{"id":"https://openalex.org/W2329530109","doi":"https://doi.org/10.3233/ifs-151986","title":"Type-2 fuzzy cross-entropy and entropy measures and their applications","display_name":"Type-2 fuzzy cross-entropy and entropy measures and their applications","publication_year":2016,"publication_date":"2016-03-10","ids":{"openalex":"https://openalex.org/W2329530109","doi":"https://doi.org/10.3233/ifs-151986","mag":"2329530109"},"language":"en","primary_location":{"id":"doi:10.3233/ifs-151986","is_oa":false,"landing_page_url":"https://doi.org/10.3233/ifs-151986","pdf_url":null,"source":{"id":"https://openalex.org/S179157397","display_name":"Journal of Intelligent & Fuzzy Systems","issn_l":"1064-1246","issn":["1064-1246","1875-8967"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Intelligent & Fuzzy 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/A5055934881","display_name":"Dengbao Yao","orcid":null},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Dengbao Yao","raw_affiliation_strings":["School of Economics and Management, Southeast University, Nanjing, Jiangsu, China"],"affiliations":[{"raw_affiliation_string":"School of Economics and Management, Southeast University, Nanjing, Jiangsu, China","institution_ids":["https://openalex.org/I76569877"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100783765","display_name":"Xiaoxing Liu","orcid":"https://orcid.org/0000-0001-8243-7895"},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoxing Liu","raw_affiliation_strings":["School of Economics and Management, Southeast University, Nanjing, Jiangsu, China"],"affiliations":[{"raw_affiliation_string":"School of Economics and Management, Southeast University, Nanjing, Jiangsu, China","institution_ids":["https://openalex.org/I76569877"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100437236","display_name":"Xu Zhang","orcid":"https://orcid.org/0000-0002-5596-9519"},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xu Zhang","raw_affiliation_strings":["School of Economics and Management, Southeast University, Nanjing, Jiangsu, China"],"affiliations":[{"raw_affiliation_string":"School of Economics and Management, Southeast University, Nanjing, Jiangsu, China","institution_ids":["https://openalex.org/I76569877"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101729663","display_name":"Cuicui Wang","orcid":"https://orcid.org/0000-0001-5729-9638"},"institutions":[{"id":"https://openalex.org/I4210088165","display_name":"Anhui Sanlian University","ror":"https://ror.org/012sfmg27","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210088165"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Cuicui Wang","raw_affiliation_strings":["Department of Foundation, Anhui Sanlian University, Hefei, Anhui, China","E-mail:"],"affiliations":[{"raw_affiliation_string":"Department of Foundation, Anhui Sanlian University, Hefei, Anhui, China","institution_ids":["https://openalex.org/I4210088165"]},{"raw_affiliation_string":"E-mail:","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5055934881"],"corresponding_institution_ids":["https://openalex.org/I76569877"],"apc_list":null,"apc_paid":null,"fwci":3.9496,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.93567517,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"30","issue":"4","first_page":"2169","last_page":"2180"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9954000115394592,"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":0.9954000115394592,"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":0.9918000102043152,"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":0.9843999743461609,"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/mathematics","display_name":"Mathematics","score":0.6157699823379517},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.5229723453521729},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5131107568740845},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.4937222898006439},{"id":"https://openalex.org/keywords/joint-entropy","display_name":"Joint entropy","score":0.4736191928386688},{"id":"https://openalex.org/keywords/fuzzy-classification","display_name":"Fuzzy classification","score":0.4299430549144745},{"id":"https://openalex.org/keywords/defuzzification","display_name":"Defuzzification","score":0.4237602949142456},{"id":"https://openalex.org/keywords/type-2-fuzzy-sets-and-systems","display_name":"Type-2 fuzzy sets and systems","score":0.41559356451034546},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.384912371635437},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.37059324979782104},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.34704118967056274},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3277199864387512},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.2163633108139038},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.17804202437400818},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.09372377395629883},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06689941883087158}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6157699823379517},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.5229723453521729},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5131107568740845},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.4937222898006439},{"id":"https://openalex.org/C106752470","wikidata":"https://www.wikidata.org/wiki/Q1364826","display_name":"Joint entropy","level":3,"score":0.4736191928386688},{"id":"https://openalex.org/C127385683","wikidata":"https://www.wikidata.org/wiki/Q1475696","display_name":"Fuzzy