{"id":"https://openalex.org/W4409681413","doi":"https://doi.org/10.1007/s40747-025-01813-z","title":"Assessment of air purifiers for improving the air quality index using circular intuitionistic fuzzy Heronian means","display_name":"Assessment of air purifiers for improving the air quality index using circular intuitionistic fuzzy Heronian means","publication_year":2025,"publication_date":"2025-04-22","ids":{"openalex":"https://openalex.org/W4409681413","doi":"https://doi.org/10.1007/s40747-025-01813-z"},"language":"en","primary_location":{"id":"doi:10.1007/s40747-025-01813-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40747-025-01813-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40747-025-01813-z.pdf","source":{"id":"https://openalex.org/S3035462843","display_name":"Complex & Intelligent Systems","issn_l":"2198-6053","issn":["2198-6053","2199-4536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complex &amp; Intelligent Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://link.springer.com/content/pdf/10.1007/s40747-025-01813-z.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028851981","display_name":"Fengyu Guo","orcid":"https://orcid.org/0000-0002-4200-809X"},"institutions":[{"id":"https://openalex.org/I108160477","display_name":"Hebei Agricultural University","ror":"https://ror.org/009fw8j44","country_code":"CN","type":"education","lineage":["https://openalex.org/I108160477"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Fengyu Guo","raw_affiliation_strings":["College of Urban and Rural Construction, Hebei Agricultural University, Baoding, 071000, China"],"affiliations":[{"raw_affiliation_string":"College of Urban and Rural Construction, Hebei Agricultural University, Baoding, 071000, China","institution_ids":["https://openalex.org/I108160477"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012918572","display_name":"Raiha Imran","orcid":"https://orcid.org/0009-0002-8678-504X"},"institutions":[{"id":"https://openalex.org/I195024194","display_name":"Riphah International University","ror":"https://ror.org/02kdm5630","country_code":"PK","type":"education","lineage":["https://openalex.org/I195024194"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Raiha Imran","raw_affiliation_strings":["Department of Mathematics, Riphah International University (Lahore Campus), Lahore, 54000, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Riphah International University (Lahore Campus), Lahore, 54000, Pakistan","institution_ids":["https://openalex.org/I195024194"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026893565","display_name":"Shi Yin","orcid":"https://orcid.org/0000-0001-6885-7412"},"institutions":[{"id":"https://openalex.org/I108160477","display_name":"Hebei Agricultural University","ror":"https://ror.org/009fw8j44","country_code":"CN","type":"education","lineage":["https://openalex.org/I108160477"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shi Yin","raw_affiliation_strings":["College of Humanities and Social Sciences, Hebei Agricultural University, Baoding, 071001, China"],"affiliations":[{"raw_affiliation_string":"College of Humanities and Social Sciences, Hebei Agricultural University, Baoding, 071001, China","institution_ids":["https://openalex.org/I108160477"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037136946","display_name":"Kifayat Ullah","orcid":"https://orcid.org/0000-0002-1438-6413"},"institutions":[{"id":"https://openalex.org/I195024194","display_name":"Riphah International University","ror":"https://ror.org/02kdm5630","country_code":"PK","type":"education","lineage":["https://openalex.org/I195024194"]},{"id":"https://openalex.org/I85461943","display_name":"Saveetha University","ror":"https://ror.org/0034me914","country_code":"IN","type":"education","lineage":["https://openalex.org/I85461943"]}],"countries":["IN","PK"],"is_corresponding":false,"raw_author_name":"Kifayat Ullah","raw_affiliation_strings":["Department of Mathematics, Riphah International University (Lahore Campus), Lahore, 54000, Pakistan","Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai, 602105, Tamil Nadu, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Riphah International University (Lahore Campus), Lahore, 