{"id":"https://openalex.org/W3000316439","doi":"https://doi.org/10.1109/access.2020.2964580","title":"Correlation Coefficients of Interval-Valued Pythagorean Hesitant Fuzzy Sets and Their Applications","display_name":"Correlation Coefficients of Interval-Valued Pythagorean Hesitant Fuzzy Sets and Their Applications","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3000316439","doi":"https://doi.org/10.1109/access.2020.2964580","mag":"3000316439"},"language":"en","primary_location":{"id":"doi:10.1109/access.2020.2964580","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2020.2964580","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1109/access.2020.2964580","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022515910","display_name":"Tingting Zheng","orcid":"https://orcid.org/0000-0001-7692-5286"},"institutions":[{"id":"https://openalex.org/I143868143","display_name":"Anhui University","ror":"https://ror.org/05th6yx34","country_code":"CN","type":"education","lineage":["https://openalex.org/I143868143"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Tingting Zheng","raw_affiliation_strings":["School of Mathematical Sciences, Anhui University, Hefei, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Anhui University, Hefei, China","institution_ids":["https://openalex.org/I143868143"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035460553","display_name":"Maoyin Zhang","orcid":null},"institutions":[{"id":"https://openalex.org/I143868143","display_name":"Anhui University","ror":"https://ror.org/05th6yx34","country_code":"CN","type":"education","lineage":["https://openalex.org/I143868143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Maoyin Zhang","raw_affiliation_strings":["School of Mathematical Sciences, Anhui University, Hefei, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Anhui University, Hefei, China","institution_ids":["https://openalex.org/I143868143"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102712516","display_name":"Longmei Li","orcid":"https://orcid.org/0000-0002-6347-6108"},"institutions":[{"id":"https://openalex.org/I143868143","display_name":"Anhui University","ror":"https://ror.org/05th6yx34","country_code":"CN","type":"education","lineage":["https://openalex.org/I143868143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Longmei Li","raw_affiliation_strings":["School of Mathematical Sciences, Anhui University, Hefei, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Anhui University, Hefei, China","institution_ids":["https://openalex.org/I143868143"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058043995","display_name":"Qiuyue Wu","orcid":"https://orcid.org/0000-0003-2813-103X"},"institutions":[{"id":"https://openalex.org/I143868143","display_name":"Anhui University","ror":"https://ror.org/05th6yx34","country_code":"CN","type":"education","lineage":["https://openalex.org/I143868143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qiuyue Wu","raw_affiliation_strings":["School of Mathematical Sciences, Anhui University, Hefei, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Anhui University, Hefei, China","institution_ids":["https://openalex.org/I143868143"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005456443","display_name":"Ligang Zhou","orcid":"https://orcid.org/0000-0002-8512-6125"},"institutions":[{"id":"https://openalex.org/I200845125","display_name":"Nanjing University of Information Science and Technology","ror":"https://ror.org/02y0rxk19","country_code":"CN","type":"education","lineage":["https://openalex.org/I200845125"]},{"id":"https://openalex.org/I143868143","display_name":"Anhui University","ror":"https://ror.org/05th6yx34","country_code":"CN","type":"education","lineage":["https://openalex.org/I143868143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ligang Zhou","raw_affiliation_strings":["China Institute of Manufacturing Development, Nanjing University of Information Science and Technology, Nanjing, China","School of Mathematical Sciences, Anhui University, Hefei, China"],"affiliations":[{"raw_affiliation_string":"China Institute of Manufacturing Development, Nanjing University of Information Science and Technology, Nanjing, China","institution_ids":["https://openalex.org/I200845125"]},{"raw_affiliation_string":"School of Mathematical Sciences, Anhui University, Hefei, China","institution_ids":["https://openalex.org/I143868143"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5022515910"],"corresponding_institution_ids":["https://openalex.org/I143868143"],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":2.6928,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.90204348,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"8","issue":null,"first_page":"9271","last_page":"9286"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9994999766349792,"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":0.9994999766349792,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9957000017166138,"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"}},{"id":"https://openalex.org/T13955","display_name":"Evaluation Methods in Various Fields","score":0.9711999893188477,"subfield":{"id":"https://openalex.org/subfields/2302","display_name":"Ecological Modeling"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/pythagorean-theorem","display_name":"Pythagorean theorem","score":0.9403761625289917},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.5945634245872498},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5772517323493958},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.5667010545730591},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5432565808296204},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.4704011380672455},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.4459788501262665},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3621918261051178},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.30127590894699097},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.19276437163352966}],"concepts":[{"id":"https://openalex.org/C100461760","wikidata":"https://www.wikidata.org/wiki/Q11518","display_name":"Pythagorean