classification","level":4,"score":0.4299430549144745},{"id":"https://openalex.org/C170260401","wikidata":"https://www.wikidata.org/wiki/Q5251735","display_name":"Defuzzification","level":5,"score":0.4237602949142456},{"id":"https://openalex.org/C17350324","wikidata":"https://www.wikidata.org/wiki/Q7860605","display_name":"Type-2 fuzzy sets and systems","level":5,"score":0.41559356451034546},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.384912371635437},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.37059324979782104},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.34704118967056274},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3277199864387512},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.2163633108139038},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.17804202437400818},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.09372377395629883},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06689941883087158}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/ifs-151986","is_oa":false,"landing_page_url":"https://doi.org/10.3233/ifs-151986","pdf_url":null,"source":{"id":"https://openalex.org/S179157397","display_name":"Journal of Intelligent & Fuzzy Systems","issn_l":"1064-1246","issn":["1064-1246","1875-8967"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Intelligent & Fuzzy Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"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":50,"referenced_works":["https://openalex.org/W264425378","https://openalex.org/W1968026678","https://openalex.org/W1968237275","https://openalex.org/W1974562332","https://openalex.org/W1975672023","https://openalex.org/W1996937753","https://openalex.org/W2000763566","https://openalex.org/W2002027507","https://openalex.org/W2002212630","https://openalex.org/W2010740403","https://openalex.org/W2012399117","https://openalex.org/W2025542264","https://openalex.org/W2026244788","https://openalex.org/W2026489439","https://openalex.org/W2026829949","https://openalex.org/W2036187701","https://openalex.org/W2037940305","https://openalex.org/W2038190934","https://openalex.org/W2038917738","https://openalex.org/W2041675778","https://openalex.org/W2041775680","https://openalex.org/W2042914607","https://openalex.org/W2053142133","https://openalex.org/W2058683246","https://openalex.org/W2062705596","https://openalex.org/W2062897401","https://openalex.org/W2072199060","https://openalex.org/W2074164494","https://openalex.org/W2076250596","https://openalex.org/W2083199031","https://openalex.org/W2089254176","https://openalex.org/W2091130862","https://openalex.org/W2091275864","https://openalex.org/W2093064982","https://openalex.org/W2103248018","https://openalex.org/W2116056277","https://openalex.org/W2126930230","https://openalex.org/W2129135389","https://openalex.org/W2131390763","https://openalex.org/W2132885717","https://openalex.org/W2155263265","https://openalex.org/W2157041604","https://openalex.org/W2164879989","https://openalex.org/W2168164276","https://openalex.org/W2598771954","https://openalex.org/W4206636130","https://openalex.org/W4245152641","https://openalex.org/W6666349324","https://openalex.org/W6677515282","https://openalex.org/W6679780668"],"related_works":["https://openalex.org/W2184441312","https://openalex.org/W2674573885","https://openalex.org/W1485268022","https://openalex.org/W1975005191","https://openalex.org/W4361984403","https://openalex.org/W3176863924","https://openalex.org/W2331106272","https://openalex.org/W1542808721","https://openalex.org/W2253053392","https://openalex.org/W2060361571"],"abstract_inverted_index":{"Type-2":[0],"fuzzy":[1,34,72,81,109,125,139,150],"sets":[2],"(T2FSs)":[3],"have":[4],"received":[5],"increasing":[6],"attention":[7],"due":[8],"to":[9,13,27,91,162],"its":[10],"great":[11],"ability":[12],"handle":[14],"imprecise":[15],"and":[16,36,64,74,111,119,127,133,152,168],"ambiguous":[17],"information":[18,97],"in":[19],"reality.":[20],"The":[21],"purpose":[22],"of":[23,32,49,57,62,95,107,148,166],"this":[24],"paper":[25],"is":[26,60],"develop":[28,169],"a":[29,41,58,170],"general":[30],"framework":[31],"type-2":[33,80,108,117,124,138],"cross-entropy":[35,82,118,126],"entropy":[37,110,128,140,151],"measures,":[38],"which":[39,66],"provides":[40],"fresh":[42],"new":[43,171],"look":[44],"into":[45],"the":[46,71,93,104,113,145,149,158,163],"un":[47],"certainty":[48],"T2FSs.":[50,100],"We":[51],"first":[52],"point":[53],"out":[54],"that":[55,137],"uncertainty":[56,160],"T2FS":[59],"consist":[61],"fuzziness":[63],"hesitancy,":[65],"could":[67,141],"be":[68,142],"described":[69],"by":[70],"factor":[73],"hesitant":[75,153],"factor,":[76],"respectively.":[77],"A":[78],"novel":[79],"has":[83],"been":[84],"initiated":[85],"based":[86],"on":[87],"these":[88],"two":[89,99],"factors":[90],"measure":[92],"discrimination":[94],"uncertain":[96],"between":[98,116],"Meanwhile,":[101],"we":[102,156],"refine":[103],"axiomatic":[105],"principles":[106],"study":[112],"inherent":[114],"relationship":[115],"entropy.":[120,154],"Moreover,":[121],"some":[122],"parameterized":[123],"measures":[129,161],"are":[130],"also":[131],"investigated,":[132],"decomposition":[134],"formula":[135],"suggests":[136],"expressed":[143],"as":[144],"weighted":[146],"average":[147],"Finally,":[155],"apply":[157],"proposed":[159],"clustering":[164],"pattern":[165],"T2FSs":[167],"multiple":[172],"attribute":[173],"decision-making":[174],"(MADM)":[175],"approach.":[176]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":5}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}