54000, Pakistan","institution_ids":["https://openalex.org/I195024194"]},{"raw_affiliation_string":"Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai, 602105, Tamil Nadu, India","institution_ids":["https://openalex.org/I85461943"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068905105","display_name":"Maria Akram","orcid":"https://orcid.org/0000-0001-5786-0480"},"institutions":[{"id":"https://openalex.org/I195024194","display_name":"Riphah International University","ror":"https://ror.org/02kdm5630","country_code":"PK","type":"education","lineage":["https://openalex.org/I195024194"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Maria Akram","raw_affiliation_strings":["Department of Mathematics, Riphah International University (Lahore Campus), Lahore, 54000, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Riphah International University (Lahore Campus), Lahore, 54000, Pakistan","institution_ids":["https://openalex.org/I195024194"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018974025","display_name":"Dragan Pamu\u010dar","orcid":"https://orcid.org/0000-0001-8522-1942"},"institutions":[{"id":"https://openalex.org/I3130874397","display_name":"Western Caspian University","ror":"https://ror.org/05cgtjz78","country_code":"AZ","type":"education","lineage":["https://openalex.org/I3130874397"]},{"id":"https://openalex.org/I4210124601","display_name":"Department of Mathematical Sciences","ror":"https://ror.org/02xkdev90","country_code":"RU","type":"government","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210124601"]},{"id":"https://openalex.org/I99908691","display_name":"Yuan Ze University","ror":"https://ror.org/01fv1ds98","country_code":"TW","type":"education","lineage":["https://openalex.org/I99908691"]}],"countries":["AZ","RU","TW"],"is_corresponding":false,"raw_author_name":"Dragan Pamucar","raw_affiliation_strings":["College of Engineering, Yuan Ze University, Taoyuan City, 320315, Taiwan","Department of Applied Mathematical Science, College of Science and Technology, Korea University, 30019, Sejong, Republic of Korea","Department of Mechanics and Mathematics, Western Caspian University, Baku, Azerbaijan"],"affiliations":[{"raw_affiliation_string":"College of Engineering, Yuan Ze University, Taoyuan City, 320315, Taiwan","institution_ids":["https://openalex.org/I99908691"]},{"raw_affiliation_string":"Department of Applied Mathematical Science, College of Science and Technology, Korea University, 30019, Sejong, Republic of Korea","institution_ids":["https://openalex.org/I4210124601"]},{"raw_affiliation_string":"Department of Mechanics and Mathematics, Western Caspian University, Baku, Azerbaijan","institution_ids":["https://openalex.org/I3130874397"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035635820","display_name":"M. I. Elashiry","orcid":"https://orcid.org/0000-0003-1327-2876"},"institutions":[{"id":"https://openalex.org/I118590987","display_name":"Northern Border University","ror":"https://ror.org/03j9tzj20","country_code":"SA","type":"education","lineage":["https://openalex.org/I118590987"]},{"id":"https://openalex.org/I66513531","display_name":"Fayoum University","ror":"https://ror.org/023gzwx10","country_code":"EG","type":"education","lineage":["https://openalex.org/I66513531"]}],"countries":["EG","SA"],"is_corresponding":false,"raw_author_name":"Mustafa Elashiry","raw_affiliation_strings":["Department of Mathematics, Faculty of Arts and Science, Northern Border University, Rafha, Saudi Arabia","Department of Mathematics, Faculty of Science, Fayoum University, El-Fayoum, Egypt"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Arts and Science, Northern Border University, Rafha, Saudi Arabia","institution_ids":["https://openalex.org/I118590987"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Fayoum University, El-Fayoum, Egypt","institution_ids":["https://openalex.org/I66513531"]}]}],"institutions":[],"countries_distinct_count":8,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5028851981"],"corresponding_institution_ids":["https://openalex.org/I108160477"],"apc_list":{"value":1320,"currency":"GBP","value_usd":1619},"apc_paid":{"value":1320,"currency":"GBP","value_usd":1619},"fwci":28.6398,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.99667635,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"11","issue":"6","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9933000206947327,"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":0.9933000206947327,"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":0.9498000144958496,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/computational-intelligence","display_name":"Computational