theorem","level":2,"score":0.9403761625289917},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.5945634245872498},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5772517323493958},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.5667010545730591},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5432565808296204},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.4704011380672455},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.4459788501262665},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3621918261051178},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.30127590894699097},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.19276437163352966},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2020.2964580","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2020.2964580","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:6126e151e4074cdba7a617d0ba859fd3","is_oa":true,"landing_page_url":"https://doaj.org/article/6126e151e4074cdba7a617d0ba859fd3","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Access, Vol 8, Pp 9271-9286 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2020.2964580","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2020.2964580","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.800000011920929,"display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G1741244853","display_name":null,"funder_award_id":"71701001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1964202683","display_name":null,"funder_award_id":"71901001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2791717321","display_name":null,"funder_award_id":"71501002","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G713217472","display_name":null,"funder_award_id":"1708085MF163","funder_id":"https://openalex.org/F4320334897","funder_display_name":"Natural Science Foundation of Anhui Province"},{"id":"https://openalex.org/G7281736853","display_name":null,"funder_award_id":"71771001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8278584388","display_name":null,"funder_award_id":"71871001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8781469201","display_name":null,"funder_award_id":"71901088","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8845602096","display_name":null,"funder_award_id":"61806001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320334897","display_name":"Natural Science Foundation of Anhui Province","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":54,"referenced_works":["https://openalex.org/W637775391","https://openalex.org/W1481435333","https://openalex.org/W1501975196","https://openalex.org/W1541340729","https://openalex.org/W1668569279","https://openalex.org/W1765570948","https://openalex.org/W1829951598","https://openalex.org/W1991419869","https://openalex.org/W1998097302","https://openalex.org/W2006727531","https://openalex.org/W2019994447","https://openalex.org/W2028612155","https://openalex.org/W2039791408","https://openalex.org/W2049627382","https://openalex.org/W2050262998","https://openalex.org/W2053211464","https://openalex.org/W2067472607","https://openalex.org/W2068069653","https://openalex.org/W2068843436","https://openalex.org/W2079457935","https://openalex.org/W2089228118","https://openalex.org/W2091287769","https://openalex.org/W2091957041","https://openalex.org/W2116365436","https://openalex.org/W2124970246","https://openalex.org/W2128871000","https://openalex.org/W2131390763","https://openalex.org/W2150546380","https://openalex.org/W2155072267","https://openalex.org/W2187360662","https://openalex.org/W2292359941","https://openalex.org/W2414387118","https://openalex.org/W2722833530","https://openalex.org/W2736056743","https://openalex.org/W2756107921","https://openalex.org/W2769339029","https://openalex.org/W2773588687","https://openalex.org/W2790196011","https://openalex.org/W2885385239","https://openalex.org/W2891429382","https://openalex.org/W2902485067","https://openalex.org/W2919513668","https://openalex.org/W2921550306","https://openalex.org/W2922569553","https://openalex.org/W2945144398","https://openalex.org/W2947090112","https://openalex.org/W2952311754","https://openalex.org/W2966281418","https://openalex.org/W2984896269","https://openalex.org/W3006208480","https://openalex.org/W3141242285","https://openalex.org/W4206464249","https://openalex.org/W4239165868","https://openalex.org/W6774041271"],"related_works":["https://openalex.org/W2995447873","https://openalex.org/W1802380781","https://openalex.org/W4210969441","https://openalex.org/W1486684451","https://openalex.org/W2116249946","https://openalex.org/W2801459815","https://openalex.org/W2099285375","https://openalex.org/W4361273540","https://openalex.org/W4361984403","https://openalex.org/W4317826560"],"abstract_inverted_index":{"An":[0],"interval-valued":[1,17,46,115,138],"Pythagorean":[2,18,25,40,47,109,116,133,139],"hesitant":[3,26,41,110,117],"fuzzy":[4,19,27,42,48,111,118,134,140,189],"set":[5],"(IVPHFS)":[6],"not":[7],"only":[8],"can":[9,207],"be":[10],"regarded":[11],"as":[12,167,191,193],"the":[13,24,30,67,79,83,90,94,103,106,146,172,187,199,209,220,225,230],"union":[14],"of":[15,32,39,70,108,132,162,175,229],"some":[16],"sets":[20,43,49],"but":[21],"also":[22],"represent":[23,56],"elements":[28,112,119,135,141],"in":[29,150,183,233],"form":[31],"interval":[33,168,176],"values.":[34],"So":[35],"IVPHFSs":[36],"are":[37,52,121,164],"extensions":[38],"(PHFSs)":[44],"and":[45,60,75,82,129,159,202,216,227,239],"(IVPFSs),":[50],"which":[51,206],"powerful":[53],"tools":[54],"to":[55,78,101,143,178,185,223],"more":[57,214],"complicated,":[58],"uncertain":[59],"vague":[61],"information.":[62],"This":[63],"paper":[64],"focuses":[65],"on":[66],"four":[68],"kinds":[69],"correlation":[71,80,85],"coefficients":[72,81,86],"for":[73,87],"PHFSs,":[74],"extends":[76],"them":[77],"weighted":[84],"IVPHFSs.":[88],"In":[89,123],"processing,":[91],"we":[92,125,197],"develop":[93],"least":[95],"common":[96],"multiple":[97,234],"expansion":[98],"(LCME)":[99],"method":[100,174],"solve":[102],"problem":[104],"that":[105],"cardinalities":[107],"(PHFEs)":[113],"(or":[114,137,148,153],"(IVPHFEs))":[120],"different.":[122],"addition,":[124],"propose":[126],"score":[127,157],"functions":[128,131,158,161],"accuracy":[130,160],"(PFEs)":[136],"(IVPFEs))":[142],"rank":[144],"all":[145],"PFEs":[147],"IVPFEs)":[149],"a":[151],"PHFE":[152],"an":[154],"IVPHFE).":[155],"Especially,":[156],"IVPFEs":[163],"both":[165],"presented":[166],"numbers.":[169],"Then":[170],"use":[171],"comparison":[173],"numbers":[177],"compare":[179],"two":[180,212],"revised":[181],"IVPHFEs":[182,213],"order":[184],"keep":[186],"original":[188],"information":[190],"far":[192],"possible.":[194],"What's":[195],"more,":[196],"define":[198],"local":[200,203],"correlations":[201],"informational":[204],"energies":[205],"depict":[208],"similarity":[210],"between":[211],"meticulously":[215],"completely.":[217],"At":[218],"last":[219],"numerical":[221],"examples":[222],"show":[224],"feasibility":[226],"applicability":[228],"proposed":[231],"methods":[232],"criteria":[235],"decision":[236],"making":[237],"(MCDM)":[238],"clustering":[240],"analysis.":[241]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
