{"id":"https://openalex.org/W4225828141","doi":"https://doi.org/10.1109/tfuzz.2022.3170208","title":"Ranking of Z-Numbers Based on the Developed Golden Rule Representative Value","display_name":"Ranking of Z-Numbers Based on the Developed Golden Rule Representative Value","publication_year":2022,"publication_date":"2022-04-26","ids":{"openalex":"https://openalex.org/W4225828141","doi":"https://doi.org/10.1109/tfuzz.2022.3170208"},"language":"en","primary_location":{"id":"doi:10.1109/tfuzz.2022.3170208","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2022.3170208","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/A5084710275","display_name":"Ruolan Cheng","orcid":"https://orcid.org/0000-0002-4108-4314"},"institutions":[{"id":"https://openalex.org/I89652312","display_name":"Northwest A&F University","ror":"https://ror.org/0051rme32","country_code":"CN","type":"education","lineage":["https://openalex.org/I89652312"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Ruolan Cheng","raw_affiliation_strings":["School of Computer and Information Science, Northwest Agriculture and Forestry University, Yangling, China"],"affiliations":[{"raw_affiliation_string":"School of Computer and Information Science, Northwest Agriculture and Forestry University, Yangling, China","institution_ids":["https://openalex.org/I89652312"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080041489","display_name":"Jianfeng Zhang","orcid":"https://orcid.org/0000-0002-0099-8400"},"institutions":[{"id":"https://openalex.org/I89652312","display_name":"Northwest A&F University","ror":"https://ror.org/0051rme32","country_code":"CN","type":"education","lineage":["https://openalex.org/I89652312"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jianfeng Zhang","raw_affiliation_strings":["School of Computer and Information Science, Northwest Agriculture and Forestry University, Yangling, China"],"affiliations":[{"raw_affiliation_string":"School of Computer and Information Science, Northwest Agriculture and Forestry University, Yangling, China","institution_ids":["https://openalex.org/I89652312"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032599820","display_name":"Bingyi Kang","orcid":"https://orcid.org/0000-0003-2637-4695"},"institutions":[{"id":"https://openalex.org/I4210151987","display_name":"Ministry of Agriculture and Rural Affairs","ror":"https://ror.org/05ckt8b96","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210127390","https://openalex.org/I4210151987"]},{"id":"https://openalex.org/I89652312","display_name":"Northwest A&F University","ror":"https://ror.org/0051rme32","country_code":"CN","type":"education","lineage":["https://openalex.org/I89652312"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bingyi Kang","raw_affiliation_strings":["School of Information Engineering, Northwest Agriculture and Forestry University, Yangling, China","Key Laboratory of Agricultural Internet of Things, Ministry of Agriculture and Rural Affairs, Northwest Agriculture and Forestry University, Yangling, China","Shaanxi Key Laboratory of Agricultural Information Perception and Intelligent Service, Northwest Agriculture and Forestry University, Yangling, China"],"affiliations":[{"raw_affiliation_string":"School of Information Engineering, Northwest Agriculture and Forestry University, Yangling, China","institution_ids":["https://openalex.org/I89652312"]},{"raw_affiliation_string":"Key Laboratory of Agricultural Internet of Things, Ministry of Agriculture and Rural Affairs, Northwest Agriculture and Forestry University, Yangling, China","institution_ids":["https://openalex.org/I4210151987"]},{"raw_affiliation_string":"Shaanxi Key Laboratory of Agricultural Information Perception and Intelligent Service, Northwest Agriculture and Forestry University, Yangling, China","institution_ids":["https://openalex.org/I89652312"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5084710275"],"corresponding_institution_ids":["https://openalex.org/I89652312"],"apc_list":null,"apc_paid":null,"fwci":4.0586,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.94245487,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"30","issue":"12","first_page":"5196","last_page":"5210"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9865999817848206,"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"}},{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9758999943733215,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.6794527173042297},{"id":"https://openalex.org/keywords/type-2-fuzzy-sets-and-systems","display_name":"Type-2 