{"id":"https://openalex.org/W2086721181","doi":"https://doi.org/10.1109/tfuzz.2010.2077641","title":"The Ordered Modular Averages","display_name":"The Ordered Modular Averages","publication_year":2010,"publication_date":"2010-09-22","ids":{"openalex":"https://openalex.org/W2086721181","doi":"https://doi.org/10.1109/tfuzz.2010.2077641","mag":"2086721181"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2010.2077641","pdf_url":null,"source":{"id":"https://openalex.org/S134177497","display_name":"IEEE Transactions on Fuzzy Systems","issn_l":"1063-6706","issn":["1063-6706","1941-0034"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-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/A5058341815","display_name":"Radko Mesiar","orcid":"https://orcid.org/0000-0001-6503-949X"},"institutions":[{"id":"https://openalex.org/I110757952","display_name":"Slovak University of Technology in Bratislava","ror":"https://ror.org/0561ghm58","country_code":"SK","type":"funder","lineage":["https://openalex.org/I110757952"]},{"id":"https://openalex.org/I187293425","display_name":"University of Ostrava","ror":"https://ror.org/00pyqav47","country_code":"CZ","type":"funder","lineage":["https://openalex.org/I187293425"]}],"countries":["CZ","SK"],"is_corresponding":false,"raw_author_name":"R Mesiar","raw_affiliation_strings":["Institute for Research and Application of Fuzzy Modelling, University of Ostrava, Ostrava, Czech Republic","the Slovak University of Technology, Bratislava, Slovakia"],"affiliations":[{"raw_affiliation_string":"the Slovak University of Technology, Bratislava, Slovakia","institution_ids":["https://openalex.org/I110757952"]},{"raw_affiliation_string":"Institute for Research and Application of Fuzzy Modelling, University of Ostrava, Ostrava, Czech Republic","institution_ids":["https://openalex.org/I187293425"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020097031","display_name":"Andrea Mesiarov\u00e1\u2010Zem\u00e1nkov\u00e1","orcid":"https://orcid.org/0000-0003-4022-0086"},"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"]}],"countries":["SK"],"is_corresponding":false,"raw_author_name":"Andrea Mesiarova-Zem\u00e1nkov\u00e1","raw_affiliation_strings":["Mathematical Institute, Slovak Academy of Sciences, Bratislava, Slovakia"],"affiliations":[{"raw_affiliation_string":"Mathematical Institute, Slovak Academy of Sciences, Bratislava, Slovakia","institution_ids":["https://openalex.org/I207624831","https://openalex.org/I4210120676"]}]}],"institution_assertions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.831,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":50,"citation_normalized_percentile":{"value":0.859682,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":95},"biblio":{"volume":"19","issue":"1","first_page":"42","last_page":"50"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9997,"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"}},"topics":[{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9997,"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"}},{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9864,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9794,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/annihilator","display_name":"Annihilator","score":0.6637479},{"id":"https://openalex.org/keywords/associative-property","display_name":"Associative property","score":0.6454109},{"id":"https://openalex.org/keywords/modularity","display_name":"Modularity","score":0.4892759}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.76468194},{"id":"https://openalex.org/C147073270","wikidata":"https://www.wikidata.org/wiki/Q567083","display_name":"Annihilator","level":3,"score":0.6637479},{"id":"https://openalex.org/C159423971","wikidata":"https://www.wikidata.org/wiki/Q177251","display_name":"Associative property","level":2,"score":0.6454109},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.59380895},{"id":"https://openalex.org/C172252984","wikidata":"https://www.wikidata.org/wiki/Q368988","display_name":"Idempotence","level":2,"score":0.5710571},{"id":"https://openalex.org/C2779478453","wikidata":"https://www.wikidata.org/wiki/Q6889748","display_name":"Modularity (biology)","level":2,"score":0.4892759},{"id":"https://openalex.org/C17618745","wikidata":"https://www.wikidata.org/wiki/Q207509","display_name":"Copula (linguistics)","level":2,"score":0.48315376},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4181251},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.31291166},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16180906},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.08417076},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2010.2077641","pdf_url":null,"source":{"id":"https://openalex.org/S134177497","display_name":"IEEE Transactions on Fuzzy Systems","issn_l":"1063-6706","issn":["1063-6706","1941-0034"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":28,"referenced_works":["https://openalex.org/W153006619","https://openalex.org/W1533336287","https://openalex.org/W1538664553","https://openalex.org/W1905771608","https://openalex.org/W1946053744","https://openalex.org/W2008293184","https://openalex.org/W2016461138","https://openalex.org/W2018056115","https://openalex.org/W2024853570","https://openalex.org/W2030582622","https://openalex.org/W2047147035","https://openalex.org/W2050709486","https://openalex.org/W2060907774","https://openalex.org/W2063975741","https://openalex.org/W2071782633","https://openalex.org/W2081754091","https://openalex.org/W2087171145","https://openalex.org/W2095371287","https://openalex.org/W2116588516","https://openalex.org/W2133265661","https://openalex.org/W2145489396","https://openalex.org/W2147595926","https://openalex.org/W2482048267","https://openalex.org/W3121868810","https://openalex.org/W4238626452","https://openalex.org/W4241861175","https://openalex.org/W4252793191","https://openalex.org/W45613487"],"related_works":["https://openalex.org/W4298246872","https://openalex.org/W3106133691","https://openalex.org/W2972271193","https://openalex.org/W2380410337","https://openalex.org/W2325449674","https://openalex.org/W2320881711","https://openalex.org/W2147350690","https://openalex.org/W2043897844","https://openalex.org/W2028522012","https://openalex.org/W2000118329"],"abstract_inverted_index":{"Ordered":[0],"modular":[1,27],"averages":[2,7],"(OMAs)":[3],"generalize":[4],"ordered":[5],"weighted":[6],"operators,":[8,57],"with":[9,44,59,64],"the":[10,13,17],"replacement":[11],"of":[12],"additivity":[14],"property":[15],"by":[16,31],"modularity.":[18,33],"OMAs":[19,51,71],"can":[20,36],"be":[21,37],"seen":[22,38],"as":[23,40,55],"a":[24,41,47],"symmetrized":[25],"idempotent":[26],"aggregation":[28],"functions,":[29],"characterized":[30],"comonotone":[32],"Each":[34],"OMA":[35],"also":[39,73],"copula-based":[42],"integral":[43],"respect":[45],"to":[46],"symmetric":[48],"capacity.":[49],"Special":[50],"are":[52,72],"characterized,":[53],"such":[54],"associative":[56],"operators":[58,63],"neutral":[60],"element,":[61],"or":[62],"an":[65],"annihilator.":[66],"Some":[67],"construction":[68],"methods":[69],"for":[70],"discussed.":[74]},"abstract_inverted_index_v3":null,"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2086721181","counts_by_year":[{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":9}],"updated_date":"2025-04-19T04:45:24.261793","created_date":"2016-06-24"}