{"id":"https://openalex.org/W4387265419","doi":"https://doi.org/10.3390/sym15101853","title":"Defuzzification of Non-Linear Pentagonal Intuitionistic Fuzzy Numbers and Application in the Minimum Spanning Tree Problem","display_name":"Defuzzification of Non-Linear Pentagonal Intuitionistic Fuzzy Numbers and Application in the Minimum Spanning Tree Problem","publication_year":2023,"publication_date":"2023-10-02","ids":{"openalex":"https://openalex.org/W4387265419","doi":"https://doi.org/10.3390/sym15101853"},"language":"en","primary_location":{"id":"doi:10.3390/sym15101853","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym15101853","pdf_url":"https://www.mdpi.com/2073-8994/15/10/1853/pdf?version=1696233297","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/15/10/1853/pdf?version=1696233297","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089562457","display_name":"Ali Mert","orcid":"https://orcid.org/0000-0002-6806-935X"},"institutions":[{"id":"https://openalex.org/I41641357","display_name":"Ege University","ror":"https://ror.org/02eaafc18","country_code":"TR","type":"education","lineage":["https://openalex.org/I41641357"]}],"countries":["TR"],"is_corresponding":true,"raw_author_name":"Ali Mert","raw_affiliation_strings":["Department of Statistics, Ege University, \u0130zmir 35040, T\u00fcrkiye"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics, Ege University, \u0130zmir 35040, T\u00fcrkiye","institution_ids":["https://openalex.org/I41641357"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5089562457"],"corresponding_institution_ids":["https://openalex.org/I41641357"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.2203,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.81481168,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":97},"biblio":{"volume":"15","issue":"10","first_page":"1853","last_page":"1853"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9995999932289124,"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":0.9995999932289124,"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/T14175","display_name":"Intuitionistic Fuzzy Systems Applications","score":0.9797999858856201,"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/T12709","display_name":"Optimization and Mathematical Programming","score":0.9595999717712402,"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/variety","display_name":"Variety (cybernetics)","score":0.7129659652709961},{"id":"https://openalex.org/keywords/defuzzification","display_name":"Defuzzification","score":0.7045038938522339},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5409144163131714},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5317833423614502},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.5040735006332397},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.4909096360206604},{"id":"https://openalex.org/keywords/mathematical-theory","display_name":"Mathematical theory","score":0.4607468843460083},{"id":"https://openalex.org/keywords/fuzzy-mathematics","display_name":"Fuzzy mathematics","score":0.4314410090446472},{"id":"https://openalex.org/keywords/fuzzy-set-operations","display_name":"Fuzzy set operations","score":0.4261002540588379},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.41757622361183167},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40868645906448364},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.39763981103897095},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.3946651816368103},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3247375190258026}],"concepts":[{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.7129659652709961},{"id":"https://openalex.org/C170260401","wikidata":"https://www.wikidata.org/wiki/Q5251735","display_name":"Defuzzification","level":5,"score":0.7045038938522339},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5409144163131714},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5317833423614502},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.5040735006332397},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.4909096360206604},{"id":"https://openalex.org/C2779193601","wikidata":"https://www.wikidata.org/wiki/Q20026918","display_name":"Mathematical theory","level":2,"score":0.4607468843460083},{"id":"https://openalex.org/C166586474","wikidata":"https://www.wikidata.org/wiki/Q5511129","display_name":"Fuzzy mathematics","level":5,"score":0.4314410090446472},{"id":"https://openalex.org/C148671577","wikidata":"https://www.wikidata.org/wiki/Q5511133","display_name":"Fuzzy set operations","level":4,"score":0.4261002540588379},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.41757622361183167},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40868645906448364},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.39763981103897095},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.3946651816368103},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3247375190258026},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym15101853","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym15101853","pdf_url":"https://www.mdpi.com/2073-8994/15/10/1853/pdf?version=1696233297","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:fd53ff58ffe84d3ab28a29107d52f17a","is_oa":false,"landing_page_url":"https://doaj.org/article/fd53ff58ffe84d3ab28a29107d52f17a","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 15, Iss 10, p 1853 