intelligence","score":0.7229222059249878},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.507839024066925},{"id":"https://openalex.org/keywords/index","display_name":"Index (typography)","score":0.4661845862865448},{"id":"https://openalex.org/keywords/air-quality-index","display_name":"Air quality index","score":0.43659716844558716},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4077223241329193},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3535788059234619},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2667105793952942},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16084107756614685},{"id":"https://openalex.org/keywords/meteorology","display_name":"Meteorology","score":0.1045968234539032}],"concepts":[{"id":"https://openalex.org/C139502532","wikidata":"https://www.wikidata.org/wiki/Q1122090","display_name":"Computational intelligence","level":2,"score":0.7229222059249878},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.507839024066925},{"id":"https://openalex.org/C2777382242","wikidata":"https://www.wikidata.org/wiki/Q6017816","display_name":"Index (typography)","level":2,"score":0.4661845862865448},{"id":"https://openalex.org/C126314574","wikidata":"https://www.wikidata.org/wiki/Q2364111","display_name":"Air quality index","level":2,"score":0.43659716844558716},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4077223241329193},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3535788059234619},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2667105793952942},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16084107756614685},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.1045968234539032},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s40747-025-01813-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40747-025-01813-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40747-025-01813-z.pdf","source":{"id":"https://openalex.org/S3035462843","display_name":"Complex & Intelligent Systems","issn_l":"2198-6053","issn":["2198-6053","2199-4536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complex &amp; Intelligent Systems","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:5ddada1e278049219563113ab98efe55","is_oa":true,"landing_page_url":"https://doaj.org/article/5ddada1e278049219563113ab98efe55","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Complex & Intelligent Systems, Vol 11, Iss 6, Pp 1-24 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s40747-025-01813-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40747-025-01813-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40747-025-01813-z.pdf","source":{"id":"https://openalex.org/S3035462843","display_name":"Complex & Intelligent Systems","issn_l":"2198-6053","issn":["2198-6053","2199-4536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complex &amp; Intelligent Systems","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7","score":0.6000000238418579}],"awards":[],"funders":[{"id":"https://openalex.org/F4320328654","display_name":"Northern Border University","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4409681413.pdf","grobid_xml":"https://content.openalex.org/works/W4409681413.grobid-xml"},"referenced_works_count":60,"referenced_works":["https://openalex.org/W1505735190","https://openalex.org/W1528458083","https://openalex.org/W1965777053","https://openalex.org/W1972144494","https://openalex.org/W1980564456","https://openalex.org/W1981107087","https://openalex.org/W1984935922","https://openalex.org/W2016698635","https://openalex.org/W2049661780","https://openalex.org/W2059263717","https://openalex.org/W2060857908","https://openalex.org/W2079457935","https://openalex.org/W2079790626","https://openalex.org/W2107782555","https://openalex.org/W2114723553","https://openalex.org/W2514466739","https://openalex.org/W2514754342","https