fuzzy sets and systems","score":0.6042306423187256},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5988023281097412},{"id":"https://openalex.org/keywords/membership-function","display_name":"Membership function","score":0.5253303050994873},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.48294299840927124},{"id":"https://openalex.org/keywords/defuzzification","display_name":"Defuzzification","score":0.4825948476791382},{"id":"https://openalex.org/keywords/fuzzy-set-operations","display_name":"Fuzzy set operations","score":0.4755675196647644},{"id":"https://openalex.org/keywords/fuzzy-classification","display_name":"Fuzzy classification","score":0.4530363976955414},{"id":"https://openalex.org/keywords/ranking","display_name":"Ranking (information retrieval)","score":0.44674527645111084},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.40352898836135864},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4005663990974426},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.3991525173187256},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34492748975753784},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3303528428077698}],"concepts":[{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.6794527173042297},{"id":"https://openalex.org/C17350324","wikidata":"https://www.wikidata.org/wiki/Q7860605","display_name":"Type-2 fuzzy sets and systems","level":5,"score":0.6042306423187256},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5988023281097412},{"id":"https://openalex.org/C5263885","wikidata":"https://www.wikidata.org/wiki/Q1967302","display_name":"Membership function","level":4,"score":0.5253303050994873},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.48294299840927124},{"id":"https://openalex.org/C170260401","wikidata":"https://www.wikidata.org/wiki/Q5251735","display_name":"Defuzzification","level":5,"score":0.4825948476791382},{"id":"https://openalex.org/C148671577","wikidata":"https://www.wikidata.org/wiki/Q5511133","display_name":"Fuzzy set operations","level":4,"score":0.4755675196647644},{"id":"https://openalex.org/C127385683","wikidata":"https://www.wikidata.org/wiki/Q1475696","display_name":"Fuzzy classification","level":4,"score":0.4530363976955414},{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.44674527645111084},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.40352898836135864},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4005663990974426},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.3991525173187256},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34492748975753784},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3303528428077698}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tfuzz.2022.3170208","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2022.3170208","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":[{"id":"https://metadata.un.org/sdg/16","score":0.8299999833106995,"display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G1277493082","display_name":null,"funder_award_id":"2452018066","funder_id":"https://openalex.org/F4320334997","funder_display_name":"Chinese Universities Scientific Fund"},{"id":"https://openalex.org/G2323030085","display_name":null,"funder_award_id":"202110712143","funder_id":"https://openalex.org/F4320336008","funder_display_name":"National College Students Innovation and Entrepreneurship Training Program"},{"id":"https://openalex.org/G4488345915","display_name":null,"funder_award_id":"2020M683575","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G7844316827","display_name":null,"funder_award_id":"61903307","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8013497826","display_name":null,"funder_award_id":"202110712146","funder_id":"https://openalex.org/F4320336008","funder_display_name":"National College Students Innovation and Entrepreneurship Training Program"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"},{"id":"https://openalex.org/F4320334997","display_name":"Chinese Universities Scientific Fund","ror":null},{"id":"https://openalex.org/F4320336008","display_name":"National College Students Innovation and Entrepreneurship Training