{"id":"https://openalex.org/W1976206702","doi":"https://doi.org/10.1109/tcyb.2013.2288731","title":"Uncertainty Representation of Grey Numbers and Grey Sets","display_name":"Uncertainty Representation of Grey Numbers and Grey Sets","publication_year":2014,"publication_date":"2014-08-14","ids":{"openalex":"https://openalex.org/W1976206702","doi":"https://doi.org/10.1109/tcyb.2013.2288731","mag":"1976206702","pmid":"https://pubmed.ncbi.nlm.nih.gov/25137681"},"language":"en","primary_location":{"id":"doi:10.1109/tcyb.2013.2288731","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2013.2288731","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":true,"oa_status":"green","oa_url":"https://nottingham-repository.worktribe.com/output/734219","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5006135936","display_name":"Yingjie Yang","orcid":"https://orcid.org/0000-0003-4525-5624"},"institutions":[{"id":"https://openalex.org/I66943878","display_name":"De Montfort University","ror":"https://ror.org/0312pnr83","country_code":"GB","type":"education","lineage":["https://openalex.org/I66943878"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Yingjie Yang","raw_affiliation_strings":["School of Computer Science and Informatics, De Montfort University, Leicester, U.K","School of Computer Science and Informatics, De Montfort University, Leicester, U.K.#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Informatics, De Montfort University, Leicester, U.K","institution_ids":["https://openalex.org/I66943878"]},{"raw_affiliation_string":"School of Computer Science and Informatics, De Montfort University, Leicester, U.K.#TAB#","institution_ids":["https://openalex.org/I66943878"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070239285","display_name":"Sifeng Liu","orcid":"https://orcid.org/0000-0002-5872-9457"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Sifeng Liu","raw_affiliation_strings":["Institute for Grey Systems Studies, Nanjing University of Aeronautics and Astronautics, Nanjing, China","(Institute for Grey Systems Studies, Nanjing University of Aeronautics and Astronautics, Nanjing, China)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Grey Systems Studies, Nanjing University of Aeronautics and Astronautics, Nanjing, China","institution_ids":["https://openalex.org/I9842412"]},{"raw_affiliation_string":"(Institute for Grey Systems Studies, Nanjing University of Aeronautics and Astronautics, Nanjing, China)","institution_ids":["https://openalex.org/I9842412"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091177679","display_name":"Robert John","orcid":"https://orcid.org/0000-0002-2341-9993"},"institutions":[{"id":"https://openalex.org/I142263535","display_name":"University of Nottingham","ror":"https://ror.org/01ee9ar58","country_code":"GB","type":"education","lineage":["https://openalex.org/I142263535"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Robert John","raw_affiliation_strings":["Automated Scheduling, Optimisation and Planning Group, School of Computer Science, University of Nottingham, Jubilee Campus, Nottingham, U.K","[Automated Scheduling, Optimisation and Planning Group, School of Computer Science, University of Nottingham, Jubilee Campus, Nottingham, U.K.]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Automated Scheduling, Optimisation and Planning Group, School of Computer Science, University of Nottingham, Jubilee Campus, Nottingham, U.K","institution_ids":["https://openalex.org/I142263535"]},{"raw_affiliation_string":"[Automated Scheduling, Optimisation and Planning Group, School of Computer Science, University of Nottingham, Jubilee Campus, Nottingham, U.K.]","institution_ids":["https://openalex.org/I142263535"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.8782,"has_fulltext":false,"cited_by_count":37,"citation_normalized_percentile":{"value":0.92849602,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"44","issue":"9","first_page":"1508","last_page":"1517"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9957000017166138,"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":0.9957000017166138,"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/T12368","display_name":"Grey System Theory Applications","score":0.9878000020980835,"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":0.9842000007629395,"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/presumption","display_name":"Presumption","score":0.7948554754257202},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6928319931030273},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.6475729942321777},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.6303803324699402},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.5807790756225586},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5316135883331299},{"id":"https://openalex.org/keywords/grey-level","display_name":"Grey level","score":0.4269822835922241},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.41688498854637146},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24607250094413757},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2371552288532257},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.13430428504943848},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.07072865962982178}],"concepts":[{"id":"https://openalex.org/C2780253743","wikidata":"https://www.wikidata.org/wiki/Q132382","display_name":"Presumption","level":2,"score":0.7948554754257202},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6928319931030273},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.6475729942321777},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.6303803324699402},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.5807790756225586},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5316135883331299},{"id":"https://openalex.org/C2994222927","wikidata":"https://www.wikidata.org/wiki/Q685727","display_name":"Grey