{"id":"https://openalex.org/W2177733278","doi":"https://doi.org/10.1109/fuzz-ieee.2015.7337941","title":"Circumcenter of centroid in ranking fuzzy number: A case of generalized trapezoidal fuzzy numbers","display_name":"Circumcenter of centroid in ranking fuzzy number: A case of generalized trapezoidal fuzzy numbers","publication_year":2015,"publication_date":"2015-08-01","ids":{"openalex":"https://openalex.org/W2177733278","doi":"https://doi.org/10.1109/fuzz-ieee.2015.7337941","mag":"2177733278"},"language":"en","primary_location":{"id":"doi:10.1109/fuzz-ieee.2015.7337941","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fuzz-ieee.2015.7337941","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)","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/A5051424885","display_name":"Lazim Abdullah","orcid":"https://orcid.org/0000-0002-6646-4751"},"institutions":[{"id":"https://openalex.org/I157696592","display_name":"Universiti Malaysia Terengganu","ror":"https://ror.org/02474f074","country_code":"MY","type":"education","lineage":["https://openalex.org/I157696592"]}],"countries":["MY"],"is_corresponding":true,"raw_author_name":"Lazim Abdullah","raw_affiliation_strings":["School of Informatics and Applied Mathematics, University Malaysia Terengganu, Kuala Terengganu, Malaysia"],"affiliations":[{"raw_affiliation_string":"School of Informatics and Applied Mathematics, University Malaysia Terengganu, Kuala Terengganu, Malaysia","institution_ids":["https://openalex.org/I157696592"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037604826","display_name":"Fateen Najwa Azman","orcid":null},"institutions":[{"id":"https://openalex.org/I157696592","display_name":"Universiti Malaysia Terengganu","ror":"https://ror.org/02474f074","country_code":"MY","type":"education","lineage":["https://openalex.org/I157696592"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"Fateen Najwa Azman","raw_affiliation_strings":["School of Informatics and Applied Mathematics, University Malaysia Terengganu, Kuala Terengganu, Malaysia"],"affiliations":[{"raw_affiliation_string":"School of Informatics and Applied Mathematics, University Malaysia Terengganu, Kuala Terengganu, Malaysia","institution_ids":["https://openalex.org/I157696592"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5051424885"],"corresponding_institution_ids":["https://openalex.org/I157696592"],"apc_list":null,"apc_paid":null,"fwci":0.4006,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.70296205,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"6","issue":null,"first_page":"1","last_page":"6"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9994999766349792,"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/T12709","display_name":"Optimization and Mathematical Programming","score":0.9950000047683716,"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/fuzzy-number","display_name":"Fuzzy number","score":0.8242565989494324},{"id":"https://openalex.org/keywords/ranking","display_name":"Ranking (information retrieval)","score":0.7370885014533997},{"id":"https://openalex.org/keywords/centroid","display_name":"Centroid","score":0.6525605916976929},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6159021854400635},{"id":"https://openalex.org/keywords/defuzzification","display_name":"Defuzzification","score":0.6141076683998108},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5458202958106995},{"id":"https://openalex.org/keywords/fuzzy-classification","display_name":"Fuzzy classification","score":0.5372787117958069},{"id":"https://openalex.org/keywords/fuzzy-set-operations","display_name":"Fuzzy set operations","score":0.5202937722206116},{"id":"https://openalex.org/keywords/fuzzy-mathematics","display_name":"Fuzzy mathematics","score":0.49333110451698303},{"id":"https://openalex.org/keywords/type-2-fuzzy-sets-and-systems","display_name":"Type-2 fuzzy sets and systems","score":0.4920639395713806},{"id":"https://openalex.org/keywords/ranking-svm","display_name":"Ranking SVM","score":0.45744770765304565},{"id":"https://openalex.org/keywords/flexibility","display_name":"Flexibility (engineering)","score":0.44333091378211975},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.3993634283542633},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.3485719561576843},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34828054904937744},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3400290012359619},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32682156562805176},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.18885692954063416}],"concepts":[{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.8242565989494324},{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.7370885014533997},{"id":"https://openalex.org/C146599234","wikidata":"https://www.wikidata.org/wiki/Q511093","display_name":"Centroid","level":2,"score":0.6525605916976929},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6159021854400635},{"id":"https://openalex.org/C170260401","wikidata":"https://www.wikidata.org/wiki/Q5251735","display_name":"Defuzzification","level":5,"score":0.6141076683998108},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5458202958106995},{"id":"https://openalex.org/C127385683","wikidata":"https://www.wikidata.org/wiki/Q1475696","display_name":"Fuzzy