":[82,204],"(similar":[83],"structures":[84,113,189],"were":[85],"considered":[86],"[8]):":[88],"either":[89],"(strictly)":[92],"prefers":[93],"alternative,":[95],"or":[96],"they":[97],"equal":[100],"interest;":[101],"he/she":[102],"could":[103],"also":[104,133],"have":[105],"no":[106],"opinion":[107],"choice.":[110],"Then":[111],"our":[112],"based":[115],"on":[116,119],"three":[117,150],"relations":[118,151],"(arbitrary,":[121],"not":[122],"necessarily":[123],"finite)":[124],"set":[125],"alternatives.":[127,163],"The":[128],"completeness":[129],"property":[130],"can":[131,208],"however":[132,180],"be":[134,209],"modelled,":[135],"although":[136],"we":[137,147,216],"follow":[139],"[2]":[140],"which":[141],"general":[144],"[12].":[145],"Additionally":[146],"assume":[148],"all":[149],"disjoint":[153],"and":[154,168,200,222,225],"their":[155],"set-theoretic":[156],"union":[157],"gives":[158],"whole":[160],"universe":[161],"constructed":[165],"positive":[167],"negative":[169],"examples":[170],"structures;":[173],"main":[175],"aim":[176],"give":[183],"terms":[191],"binary":[194],"relation,":[195],"called":[196],"characteristic":[197],"[10],":[199],"show":[202,217],"corresponding":[206],"structure":[207],"obtained":[210],"only":[211],"using":[212],"relation.":[214],"Finally,":[215],"connection":[219],"between":[220],"tournament":[221],"total":[223],"usual":[226],"properties":[227],"ordering":[230],"relations.":[231]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}