://openalex.org/W2563128797","https://openalex.org/W2582765108","https://openalex.org/W2593392677","https://openalex.org/W2804747855","https://openalex.org/W2883333523","https://openalex.org/W2897932070","https://openalex.org/W2900419240","https://openalex.org/W2990272482","https://openalex.org/W3004286422","https://openalex.org/W3013882886","https://openalex.org/W3046761565","https://openalex.org/W3174796173","https://openalex.org/W3186343317","https://openalex.org/W3210381108","https://openalex.org/W4205627072","https://openalex.org/W4211007335","https://openalex.org/W4224277527","https://openalex.org/W4228999430","https://openalex.org/W4230733346","https://openalex.org/W4301372235","https://openalex.org/W4308645606","https://openalex.org/W4313266930","https://openalex.org/W4313318325","https://openalex.org/W4313546133","https://openalex.org/W4319455029","https://openalex.org/W4327757656","https://openalex.org/W4364359932","https://openalex.org/W4368618039","https://openalex.org/W4379645967","https://openalex.org/W4381681247","https://openalex.org/W4385358469","https://openalex.org/W4385447163","https://openalex.org/W4385829274","https://openalex.org/W4387632406","https://openalex.org/W4388574358","https://openalex.org/W4391644818","https://openalex.org/W4401081015","https://openalex.org/W4401117995","https://openalex.org/W4401243911","https://openalex.org/W4401581591","https://openalex.org/W4402003802","https://openalex.org/W4402067407","https://openalex.org/W4406183020"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"The":[0,74],"impact":[1],"of":[2,18,61,68,225,237],"airborne":[3,52],"pollutants":[4,53,70],"present":[5],"in":[6,64,71,82,92,99,123],"the":[7,10,59,66,72,84,105,138,144,150,157,161,206,210,215,235,238],"environment,":[8,163],"entering":[9],"body":[11],"through":[12],"breathing,":[13],"can":[14],"cause":[15],"significant":[16,80],"risks":[17],"respiratory":[19],"and":[20,40,87,110,117,135,172,175,184,187,217,227],"heart-related":[21],"health":[22],"problems":[23,151],"for":[24],"individuals.":[25],"For":[26],"this,":[27,104],"different":[28],"air":[29,62,69],"purifiers":[30,63],"are":[31],"commonly":[32],"used":[33,122],"to":[34,50,197,233],"eliminate":[35],"delicate":[36],"particulate":[37],"matter":[38],"PM2.5,":[39],"various":[41],"studies":[42],"have":[43,120,189],"examined":[44],"their":[45],"effectiveness.":[46],"This":[47],"paper":[48,220],"aims":[49],"analyze":[51],"and,":[54],"by":[55,204],"considering":[56,103],"them,":[57],"assess":[58],"performance":[60],"reducing":[65],"concentration":[67],"environment.":[73,155,212],"aggregation":[75],"operator":[76,109,159],"(AO)":[77],"plays":[78],"a":[79,90,93,153,199,222,228],"role":[81],"aggregating":[83],"multiple":[85],"criteria":[86],"gives":[88],"us":[89,98],"result":[91],"singleton":[94],"set,":[95],"which":[96],"assists":[97],"decision-making":[100,201],"(DM).":[101],"So,":[102,156],"Heronian":[106,169],"mean":[107,170],"(HM)":[108],"its":[111],"special":[112],"cases":[113],"such":[114,164],"as":[115,143,165],"averaging":[116,174],"geometric":[118,176],"operators":[119,208],"been":[121,179,190],"this":[124,219],"paper.":[125],"Moreover,":[126],"circular":[127,154,166,211],"intuitionistic":[128,139,167],"fuzzy":[129,140,168],"(C-IF)":[130],"theory":[131],"is":[132],"more":[133],"efficient":[134],"comprehensive":[136],"than":[137],"set":[141],"(IFS),":[142],"standard":[145],"IFS":[146],"cannot":[147],"cope":[148],"with":[149],"within":[152,209],"HM":[158],"under":[160],"C-IF":[162],"(C-IFHM)":[171],"it\u2019s":[173],"operator,":[177],"has":[178],"presented.":[180],"Further,":[181],"some":[182],"prevalent":[183],"crucial":[185],"properties":[186],"theorems":[188],"defined.":[191],"Then,":[192],"an":[193],"algorithm":[194],"was":[195,231],"developed":[196],"solve":[198],"multicriteria":[200],"(MCDM)":[202],"problem":[203],"using":[205],"proposed":[207,239],"To":[213],"validate":[214],"effectiveness":[216],"priority,":[218],"presents":[221],"numerical":[223],"example":[224],"MCDM,":[226],"comparison":[229],"analysis":[230],"conducted":[232],"verify":[234],"practicality":[236],"approach.":[240]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":10}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}
