{"id":"https://openalex.org/W2143760316","doi":"https://doi.org/10.1109/tfuzz.2012.2227488","title":"On KM Algorithms for Solving Type-2 Fuzzy Set Problems","display_name":"On KM Algorithms for Solving Type-2 Fuzzy Set Problems","publication_year":2012,"publication_date":"2012-11-21","ids":{"openalex":"https://openalex.org/W2143760316","doi":"https://doi.org/10.1109/tfuzz.2012.2227488","mag":"2143760316"},"language":"en","primary_location":{"id":"doi:10.1109/tfuzz.2012.2227488","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2012.2227488","pdf_url":null,"source":{"id":"https://openalex.org/S134177497","display_name":"IEEE Transactions on Fuzzy Systems","issn_l":"1063-6706","issn":["1063-6706","1941-0034"],"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 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/A5028699912","display_name":"Jerry M. Mendel","orcid":"https://orcid.org/0000-0001-6377-2452"},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jerry M. Mendel","raw_affiliation_strings":["Signal and Image Processing Institute, University of Southern California, Los Angeles, CA, USA","[Signal and Image Processing Institute, University of Southern California, Los Angeles, CA, USA]"],"affiliations":[{"raw_affiliation_string":"Signal and Image Processing Institute, University of Southern California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I1174212"]},{"raw_affiliation_string":"[Signal and Image Processing Institute, University of Southern California, Los Angeles, CA, USA]","institution_ids":["https://openalex.org/I1174212"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5028699912"],"corresponding_institution_ids":["https://openalex.org/I1174212"],"apc_list":null,"apc_paid":null,"fwci":16.054,"has_fulltext":false,"cited_by_count":184,"citation_normalized_percentile":{"value":0.9916895,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"21","issue":"3","first_page":"426","last_page":"446"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9891999959945679,"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"}},{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9879999756813049,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/algorithm","display_name":"Algorithm","score":0.7811564207077026},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.6335076689720154},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.6130358576774597},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6012245416641235},{"id":"https://openalex.org/keywords/centroid","display_name":"Centroid","score":0.5736982226371765},{"id":"https://openalex.org/keywords/fuzzy-set-operations","display_name":"Fuzzy set operations","score":0.5068512558937073},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.4965553879737854},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4576529264450073},{"id":"https://openalex.org/keywords/defuzzification","display_name":"Defuzzification","score":0.4535329341888428},{"id":"https://openalex.org/keywords/fuzzy-classification","display_name":"Fuzzy classification","score":0.41798821091651917},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4142007827758789},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.3212834596633911},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.3158388137817383},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.27547258138656616},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.20372825860977173}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.7811564207077026},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.6335076689720154},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.6130358576774597},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6012245416641235},{"id":"https://openalex.org/C146599234","wikidata":"https://www.wikidata.org/wiki/Q511093","display_name":"Centroid","level":2,"score":0.5736982226371765},{"id":"https://openalex.org/C148671577","wikidata":"https://www.wikidata.org/wiki/Q5511133","display_name":"Fuzzy set operations","level":4,"score":0.5068512558937073},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.4965553879737854},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4576529264450073},{"id":"https://openalex.org/C170260401","wikidata":"https://www.wikidata.org/wiki/Q5251735","display_name":"Defuzzification","level":5,"score":0.4535329341888428},{"id":"https://openalex.org/C127385683","wikidata":"https://www.wikidata.org/wiki/Q1475696","display_name":"Fuzzy classification","level":4,"score":0.41798821091651917},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4142007827758789},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.3212834596633911},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.3158388137817383},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.27547258138656616},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.20372825860977173},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tfuzz.2012.2227488","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2012.2227488","pdf_url":null,"source":{"id":"https://openalex.org/S134177497","display_name":"IEEE