{"id":"https://openalex.org/W2129105253","doi":"https://doi.org/10.1109/fskd.2010.5569774","title":"(T) fuzzy integral of multi-dimensional function","display_name":"(T) fuzzy integral of multi-dimensional function","publication_year":2010,"publication_date":"2010-08-01","ids":{"openalex":"https://openalex.org/W2129105253","doi":"https://doi.org/10.1109/fskd.2010.5569774","mag":"2129105253"},"language":"en","primary_location":{"id":"doi:10.1109/fskd.2010.5569774","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fskd.2010.5569774","pdf_url":null,"source":{"id":"https://openalex.org/S4363608217","display_name":"2010 Seventh International Conference on Fuzzy Systems and Knowledge Discovery","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2010 Seventh International Conference on Fuzzy Systems and Knowledge Discovery","raw_type":"proceedings-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/A5100614461","display_name":"Wanli Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I25757504","display_name":"China University of Mining and Technology","ror":"https://ror.org/01xt2dr21","country_code":"CN","type":"education","lineage":["https://openalex.org/I25757504"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Wanli Liu","raw_affiliation_strings":["Department of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu, China","Department of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu, China 221008"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu, China","institution_ids":["https://openalex.org/I25757504"]},{"raw_affiliation_string":"Department of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu, China 221008","institution_ids":["https://openalex.org/I25757504"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5105516243","display_name":"Xiaoqiu Song","orcid":"https://orcid.org/0000-0002-0886-3682"},"institutions":[{"id":"https://openalex.org/I25757504","display_name":"China University of Mining and Technology","ror":"https://ror.org/01xt2dr21","country_code":"CN","type":"education","lineage":["https://openalex.org/I25757504"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoqiu Song","raw_affiliation_strings":["Department of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu, China","Department of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu, China 221008"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu, China","institution_ids":["https://openalex.org/I25757504"]},{"raw_affiliation_string":"Department of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu, China 221008","institution_ids":["https://openalex.org/I25757504"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054668754","display_name":"Qiuzhao Zhang","orcid":"https://orcid.org/0000-0001-8050-3991"},"institutions":[{"id":"https://openalex.org/I25757504","display_name":"China University of Mining and Technology","ror":"https://ror.org/01xt2dr21","country_code":"CN","type":"education","lineage":["https://openalex.org/I25757504"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qiuzhao Zhang","raw_affiliation_strings":["School of Environment Science and Spatial Informatics, China University of Mining and Technology, China"],"affiliations":[{"raw_affiliation_string":"School of Environment Science and Spatial Informatics, China University of Mining and Technology, China","institution_ids":["https://openalex.org/I25757504"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100614461"],"corresponding_institution_ids":["https://openalex.org/I25757504"],"apc_list":null,"apc_paid":null,"fwci":2.7692,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.85915493,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"62","issue":null,"first_page":"1","last_page":"5"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9998000264167786,"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/T10050","display_name":"Multi-Criteria Decision Making","score":0.996399998664856,"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/T12709","display_name":"Optimization and Mathematical Programming","score":0.9751999974250793,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.6286612153053284},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5959070920944214},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5865219235420227},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.56013023853302},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.48202216625213623},{"id":"https://openalex.org/keywords/fuzzy-measure-theory","display_name":"Fuzzy measure theory","score":0.47903624176979065},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.4517289698123932},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.43220359086990356},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4078121483325958},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35646483302116394},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34350883960723877},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.3434380888938904},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3409755825996399},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3327248692512512},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.328580379486084},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.3144122362136841},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1648988127708435},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.08261770009994507}],"concepts":[{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.6286612153053284},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5959070920944214},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5865219235420227},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.56013023853302},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.48202216625213623},{"id":"https://openalex.org/C100516043","wikidata":"https://www.wikidata.org/wiki/Q4455138","display_name":"Fuzzy measure theory","level":5,"score":0.47903624176979065},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.4517289698123932},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.43220359086990356},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4078121483325958},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35646483302116394},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34350883960723877},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.3434380888938904},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3409755825996399},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3327248692512512},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.328580379486084},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.3144122362136841},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1648988127708435},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.08261770009994507},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/fskd.2010.5569774","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fskd.2010.5569774","pdf_url":null,"source":{"id":"https://openalex.org/S4363608217","display_name":"2010 Seventh International Conference on Fuzzy Systems and Knowledge Discovery","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2010 Seventh International Conference on Fuzzy Systems and Knowledge Discovery","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W2012706073","https://openalex.org/W2022730486","https://openalex.org/W2043021764","https://openalex.org/W2052753108","https://openalex.org/W2158988058","https://openalex.org/W2370129269"],"related_works":["https://openalex.org/W2280435155","https://openalex.org/W2163770090","https://openalex.org/W2097081898","https://openalex.org/W2162798826","https://openalex.org/W112649326","https://openalex.org/W2135089589","https://openalex.org/W2390411038","https://openalex.org/W2130366545","https://openalex.org/W2037428035","https://openalex.org/W2355940045"],"abstract_inverted_index":{"Firstly,":[0],"based":[1],"on":[2,31],"the":[3,32,51,58],"T":[4,47,54],"fuzzy":[5,9,55],"measure":[6],"and":[7,23,27,48,62,68],"(T)":[8],"integral":[10],"of":[11,35,53],"one-dimensional":[12,76],"function,":[13],"this":[14],"paper":[15],"defines":[16],"multi-dimensional":[17,38,59,65],"simple":[18,60],"function":[19,61,67],"using":[20],"generalized":[21],"T-norm":[22],"S":[24],"-":[25],"norm":[26],"obtains":[28],"a":[29,36,63],"theorem":[30],"representation":[33],"form":[34],"common":[37,64],"measurable":[39,66],"function.":[40],"Then":[41],"it":[42],"introduces":[43],"two":[44],"operational":[45],"symbols":[46],"S,":[49],"presents":[50],"definitions":[52],"integrals":[56],"for":[57],"discusses":[69],"some":[70],"properties":[71],"which":[72],"are":[73],"similar":[74],"to":[75],"case.":[77]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
