{"id":"https://openalex.org/W2963342554","doi":"https://doi.org/10.1080/03081079.2019.1643338","title":"Observables on lexicographic MV-algebras","display_name":"Observables on lexicographic MV-algebras","publication_year":2019,"publication_date":"2019-07-22","ids":{"openalex":"https://openalex.org/W2963342554","doi":"https://doi.org/10.1080/03081079.2019.1643338","mag":"2963342554"},"language":"en","primary_location":{"id":"doi:10.1080/03081079.2019.1643338","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03081079.2019.1643338","pdf_url":null,"source":{"id":"https://openalex.org/S145553572","display_name":"International Journal of General Systems","issn_l":"0308-1079","issn":["0308-1079","1026-7492","1563-5104"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of General Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056475733","display_name":"Anatolij Dvure\u010denskij","orcid":null},"institutions":[{"id":"https://openalex.org/I4210120676","display_name":"Mathematical Institute of the Slovak Academy of Sciences","ror":"https://ror.org/02fhy7464","country_code":"SK","type":"facility","lineage":["https://openalex.org/I207624831","https://openalex.org/I4210120676"]},{"id":"https://openalex.org/I207624831","display_name":"Slovak Academy of Sciences","ror":"https://ror.org/03h7qq074","country_code":"SK","type":"funder","lineage":["https://openalex.org/I207624831"]},{"id":"https://openalex.org/I70703428","display_name":"Palack\u00fd University Olomouc","ror":"https://ror.org/04qxnmv42","country_code":"CZ","type":"education","lineage":["https://openalex.org/I70703428"]}],"countries":["CZ","SK"],"is_corresponding":true,"raw_author_name":"Anatolij Dvure\u010denskij","raw_affiliation_strings":["Depart. Algebra Geom., Palack\u00fd Univer., Olomouc, Czech Republic","Mathematical Institute, Slovak Academy of Sciences, Bratislava, Slovakia"],"affiliations":[{"raw_affiliation_string":"Depart. Algebra Geom., Palack\u00fd Univer., Olomouc, Czech Republic","institution_ids":["https://openalex.org/I70703428"]},{"raw_affiliation_string":"Mathematical Institute, Slovak Academy of Sciences, Bratislava, Slovakia","institution_ids":["https://openalex.org/I207624831","https://openalex.org/I4210120676"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5056475733"],"corresponding_institution_ids":["https://openalex.org/I207624831","https://openalex.org/I4210120676","https://openalex.org/I70703428"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.11271888,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"48","issue":"7","first_page":"738","last_page":"774"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9998999834060669,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9998999834060669,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9983000159263611,"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/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9952999949455261,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7556331157684326},{"id":"https://openalex.org/keywords/observable","display_name":"Observable","score":0.7293808460235596},{"id":"https://openalex.org/keywords/resolution","display_name":"Resolution (logic)","score":0.6189549565315247},{"id":"https://openalex.org/keywords/lexicographical-order","display_name":"Lexicographical order","score":0.6040151119232178},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4525413513183594},{"id":"https://openalex.org/keywords/homomorphism","display_name":"Homomorphism","score":0.4302464723587036},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.4206969738006592},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.41202616691589355},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4057046175003052},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3948269784450531},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15265464782714844},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08043786883354187},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07019433379173279}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7556331157684326},{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.7293808460235596},{"id":"https://openalex.org/C138268822","wikidata":"https://www.wikidata.org/wiki/Q1051925","display_name":"Resolution (logic)","level":2,"score":0.6189549565315247},{"id":"https://openalex.org/C159254197","wikidata":"https://www.wikidata.org/wiki/Q1144915","display_name":"Lexicographical order","level":2,"score":0.6040151119232178},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4525413513183594},{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.4302464723587036},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4206969738006592},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.41202616691589355},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4057046175003052},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3948269784450531},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15265464782714844},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08043786883354187},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07019433379173279},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/03081079.2019.1643338","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03081079.2019.1643338","pdf_url":null,"source":{"id":"https://openalex.org/S145553572","display_name":"International Journal of General Systems","issn_l":"0308-1079","issn":["0308-1079","1026-7492","1563-5104"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of General Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W315585249","https://openalex.org/W1490505438","https://openalex.org/W1547322272","https://openalex.org/W1566552629","https://openalex.org/W1573036064","https://openalex.org/W1599755535","https://openalex.org/W1607666149","https://openalex.org/W1969303818","https://openalex.org/W1981849484","https://openalex.org/W1985104705","https://openalex.org/W1989551546","https://openalex.org/W1997025586","https://openalex.org/W2002700343","https://openalex.org/W2012072427","https://openalex.org/W2017170340","https://openalex.org/W2022830456","https://openalex.org/W2051190590","https://openalex.org/W2060775031","https://openalex.org/W2090934153","https://openalex.org/W2110364369","https://openalex.org/W2120713972","https://openalex.org/W2140544193","https://openalex.org/W2186255523","https://openalex.org/W2338601465","https://openalex.org/W2523244455","https://openalex.org/W2529931867","https://openalex.org/W2566736669","https://openalex.org/W2903143502","https://openalex.org/W3098574699","https://openalex.org/W3102862392","https://openalex.org/W4211185072","https://openalex.org/W4301084947"],"related_works":["https://openalex.org/W1993634787","https://openalex.org/W3125614403","https://openalex.org/W2476923378","https://openalex.org/W2803221307","https://openalex.org/W2951826204","https://openalex.org/W4211001408","https://openalex.org/W2903963821","https://openalex.org/W2366147410","https://openalex.org/W62366039","https://openalex.org/W239928435"],"abstract_inverted_index":{"We":[0],"study":[1],"observables":[2],"on":[3,46],"a":[4,26,34,40,67,109],"special":[5,41],"kind":[6,42],"of":[7,19,29,43,50,69,71,101],"MV-algebras":[8,18],"which":[9,78],"are":[10,15,39],"lexicographic":[11,58],"MV-algebras,":[12],"i.e.":[13],"they":[14],"isomorphic":[16],"to":[17,85,92,95,105],"the":[20,47,51,57,72,102],"form":[21],"M=\u0393(H\u00d7\u2192G,(u,0)),":[22],"where":[23],"(H,u)":[24],"is":[25,33,66,79,104],"unital":[27],"subgroup":[28],"(R,1)":[30],"and":[31,83,87,94],"G":[32],"Dedekind":[35],"\u03c3-complete":[36],"\u2113-group.":[37],"Observables":[38],"\u03c3-homomorphisms":[44],"defined":[45],"Borel":[48],"\u03c3-algebra":[49],"real":[52,76],"line":[53],"with":[54],"values":[55],"in":[56],"MV-algebra.":[59],"They":[60],"model":[61],"measurable":[62],"functions.":[63],"Spectral":[64],"resolution":[65,111],"system":[68],"elements":[70],"MV-algebra":[73],"indexed":[74],"by":[75],"numbers":[77],"monotone,":[80],"\u201cleft":[81],"continuous\u201d,":[82],"going":[84],"0":[86],"1":[88],"if":[89],"t":[90],"goes":[91],"\u2212\u221e":[93],"+\u221e,":[96],"respectively.":[97],"The":[98],"main":[99],"task":[100],"paper":[103],"show":[106],"when":[107],"does":[108],"spectral":[110],"{xt:t\u2208R}":[112],"determine":[113],"an":[114],"observable":[115],"x":[116],"such":[117],"that":[118],"x((\u2212\u221e,t))=xt":[119],"for":[120],"each":[121],"t\u2208R.":[122]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}