classification","level":4,"score":0.5372787117958069},{"id":"https://openalex.org/C148671577","wikidata":"https://www.wikidata.org/wiki/Q5511133","display_name":"Fuzzy set operations","level":4,"score":0.5202937722206116},{"id":"https://openalex.org/C166586474","wikidata":"https://www.wikidata.org/wiki/Q5511129","display_name":"Fuzzy mathematics","level":5,"score":0.49333110451698303},{"id":"https://openalex.org/C17350324","wikidata":"https://www.wikidata.org/wiki/Q7860605","display_name":"Type-2 fuzzy sets and systems","level":5,"score":0.4920639395713806},{"id":"https://openalex.org/C124975894","wikidata":"https://www.wikidata.org/wiki/Q7293290","display_name":"Ranking SVM","level":3,"score":0.45744770765304565},{"id":"https://openalex.org/C2780598303","wikidata":"https://www.wikidata.org/wiki/Q65921492","display_name":"Flexibility (engineering)","level":2,"score":0.44333091378211975},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.3993634283542633},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.3485719561576843},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34828054904937744},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3400290012359619},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32682156562805176},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.18885692954063416}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/fuzz-ieee.2015.7337941","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fuzz-ieee.2015.7337941","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7200000286102295,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W111796927","https://openalex.org/W120108131","https://openalex.org/W194786220","https://openalex.org/W1968091565","https://openalex.org/W1969140532","https://openalex.org/W1973256758","https://openalex.org/W1982710770","https://openalex.org/W1987249808","https://openalex.org/W1990794890","https://openalex.org/W1994178762","https://openalex.org/W1994997349","https://openalex.org/W2001277869","https://openalex.org/W2006489162","https://openalex.org/W2016303054","https://openalex.org/W2026832772","https://openalex.org/W2036861478","https://openalex.org/W2039796074","https://openalex.org/W2055394893","https://openalex.org/W2058295453","https://openalex.org/W2075722074","https://openalex.org/W2078538587","https://openalex.org/W2095690503","https://openalex.org/W2107390469","https://openalex.org/W2149276443","https://openalex.org/W2185491205","https://openalex.org/W2324038710","https://openalex.org/W2475314306","https://openalex.org/W4233704167","https://openalex.org/W4285719527","https://openalex.org/W6686242389","https://openalex.org/W6700705605"],"related_works":["https://openalex.org/W2184441312","https://openalex.org/W1485268022","https://openalex.org/W2674573885","https://openalex.org/W2253053392","https://openalex.org/W1542808721","https://openalex.org/W2331106272","https://openalex.org/W3176863924","https://openalex.org/W1489009679","https://openalex.org/W3186561448","https://openalex.org/W2025902904"],"abstract_inverted_index":{"Many":[0],"approaches":[1],"have":[2],"been":[3],"proposed":[4],"to":[5,14,27,53,61,78,104,130],"quest":[6],"appropriate":[7],"methods":[8,23],"in":[9,84],"ranking":[10,32,50,67,107],"fuzzy":[11,18,33,55,68,102,120],"numbers.":[12],"Due":[13],"the":[15,48,71,76,80,85,92,94,96,99,106,112,132],"flexibility":[16],"of":[17,21,31,37,73,82,101],"numbers,":[19],"most":[20],"these":[22],"are":[24],"not":[25],"able":[26],"calculate":[28],"all":[29],"kinds":[30],"numbers":[34,56,69,103,121],"and":[35,41,98,122],"some":[36],"them":[38],"give":[39],"inconsistent":[40],"counter":[42],"intuitive":[43],"results.":[44],"As":[45],"a":[46,63],"result,":[47],"final":[49],"sometimes":[51],"fails":[52],"discriminate":[54],"effectively.":[57],"This":[58],"paper":[59],"aims":[60],"propose":[62],"new":[64,88,113],"method":[65,89,114],"for":[66,111],"using":[70],"circumcenter":[72,123],"centroid":[74],"with":[75],"hope":[77],"reduce":[79],"problem":[81],"indiscriminate":[83],"ranking.":[86],"The":[87,109],"mainly":[90],"considers":[91],"distance,":[93],"spread,":[95],"height":[97],"area":[100],"compute":[105],"order.":[108],"calculation":[110,133],"is":[115,128],"derived":[116],"from":[117],"generalized":[118],"trapezoidal":[119],"concepts.":[124],"A":[125],"numerical":[126],"example":[127],"given":[129],"illustrate":[131],"more":[134],"explicitly.":[135]},"counts_by_year":[{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}