{"id":"https://openalex.org/W3123934493","doi":"https://doi.org/10.3233/kes-180163","title":"A necessary condition for comparing and ranking of triangular fuzzy numbers on the basis of height-independent ranking techniques","display_name":"A necessary condition for comparing and ranking of triangular fuzzy numbers on the basis of height-independent ranking techniques","publication_year":2021,"publication_date":"2021-01-18","ids":{"openalex":"https://openalex.org/W3123934493","doi":"https://doi.org/10.3233/kes-180163","mag":"3123934493"},"language":"en","primary_location":{"id":"doi:10.3233/kes-180163","is_oa":false,"landing_page_url":"https://doi.org/10.3233/kes-180163","pdf_url":null,"source":{"id":"https://openalex.org/S133764092","display_name":"International Journal of Knowledge-based and Intelligent Engineering Systems","issn_l":"1327-2314","issn":["1327-2314","1875-8827"],"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":"International Journal of Knowledge-based and Intelligent Engineering 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/A5043720844","display_name":"Alireza Sotoudeh-Anvari","orcid":"https://orcid.org/0000-0001-8944-836X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Alireza Sotoudeh-Anvari","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5043720844"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1743,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.49195086,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"24","issue":"4","first_page":"269","last_page":"277"},"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":0.9976000189781189,"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":0.9908999800682068,"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/defuzzification","display_name":"Defuzzification","score":0.8241904377937317},{"id":"https://openalex.org/keywords/ranking","display_name":"Ranking (information retrieval)","score":0.8010097742080688},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.6739234924316406},{"id":"https://openalex.org/keywords/centroid","display_name":"Centroid","score":0.6511995792388916},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.5920379161834717},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.570740282535553},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5463510155677795},{"id":"https://openalex.org/keywords/fuzzy-set-operations","display_name":"Fuzzy set operations","score":0.44895023107528687},{"id":"https://openalex.org/keywords/fuzzy-mathematics","display_name":"Fuzzy mathematics","score":0.42598482966423035},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3781493306159973},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37115156650543213},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.36921560764312744},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.35544252395629883},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.32350075244903564}],"concepts":[{"id":"https://openalex.org/C170260401","wikidata":"https://www.wikidata.org/wiki/Q5251735","display_name":"Defuzzification","level":5,"score":0.8241904377937317},{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.8010097742080688},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.6739234924316406},{"id":"https://openalex.org/C146599234","wikidata":"https://www.wikidata.org/wiki/Q511093","display_name":"Centroid","level":2,"score":0.6511995792388916},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.5920379161834717},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.570740282535553},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5463510155677795},{"id":"https://openalex.org/C148671577","wikidata":"https://www.wikidata.org/wiki/Q5511133","display_name":"Fuzzy set operations","level":4,"score":0.44895023107528687},{"id":"https://openalex.org/C166586474","wikidata":"https://www.wikidata.org/wiki/Q5511129","display_name":"Fuzzy mathematics","level":5,"score":0.42598482966423035},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3781493306159973},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37115156650543213},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.36921560764312744},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.35544252395629883},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.32350075244903564},{"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:10.3233/kes-180163","is_oa":false,"landing_page_url":"https://doi.org/10.3233/kes-180163","pdf_url":null,"source":{"id":"https://openalex.org/S133764092","display_name":"International Journal of Knowledge-based and Intelligent Engineering Systems","issn_l":"1327-2314","issn":["1327-2314","1875-8827"],"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":"International Journal of Knowledge-based and Intelligent Engineering 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":41,"referenced_works":["https://openalex.org/W1577375662","https://openalex.org/W1969140532","https://openalex.org/W1969535228","https://openalex.org/W1973256758","https://openalex.org/W1973926738","https://openalex.org/W1974146053","https://openalex.org/W1987249808","https://openalex.org/W1987606774","https://openalex.org/W1991901402","https://openalex.org/W2005481082","https://openalex.org/W2012169861","https://openalex.org/W2014850007","https://openalex.org/W2019482291","https://openalex.org/W2021804535","https://openalex.org/W2024164940","https://openalex.org/W2028794447","https://openalex.org/W2036341849","https://openalex.org/W2038413434","https://openalex.org/W2038604975","https://openalex.org/W2049447733","https://openalex.org/W2057131692","https://openalex.org/W2062228170","https://openalex.org/W2085060396","https://openalex.org/W2086390519","https://openalex.org/W2149276443","https://openalex.org/W2185491205","https://openalex.org/W2254372016","https://openalex.org/W2276296411","https://openalex.org/W2293740060","https://openalex.org/W2331452232","https://openalex.org/W2469257262","https://openalex.org/W2537985869","https://openalex.org/W2747995241","https://openalex.org/W2772745517","https://openalex.org/W2810237633","https://openalex.org/W2886456973","https://openalex.org/W3010279532","https://openalex.org/W6686242389","https://openalex.org/W6692060804","https://openalex.org/W6742931968","https://openalex.org/W6753336708"],"related_works":["https://openalex.org/W2184441312","https://openalex.org/W4388451300","https://openalex.org/W4242970302","https://openalex.org/W2253053392","https://openalex.org/W3176863924","https://openalex.org/W2331106272","https://openalex.org/W1542808721","https://openalex.org/W2674573885","https://openalex.org/W1552946134","https://openalex.org/W2989705030"],"abstract_inverted_index":{"The":[0,141],"open":[1],"problem":[2,25],"of":[3,9,49,56,75,84,114],"comparing":[4],"fuzzy":[5,15,51,129,133],"numbers":[6,52,130],"as":[7,63],"one":[8],"the":[10,54,73,81,103,108,112],"most":[11],"important":[12],"issues":[13],"in":[14,88,102],"sets":[16],"has":[17,26,150],"been":[18,28],"studied":[19],"by":[20],"many":[21],"researchers.":[22],"However,":[23],"this":[24,78,124],"not":[27],"solved":[29],"up":[30],"to":[31,100,131],"now":[32],"and":[33,70,98,136,149],"perhaps":[34],"it":[35],"will":[36],"never":[37],"be":[38],"fully":[39],"answered.":[40],"This":[41],"work":[42],"proposes":[43],"a":[44,85,132],"necessary":[45,86,125],"condition":[46,87,126],"for":[47,127],"ranking":[48,60,89,128],"triangular":[50],"on":[53],"basis":[55],"some":[57],"efficient":[58,99],"height-independent":[59],"methods":[61],"such":[62],"centroids,":[64],"total":[65],"integral":[66],"value,":[67],"signed":[68],"distance":[69],"defuzzification.":[71],"To":[72,106],"best":[74],"our":[76,145],"knowledge,":[77],"paper":[79],"provides":[80],"first":[82],"use":[83,101],"methods.":[90],"Fortunately,":[91],"suggested":[92,109],"approach":[93,110,146],"is":[94,147],"very":[95],"straightforward,":[96],"fast":[97],"real":[104],"problems.":[105],"evaluate":[107],"with":[111],"result":[113],"existing":[115],"methods,":[116],"six":[117],"examples":[118],"are":[119],"presented.":[120],"Finally,":[121],"we":[122],"apply":[123],"failure":[134],"mode":[135],"effect":[137],"analysis":[138],"(FMEA)":[139],"problem.":[140],"results":[142],"show":[143],"that":[144],"practical":[148],"reasonable":[151],"outcome.":[152]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}