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/15/10/1853/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym15101853","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym15101853","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym15101853","pdf_url":"https://www.mdpi.com/2073-8994/15/10/1853/pdf?version=1696233297","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4387265419.pdf","grobid_xml":"https://content.openalex.org/works/W4387265419.grobid-xml"},"referenced_works_count":69,"referenced_works":["https://openalex.org/W241730991","https://openalex.org/W1975616839","https://openalex.org/W1976709807","https://openalex.org/W1980564456","https://openalex.org/W1981715766","https://openalex.org/W1986274141","https://openalex.org/W2001885528","https://openalex.org/W2007971910","https://openalex.org/W2018250306","https://openalex.org/W2021123788","https://openalex.org/W2023447058","https://openalex.org/W2034508098","https://openalex.org/W2048120646","https://openalex.org/W2048394994","https://openalex.org/W2052515307","https://openalex.org/W2091617649","https://openalex.org/W2117079902","https://openalex.org/W2125306618","https://openalex.org/W2139089045","https://openalex.org/W2147736422","https://openalex.org/W2154041520","https://openalex.org/W2270529708","https://openalex.org/W2331407440","https://openalex.org/W2335878523","https://openalex.org/W2341296293","https://openalex.org/W2345111119","https://openalex.org/W2525961359","https://openalex.org/W2623842182","https://openalex.org/W2768841407","https://openalex.org/W2769072697","https://openalex.org/W2778027311","https://openalex.org/W2790253481","https://openalex.org/W2794037958","https://openalex.org/W2810274624","https://openalex.org/W2885877913","https://openalex.org/W2896286744","https://openalex.org/W2900647463","https://openalex.org/W2904068169","https://openalex.org/W2950834400","https://openalex.org/W2955427316","https://openalex.org/W2955533947","https://openalex.org/W2963681089","https://openalex.org/W2979695059","https://openalex.org/W3002188558","https://openalex.org/W3041770475","https://openalex.org/W3071972992","https://openalex.org/W3087183202","https://openalex.org/W3156814830","https://openalex.org/W3186663877","https://openalex.org/W3200750209","https://openalex.org/W4211007335","https://openalex.org/W4213240390","https://openalex.org/W4302288235","https://openalex.org/W4318999699","https://openalex.org/W4327953255","https://openalex.org/W4367311601","https://openalex.org/W4376109558","https://openalex.org/W4377042151","https://openalex.org/W4379143839","https://openalex.org/W4382280607","https://openalex.org/W4382937387","https://openalex.org/W4383499955","https://openalex.org/W4385986508","https://openalex.org/W6644374215","https://openalex.org/W6678405585","https://openalex.org/W6680257327","https://openalex.org/W6702885112","https://openalex.org/W6704246323","https://openalex.org/W6765336603"],"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":{"In":[0,103,171,242],"recent":[1],"years,":[2],"with":[3],"the":[4,16,34,41,44,62,90,94,104,128,151,167,220,251,257,273,285,288],"variety":[5,168,201],"of":[6,14,18,43,58,131,141,169,253],"digital":[7],"objects":[8],"around":[9,36],"us":[10,37],"becoming":[11],"a":[12,145,176,188,223,247,254],"source":[13],"information,":[15],"fields":[17],"artificial":[19],"intelligence":[20],"(AI)":[21],"and":[22,32,52,64,78,93,109,119,138,178,184],"machine":[23],"learning":[24],"(ML)":[25],"have":[26],"experienced":[27],"very":[28],"rapid":[29],"development.":[30],"Processing":[31],"converting":[33],"information":[35,45,69,73,156],"into":[38,80,162,222],"data":[39,60,81],"within":[40],"framework":[42],"processing":[46],"theory":[47,92],"is":[48,143],"important,":[49],"as":[50,89,150,281],"AI":[51,148,207],"ML":[53],"techniques":[54],"need":[55,217],"large":[56],"amounts":[57],"reliable":[59],"in":[61,147,202,212,231,236,272,287],"training":[63],"validation":[65],"stages.":[66],"Even":[67],"though":[68],"naturally":[70],"contains":[71],"uncertainty,":[72],"must":[74],"still":[75],"be":[76,160],"modeled":[77],"converted":[79],"without":[82,165],"neglecting":[83,166],"this":[84,101,172,186,243],"uncertainty.":[85,170,203],"Mathematical":[86],"techniques,":[87],"such":[88,228,232],"fuzzy":[91,96,106,117,121,192,259],"intuitionistic":[95,105,116,120,191,258],"theory,":[97,107],"are":[98,112,125,210,238],"used":[99,235],"for":[100,182,250],"purpose.":[102],"membership":[108],"non-membership":[110],"functions":[111],"employed":[113],"to":[114,159,199,218,226,283],"describe":[115],"sets":[118],"numbers":[122],"(IFNs).":[123],"IFNs":[124,164,229],"characterized":[126],"by":[127,154,278],"mathematical":[129,180],"statements":[130],"these":[132],"two":[133],"functions.":[134],"A":[135],"more":[136,290],"general":[137,177],"inclusive":[139,179],"definition":[140,181],"IFN":[142,183,187,221],"always":[144],"requirement":[146],"technologies,":[149],"uncertainty":[152,286],"introduced":[153],"various":[155],"sources":[157],"needs":[158],"transformed":[161],"similar":[163],"paper,":[173,244],"we":[174,216,245],"proposed":[175,246],"called":[185,239],"non-linear":[189],"pentagonal":[190],"number":[193,225],"(NLPIFN),":[194],"which":[195],"allows":[196],"its":[197],"users":[198],"maintain":[200],"We":[204,267],"know":[205],"that":[206],"technology":[208],"implementations":[209],"performed":[211],"computerized":[213],"environments,":[214],"so":[215],"transform":[219],"crisp":[224],"make":[227],"available":[230],"environments.":[233],"Techniques":[234],"transformation":[237],"defuzzification":[240,252],"methods.":[241],"short-cut":[248],"formula":[249],"NLPIFN":[255],"using":[256],"weighted":[260],"averaging":[261],"based":[262],"on":[263],"levels":[264],"(IF-WABL)":[265],"method.":[266],"also":[268],"implemented":[269],"our":[270],"findings":[271],"minimum":[274],"spanning":[275],"tree":[276],"problem":[277],"taking":[279],"weights":[280],"NLPIFNs":[282],"determine":[284],"process":[289],"precisely.":[291]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
