{"id":"https://openalex.org/W2940816634","doi":"https://doi.org/10.1109/tcyb.2019.2908657","title":"Additive Integrals of $q$ -Rung Orthopair Fuzzy Functions","display_name":"Additive Integrals of $q$ -Rung Orthopair Fuzzy Functions","publication_year":2019,"publication_date":"2019-04-27","ids":{"openalex":"https://openalex.org/W2940816634","doi":"https://doi.org/10.1109/tcyb.2019.2908657","mag":"2940816634","pmid":"https://pubmed.ncbi.nlm.nih.gov/31034429"},"language":"en","primary_location":{"id":"doi:10.1109/tcyb.2019.2908657","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2019.2908657","pdf_url":null,"source":{"id":"https://openalex.org/S4210191041","display_name":"IEEE Transactions on Cybernetics","issn_l":"2168-2267","issn":["2168-2267","2168-2275"],"is_oa":false,"is_in_doaj":false,"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Cybernetics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5087409056","display_name":"Jie Gao","orcid":"https://orcid.org/0000-0001-7420-8558"},"institutions":[{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jie Gao","raw_affiliation_strings":["Institute for Disaster Management and Reconstruction, Sichuan University, Chengdu, China"],"raw_orcid":"https://orcid.org/0000-0001-7420-8558","affiliations":[{"raw_affiliation_string":"Institute for Disaster Management and Reconstruction, Sichuan University, Chengdu, China","institution_ids":["https://openalex.org/I24185976"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034235282","display_name":"Zhilei Liang","orcid":"https://orcid.org/0000-0001-9888-4307"},"institutions":[{"id":"https://openalex.org/I204831749","display_name":"Southwestern University of Finance and Economics","ror":"https://ror.org/04ewct822","country_code":"CN","type":"education","lineage":["https://openalex.org/I204831749"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhilei Liang","raw_affiliation_strings":["School of Economic mathematics, Southwestern University of Finance and Economics, Chengdu, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Economic mathematics, Southwestern University of Finance and Economics, Chengdu, China","institution_ids":["https://openalex.org/I204831749"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100437308","display_name":"Zeshui Xu","orcid":"https://orcid.org/0000-0003-3547-2908"},"institutions":[{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]},{"id":"https://openalex.org/I4391767678","display_name":"State Key Laboratory of Hydraulics and Mountain River Engineering","ror":"https://ror.org/02169wb20","country_code":null,"type":"facility","lineage":["https://openalex.org/I24185976","https://openalex.org/I4391767678"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zeshui Xu","raw_affiliation_strings":["Business School, State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu, China"],"raw_orcid":"https://orcid.org/0000-0003-3547-2908","affiliations":[{"raw_affiliation_string":"Business School, State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu, China","institution_ids":["https://openalex.org/I24185976","https://openalex.org/I4391767678"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5087409056"],"corresponding_institution_ids":["https://openalex.org/I24185976"],"apc_list":null,"apc_paid":null,"fwci":4.537,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.94627145,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"50","issue":"10","first_page":"4406","last_page":"4419"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9997000098228455,"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":0.9997000098228455,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9986000061035156,"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"}},{"id":"https://openalex.org/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9955999851226807,"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/fuzzy-logic","display_name":"Fuzzy logic","score":0.6550759673118591},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6488806009292603},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.5048409104347229},{"id":"https://openalex.org/keywords/ambiguity","display_name":"Ambiguity","score":0.45650702714920044},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36509275436401367},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3302996754646301},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.32800015807151794},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32754814624786377},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2129814326763153},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07563889026641846}],"concepts":[{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.6550759673118591},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6488806009292603},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.5048409104347229},{"id":"https://openalex.org/C2780522230","wikidata":"https://www.wikidata.org/wiki/Q1140419","display_name":"Ambiguity","level":2,"score":0.45650702714920044},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36509275436401367},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3302996754646301},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32800015807151794},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32754814624786377},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2129814326763153},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07563889026641846},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tcyb.2019.2908657","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2019.2908657","pdf_url":null,"source":{"id":"https://openalex.org/S4210191041","display_name":"IEEE