level","level":3,"score":0.4269822835922241},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.41688498854637146},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24607250094413757},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2371552288532257},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.13430428504943848},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.07072865962982178},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/tcyb.2013.2288731","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2013.2288731","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:25137681","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/25137681","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},{"id":"pmh:oai:www.dora.dmu.ac.uk:2086/11661","is_oa":false,"landing_page_url":"http://hdl.handle.net/2086/11661","pdf_url":null,"source":{"id":"https://openalex.org/S4306400394","display_name":"DMU Open Research Archive (De Montfort University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66943878","host_organization_name":"De Montfort University","host_organization_lineage":["https://openalex.org/I66943878"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:eprints.nottingham.ac.uk:3369","is_oa":false,"landing_page_url":"http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6668878","pdf_url":null,"source":{"id":"https://openalex.org/S4306402014","display_name":"Nottingham ePrints (University of Nottingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I142263535","host_organization_name":"University of Nottingham","host_organization_lineage":["https://openalex.org/I142263535"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:nottingham-repository.worktribe.com:734219","is_oa":true,"landing_page_url":"https://nottingham-repository.worktribe.com/output/734219","pdf_url":null,"source":{"id":"https://openalex.org/S4306402483","display_name":"Repository@Nottingham (University of Nottingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I142263535","host_organization_name":"University of Nottingham","host_organization_lineage":["https://openalex.org/I142263535"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal Article"}],"best_oa_location":{"id":"pmh:oai:nottingham-repository.worktribe.com:734219","is_oa":true,"landing_page_url":"https://nottingham-repository.worktribe.com/output/734219","pdf_url":null,"source":{"id":"https://openalex.org/S4306402483","display_name":"Repository@Nottingham (University of Nottingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I142263535","host_organization_name":"University of Nottingham","host_organization_lineage":["https://openalex.org/I142263535"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal Article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.6399999856948853,"id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G4813020621","display_name":"\u57fa\u4e8eGERTS\u4eff\u771f\u7f51\u7edc\u7684\u975e\u5e38\u89c4\u7a81\u53d1\u4e8b\u4ef6\u60c5\u666f\u63a8\u6f14\u4e0e\u6d4b\u7b97\u95ee\u9898\u7814\u7a76","funder_award_id":"90924022","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G534277462","display_name":"\u57fa\u4e8e\u535a\u5f08\u4e3b\u4f53\u5229\u76ca\u6d41\u52a8GERT\u7f51\u7edc\u7684\u7ecf\u6d4e\u201c\u6ce1\u6cab\u201d\u5f62\u6210\u4e0e\u653f\u7b56\u201c\u5bf9\u51b2\u201d\u95ee\u9898\u7814\u7a76","funder_award_id":"70971064","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"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W182476373","https://openalex.org/W301079972","https://openalex.org/W1504704583","https://openalex.org/W1545067530","https://openalex.org/W1898259180","https://openalex.org/W1980564456","https://openalex.org/W1988242538","https://openalex.org/W1993810822","https://openalex.org/W1998169032","https://openalex.org/W1998780970","https://openalex.org/W2007135652","https://openalex.org/W2013377700","https://openalex.org/W2023892208","https://openalex.org/W2029074979","https://openalex.org/W2029377923","https://openalex.org/W2036244229","https://openalex.org/W2039556522","https://openalex.org/W2058379370","https://openalex.org/W2070411573","https://openalex.org/W2093689394","https://openalex.org/W2124024979","https://openalex.org/W2124772763","https://openalex.org/W2287304319","https://openalex.org/W2321427846","https://openalex.org/W2402944606","https://openalex.org/W2912565176","https://openalex.org/W2940898093","https://openalex.org/W4211007335","https://openalex.org/W4292295629","https://openalex.org/W6660037165","https://openalex.org/W6696105490","https://openalex.org/W6713465598"],"related_works":["https://openalex.org/W2375756267","https://openalex.org/W2590979390","https://openalex.org/W2349734842","https://openalex.org/W2364798167","https://openalex.org/W2384536573","https://openalex.org/W811031611","https://openalex.org/W2357293271","https://openalex.org/W2347517220","https://openalex.org/W1510344287","https://openalex.org/W2009346655"],"abstract_inverted_index":{"In":[0,30],"the":[1,21,75,111,116],"literature,":[2],"there":[3],"is":[4],"a":[5,8,27,54,60,64,91,95],"presumption":[6,19],"that":[7,74,123],"grey":[9,28,38,41,61,65,92,96,101,124],"set":[10,15],"and":[11,40,47,63,87,94,103,126],"an":[12,81],"interval-valued":[13,104,127],"fuzzy":[14,105,128],"are":[16,50,70,107],"equivalent.":[17],"This":[18],"ignores":[20],"existence":[22],"of":[23,35,37,44,57,84,113,115],"discrete":[24],"components":[25],"in":[26,59,90,138],"number.":[29],"this":[31],"paper,":[32],"new":[33],"measurements":[34],"uncertainties":[36,58,89],"numbers":[39],"sets,":[42],"consisting":[43],"both":[45,85],"absolute":[46,86],"relative":[48,88],"uncertainties,":[49],"defined":[51],"to":[52,72],"give":[53,80],"comprehensive":[55],"representation":[56,83,137],"number":[62,93],"set.":[66,97],"Some":[67],"simple":[68],"examples":[69],"provided":[71],"illustrate":[73],"proposed":[76,117],"uncertainty":[77,118,136],"measurement":[78],"can":[79],"effective":[82],"The":[98,120],"relationships":[99],"between":[100],"sets":[102,106,125,129],"also":[108],"analyzed":[109],"from":[110],"point":[112],"view":[114],"representation.":[119],"analysis":[121],"demonstrates":[122],"provide":[130],"different":[131],"but":[132],"overlapping":[133],"models":[134],"for":[135],"sets.":[139]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
