{"id":"https://openalex.org/W2049852473","doi":"https://doi.org/10.1142/s0218488599000544","title":"ON THE SUM OF OBSERVABLES IN PRODUCT MV ALGEBRAS","display_name":"ON THE SUM OF OBSERVABLES IN PRODUCT MV ALGEBRAS","publication_year":1999,"publication_date":"1999-12-01","ids":{"openalex":"https://openalex.org/W2049852473","doi":"https://doi.org/10.1142/s0218488599000544","mag":"2049852473"},"language":"en","primary_location":{"id":"doi:10.1142/s0218488599000544","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218488599000544","pdf_url":null,"source":{"id":"https://openalex.org/S69518169","display_name":"International Journal of Uncertainty Fuzziness and Knowledge-Based Systems","issn_l":"0218-4885","issn":["0218-4885","1793-6411"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Uncertainty, Fuzziness and Knowledge-Based 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/A5046677063","display_name":"Beloslav Rie\u010dan","orcid":null},"institutions":[{"id":"https://openalex.org/I207624831","display_name":"Slovak Academy of Sciences","ror":"https://ror.org/03h7qq074","country_code":"SK","type":"government","lineage":["https://openalex.org/I207624831"]},{"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/I59655833","display_name":"Matej Bel University","ror":"https://ror.org/016e5hy63","country_code":"SK","type":"education","lineage":["https://openalex.org/I59655833"]}],"countries":["SK"],"is_corresponding":true,"raw_author_name":"BELOSLAV RIE\u010cAN","raw_affiliation_strings":["Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Tajovsk\u00e9ho 40, SK-974 01 Bansk\u00e1 Bystrica, Slovakia","Mathematical Institute, Slovak Academy of Sciences, \u0160tef\u00e1nikova 49, SK-814 73, Bratislava, Slovakia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Tajovsk\u00e9ho 40, SK-974 01 Bansk\u00e1 Bystrica, Slovakia","institution_ids":["https://openalex.org/I59655833"]},{"raw_affiliation_string":"Mathematical Institute, Slovak Academy of Sciences, \u0160tef\u00e1nikova 49, SK-814 73, Bratislava, Slovakia","institution_ids":["https://openalex.org/I207624831","https://openalex.org/I4210120676"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5046677063"],"corresponding_institution_ids":["https://openalex.org/I207624831","https://openalex.org/I4210120676","https://openalex.org/I59655833"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.18117109,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"07","issue":"06","first_page":"671","last_page":"677"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","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/T11727","display_name":"Advanced Algebra and Logic","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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9829999804496765,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9801999926567078,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/observable","display_name":"Observable","score":0.9095587730407715},{"id":"https://openalex.org/keywords/distributive-property","display_name":"Distributive property","score":0.685555100440979},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6201353669166565},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5920408964157104},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5764676928520203},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5004732608795166},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.487748920917511},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.41410335898399353},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.35119718313217163},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32188138365745544},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.22586151957511902},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20874005556106567},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07651031017303467}],"concepts":[{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.9095587730407715},{"id":"https://openalex.org/C11821877","wikidata":"https://www.wikidata.org/wiki/Q187959","display_name":"Distributive property","level":2,"score":0.685555100440979},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6201353669166565},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5920408964157104},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5764676928520203},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5004732608795166},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.487748920917511},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.41410335898399353},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.35119718313217163},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32188138365745544},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.22586151957511902},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20874005556106567},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07651031017303467},{"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:10.1142/s0218488599000544","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218488599000544","pdf_url":null,"source":{"id":"https://openalex.org/S69518169","display_name":"International Journal of Uncertainty Fuzziness and Knowledge-Based Systems","issn_l":"0218-4885","issn":["0218-4885","1793-6411"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Decent work and economic growth","score":0.4399999976158142,"id":"https://metadata.un.org/sdg/8"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":3,"referenced_works":["https://openalex.org/W1983814776","https://openalex.org/W1989551546","https://openalex.org/W2325589927"],"related_works":["https://openalex.org/W2094667621","https://openalex.org/W1994680671","https://openalex.org/W2382957647","https://openalex.org/W1509295490","https://openalex.org/W2002320543","https://openalex.org/W2000283393","https://openalex.org/W2962878999","https://openalex.org/W1749534632","https://openalex.org/W3013987451","https://openalex.org/W2078516608"],"abstract_inverted_index":{"As":[0],"an":[1],"alternative":[2],"to":[3],"quantum":[4],"logics":[5],"MV":[6,19,37,49],"algebras":[7,20],"have":[8,22],"been":[9,23,40],"suggested":[10],"2,20":[11],".":[12,31,43],"In":[13,44,70],"a":[14],"quite":[15],"general":[16],"class":[17],"of":[18,26,35,54,67,79,81],"there":[21],"constructed":[24,59],"sum":[25,66,83],"any":[27,45,55,68],"two":[28,77],"observables":[29,56],"10,14,20":[30],"Recently":[32],"the":[33,51,62,65,76,82],"notion":[34],"product":[36,48],"algebra":[38,50],"has":[39],"introduced":[41],"4,5,12,17":[42],"weakly":[46],"\u03c3-distributive":[47],"joint":[52],"observable":[53],"can":[57],"be":[58],"and":[60],"on":[61],"base":[63],"also":[64],"observables.":[69],"this":[71],"paper":[72],"we":[73],"show":[74],"that":[75],"concepts":[78],"constructing":[80],"are":[84],"equivalent.":[85]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