Transactions on Cybernetics","issn_l":"2168-2267","issn":["2168-2267","2168-2275"],"is_oa":false,"is_in_doaj":false,"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Cybernetics","raw_type":"journal-article"},{"id":"pmid:31034429","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/31034429","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on cybernetics","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3405032213","display_name":null,"funder_award_id":"201706240200","funder_id":"https://openalex.org/F4320322725","funder_display_name":"China Scholarship Council"},{"id":"https://openalex.org/G597183912","display_name":null,"funder_award_id":"71771155","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6312906571","display_name":null,"funder_award_id":"71571123","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322725","display_name":"China Scholarship Council","ror":"https://ror.org/04atp4p48"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W45798882","https://openalex.org/W1662577487","https://openalex.org/W1668569279","https://openalex.org/W1969243969","https://openalex.org/W1975777423","https://openalex.org/W1980564456","https://openalex.org/W2006285333","https://openalex.org/W2013932252","https://openalex.org/W2017977229","https://openalex.org/W2050082080","https://openalex.org/W2084063803","https://openalex.org/W2094381401","https://openalex.org/W2285989436","https://openalex.org/W2342656879","https://openalex.org/W2514754342","https://openalex.org/W2563128797","https://openalex.org/W2587709158","https://openalex.org/W2735403265","https://openalex.org/W2746747652","https://openalex.org/W2756292711","https://openalex.org/W2760702401","https://openalex.org/W2789682920","https://openalex.org/W2793014487","https://openalex.org/W2796547704","https://openalex.org/W2801101481","https://openalex.org/W2884166416","https://openalex.org/W2884892695","https://openalex.org/W2904970805","https://openalex.org/W3148374392","https://openalex.org/W4230571157"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2353179089","https://openalex.org/W2923538289","https://openalex.org/W2353125546","https://openalex.org/W2470643824","https://openalex.org/W4400595174","https://openalex.org/W2349635380","https://openalex.org/W4353089801","https://openalex.org/W2353819554","https://openalex.org/W2359488321"],"abstract_inverted_index":{"The":[0,22],"q":[1,7,29,35,41,48,54,64,70,81,87,99,126,137,168,182,199,235,242],"-rung":[2,30,36,49,82,236],"orthopair":[3,31,37,50,83,237],"fuzzy":[4,32,38,51,84,119,238],"set":[5],"(":[6,40,53,86],"-ROFS)":[8],"is":[9,34,47,90,110],"a":[10],"powerful":[11,106],"tool":[12],"to":[13,77,201,211,226],"deal":[14],"with":[15,103,132,240],"uncertainty":[16],"and":[17,43,61,94,105,113,116,173,189,206,230],"ambiguity":[18],"in":[19,66],"real":[20],"life.":[21],"theoretical":[23,101,121,216],"basis":[24],"for":[25],"processing":[26],"the":[27,44,57,67,80,91,98,111,118,124,133,144,161,175,198,202,215,228,241],"continuous":[28,234],"information":[33],"calculus":[39,120],"-ROFC)":[42],"main":[45],"object":[46],"functions":[52,208],"-ROFFs).":[55],"Recently,":[56],"authors":[58],"proposed":[59],"derivatives":[60],"differentials":[62],"of":[63,69,97,123,136,147,152,164,167,181,232],"-ROFFs":[65,169],"framework":[68],"-ROFC.":[71],"In":[72,128],"this":[73],"paper,":[74],"we":[75,130,159,196,221],"aim":[76],"further":[78],"study":[79],"integral":[85,135,177],"-ROFI).":[88],"It":[89],"most":[92],"important":[93],"fundamental":[95],"part":[96],"-ROFC":[100],"system":[102],"direct":[104],"applications.":[107],"Our":[108],"contribution":[109],"indefinite":[112,134],"definite":[114,165],"integrals,":[115],"bridges":[117],"gap":[122],"nonlinear":[125],"-ROFFs.":[127],"particular,":[129],"begin":[131],"-ROFFs,":[138],"which":[139],"can":[140],"be":[141,212],"regarded":[142],"as":[143,185],"anti-derivatives":[145],"operations":[146],"our":[148],"previous":[149],"work.":[150],"Some":[151,179],"their":[153],"basic":[154],"properties":[155,180],"are":[156,193,209],"discussed.":[157],"Next,":[158],"give":[160],"accurate":[162],"concept":[163],"integrals":[166],"under":[170],"additive":[171],"operations,":[172,188],"obtain":[174],"explicit":[176],"formula.":[178],"-ROFIs,":[183],"such":[184],"comparison,":[186],"algebraic":[187],"mean":[190],"value":[191],"theorem":[192],"analyzed.":[194],"Finally,":[195],"generalize":[197],"-ROFI":[200],"case":[203],"when":[204],"membership":[205],"nonmembership":[207],"allowed":[210],"correlated.":[213],"After":[214],"results":[217],"have":[218],"been":[219],"established,":[220],"present":[222],"some":[223],"numerical":[224],"examples":[225],"demonstrate":[227],"rationality":[229],"effectiveness":[231],"integrating":[233],"data":[239],"-ROFIs.":[243]},"counts_by_year":[{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}