Program","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":55,"referenced_works":["https://openalex.org/W1981144549","https://openalex.org/W1997952930","https://openalex.org/W1997967425","https://openalex.org/W2005368914","https://openalex.org/W2042774699","https://openalex.org/W2064003023","https://openalex.org/W2079325629","https://openalex.org/W2080561531","https://openalex.org/W2089572792","https://openalex.org/W2096175520","https://openalex.org/W2122361993","https://openalex.org/W2132885717","https://openalex.org/W2180415311","https://openalex.org/W2317916567","https://openalex.org/W2319712203","https://openalex.org/W2344395450","https://openalex.org/W2461533535","https://openalex.org/W2484365097","https://openalex.org/W2489692099","https://openalex.org/W2509038672","https://openalex.org/W2512389528","https://openalex.org/W2549472391","https://openalex.org/W2560073144","https://openalex.org/W2618591006","https://openalex.org/W2736336607","https://openalex.org/W2745098780","https://openalex.org/W2755209665","https://openalex.org/W2756214476","https://openalex.org/W2758653053","https://openalex.org/W2759156905","https://openalex.org/W2790388419","https://openalex.org/W2792740237","https://openalex.org/W2797554143","https://openalex.org/W2890735275","https://openalex.org/W2904900506","https://openalex.org/W2913054510","https://openalex.org/W2921842513","https://openalex.org/W2949866758","https://openalex.org/W2950090497","https://openalex.org/W2955987323","https://openalex.org/W2964392875","https://openalex.org/W2966911336","https://openalex.org/W3016820223","https://openalex.org/W3022177128","https://openalex.org/W3028762139","https://openalex.org/W3030646047","https://openalex.org/W3092353747","https://openalex.org/W3092625516","https://openalex.org/W3127356133","https://openalex.org/W3182515817","https://openalex.org/W4211007335","https://openalex.org/W4301347335","https://openalex.org/W6674650171","https://openalex.org/W6699821906","https://openalex.org/W6700380933"],"related_works":["https://openalex.org/W2674573885","https://openalex.org/W1487720066","https://openalex.org/W2781808531","https://openalex.org/W1975005191","https://openalex.org/W4361984403","https://openalex.org/W2791187250","https://openalex.org/W2145270521","https://openalex.org/W2066929655","https://openalex.org/W2890798884","https://openalex.org/W2608292510"],"abstract_inverted_index":{"Real-world":[0],"decision-making":[1,39],"is":[2,9,32,49,108,118,168],"based":[3],"on":[4],"human":[5],"cognitive":[6],"information,":[7,22],"which":[8],"characterized":[10],"by":[11,54],"fuzziness":[12,92],"and":[13,64,75,91,133,195,221],"partial":[14],"reliability.":[15],"In":[16],"order":[17],"to":[18,56,79,98,110,120,179,209],"better":[19],"describe":[20,210],"such":[21],"Zadeh":[23],"proposed":[24,185,216,231],"the":[25,30,38,42,80,83,89,100,131,149,153,158,161,171,177,182,189,193,198,201,211,215,227,230],"concept":[26,52],"of":[27,82,93,102,130,152,176,192,200,214,229],"Z-number.":[28,84],"Ranking":[29],"Z-number":[31,132,154,178,194],"an":[33],"indispensable":[34],"step":[35],"in":[36,160,181],"solving":[37],"problem":[40],"under":[41],"Z-number-based":[43],"information.":[44],"Golden":[45],"rule":[46,69,125,173],"representative":[47,70,126,174],"value":[48,71,127,167,175],"a":[50,66,122,140],"new":[51,67,86,123,136],"introduced":[53],"Yager":[55],"rank":[57],"interval":[58],"values.":[59],"This":[60,143],"article":[61],"expands":[62],"it":[63,78],"proposes":[65],"golden":[68,124,172],"for":[72],"fuzzy":[73,94,106,128,137,144,150],"numbers,":[74],"then,":[76],"apply":[77],"ranking":[81],"Some":[85,204],"rules":[87],"involving":[88],"centroid":[90],"numbers":[95],"are":[96,207],"constructed":[97],"capture":[99],"preference":[101],"decision-makers.":[103],"The":[104,114,165,184,218],"Takagi\u2013Sugeno\u2013Kang":[105],"model":[107],"used":[109,119,208],"implement":[111],"these":[112],"rules.":[113],"obtained":[115],"Rep":[116],"function":[117],"construct":[121],"subset":[129,138,145],"associate":[134],"this":[135],"with":[139,223],"scalar":[141,166],"value.":[142],"not":[146],"only":[147],"implies":[148],"aspect":[151],"but":[155],"also":[156],"contains":[157],"information":[159,191],"hidden":[162],"probability":[163],"distribution.":[164],"regarded":[169],"as":[170],"participate":[180],"ranking.":[183],"method":[186],"greatly":[187],"retains":[188],"original":[190],"can":[196],"overcome":[197],"shortcomings":[199],"existing":[202,224],"methods.":[203],"numerical":[205],"examples":[206],"specific":[212],"process":[213],"method.":[217,232],"comparative":[219],"analysis":[220],"discussion":[222],"methods":[225],"clarify":[226],"advantages":[228]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":5}],"updated_date":"2026-03-27T14:29:43.386196","created_date":"2025-10-10T00:00:00"}