Transactions on Fuzzy Systems","issn_l":"1063-6706","issn":["1063-6706","1941-0034"],"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 Fuzzy Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":83,"referenced_works":["https://openalex.org/W113878345","https://openalex.org/W1492038503","https://openalex.org/W1524157153","https://openalex.org/W1787190784","https://openalex.org/W1905024069","https://openalex.org/W1905844197","https://openalex.org/W1977425756","https://openalex.org/W1983658296","https://openalex.org/W1991377734","https://openalex.org/W1991497142","https://openalex.org/W1992037970","https://openalex.org/W1995643732","https://openalex.org/W1999221008","https://openalex.org/W2000976145","https://openalex.org/W2002695893","https://openalex.org/W2013858655","https://openalex.org/W2025544956","https://openalex.org/W2039037639","https://openalex.org/W2039652152","https://openalex.org/W2053425102","https://openalex.org/W2057794837","https://openalex.org/W2058683246","https://openalex.org/W2084597926","https://openalex.org/W2088907949","https://openalex.org/W2094760805","https://openalex.org/W2103232511","https://openalex.org/W2103299443","https://openalex.org/W2105234323","https://openalex.org/W2105985709","https://openalex.org/W2106127254","https://openalex.org/W2107229865","https://openalex.org/W2108225531","https://openalex.org/W2111628113","https://openalex.org/W2112189957","https://openalex.org/W2114985809","https://openalex.org/W2115385411","https://openalex.org/W2116046819","https://openalex.org/W2116579452","https://openalex.org/W2117961832","https://openalex.org/W2120165455","https://openalex.org/W2123964448","https://openalex.org/W2128042275","https://openalex.org/W2128251760","https://openalex.org/W2130135344","https://openalex.org/W2130902850","https://openalex.org/W2132885717","https://openalex.org/W2134306672","https://openalex.org/W2135557549","https://openalex.org/W2141178894","https://openalex.org/W2147708960","https://openalex.org/W2149604064","https://openalex.org/W2150879558","https://openalex.org/W2151073185","https://openalex.org/W2151614844","https://openalex.org/W2152329090","https://openalex.org/W2153406165","https://openalex.org/W2153744349","https://openalex.org/W2154186319","https://openalex.org/W2155263265","https://openalex.org/W2155976821","https://openalex.org/W2157423656","https://openalex.org/W2157542158","https://openalex.org/W2158759539","https://openalex.org/W2161771180","https://openalex.org/W2162706466","https://openalex.org/W2164879989","https://openalex.org/W2165094119","https://openalex.org/W2165396372","https://openalex.org/W2169966872","https://openalex.org/W2342228773","https://openalex.org/W2352588623","https://openalex.org/W2477719344","https://openalex.org/W2482430271","https://openalex.org/W2913642042","https://openalex.org/W4205471131","https://openalex.org/W4206636130","https://openalex.org/W4247749894","https://openalex.org/W6604586926","https://openalex.org/W6639706781","https://openalex.org/W6674394400","https://openalex.org/W6682133608","https://openalex.org/W6682291467","https://openalex.org/W6683094445"],"related_works":["https://openalex.org/W2184441312","https://openalex.org/W647390320","https://openalex.org/W4242970302","https://openalex.org/W2571050636","https://openalex.org/W1485268022","https://openalex.org/W2331106272","https://openalex.org/W1975005191","https://openalex.org/W3176863924","https://openalex.org/W1542808721","https://openalex.org/W2253053392"],"abstract_inverted_index":{"Computing":[0],"the":[1,24,43,56,65,70,80,87],"centroid":[2,47],"and":[3,10,48,97,110],"performing":[4],"type-reduction":[5,49],"for":[6,82,105],"type-2":[7,107],"fuzzy":[8,108,111],"sets":[9,109],"systems":[11],"are":[12,23,35],"operations":[13],"that":[14,58],"must":[15],"be":[16],"taken":[17],"into":[18],"consideration.":[19],"Karnik-Mendel":[20],"(KM)":[21],"algorithms":[22,34,89,104],"standard":[25],"ways":[26],"to":[27,62,74,90],"do":[28],"these":[29,33],"operations;":[30],"however,":[31],"because":[32],"iterative,":[36],"much":[37],"research":[38,57],"has":[39,59],"been":[40,60],"conducted":[41,61],"during":[42],"past":[44],"decade":[45],"about":[46],"computations.":[50],"This":[51],"tutorial":[52],"paper":[53],"focuses":[54],"on":[55],"1)":[63],"improve":[64],"KM":[66,71,83,88,103],"algorithms;":[67,77,84],"2)":[68],"understand":[69],"algorithms,":[72],"leading":[73],"further":[75],"improved":[76],"3)":[78],"eliminate":[79],"need":[81],"4)":[85],"use":[86,99],"solve":[91],"other":[92],"(nonfuzzy":[93],"logic":[94,112],"system)":[95],"problems;":[96],"5)":[98],"(or":[100],"not":[101],"use)":[102],"general":[106],"systems.":[113]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":19},{"year":2021,"cited_by_count":21},{"year":2020,"cited_by_count":12},{"year":2019,"cited_by_count":19},{"year":2018,"cited_by_count":19},{"year":2017,"cited_by_count":19},{"year":2016,"cited_by_count":15},{"year":2015,"cited_by_count":17},{"year":2014,"cited_by_count":13},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-31T07:56:22.981413","created_date":"2025-10-10T00:00:00"}
