{"id":"https://openalex.org/W4386579178","doi":"https://doi.org/10.1007/s40314-023-02420-9","title":"Similarity measures of Pythagorean fuzzy sets based on Lp metric and its applications to multicriteria decision-making with Pythagorean VIKOR and clustering","display_name":"Similarity measures of Pythagorean fuzzy sets based on Lp metric and its applications to multicriteria decision-making with Pythagorean VIKOR and clustering","publication_year":2023,"publication_date":"2023-09-09","ids":{"openalex":"https://openalex.org/W4386579178","doi":"https://doi.org/10.1007/s40314-023-02420-9"},"language":"en","primary_location":{"id":"doi:10.1007/s40314-023-02420-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-023-02420-9","pdf_url":null,"source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"0101-8205","issn":["0101-8205","1807-0302","2238-3603"],"is_oa":false,"is_in_doaj":false,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational and Applied Mathematics","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/A5046124406","display_name":"Zahid Hussain","orcid":"https://orcid.org/0000-0002-6101-6685"},"institutions":[{"id":"https://openalex.org/I236232284","display_name":"Karakoram International University","ror":"https://ror.org/0324r4e56","country_code":"PK","type":"education","lineage":["https://openalex.org/I236232284"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Zahid Hussain","raw_affiliation_strings":["Department of Mathematical Science, Karakoram International University, Gilgit-Baltistan, 15100, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-6101-6685","affiliations":[{"raw_affiliation_string":"Department of Mathematical Science, Karakoram International University, Gilgit-Baltistan, 15100, Pakistan","institution_ids":["https://openalex.org/I236232284"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102554136","display_name":"Hafeeza Afzal","orcid":null},"institutions":[{"id":"https://openalex.org/I236232284","display_name":"Karakoram International University","ror":"https://ror.org/0324r4e56","country_code":"PK","type":"education","lineage":["https://openalex.org/I236232284"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Hafeeza Afzal","raw_affiliation_strings":["Department of Mathematical Science, Karakoram International University, Gilgit-Baltistan, 15100, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Science, Karakoram International University, Gilgit-Baltistan, 15100, Pakistan","institution_ids":["https://openalex.org/I236232284"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101861699","display_name":"R. Jahir Hussain","orcid":"https://orcid.org/0000-0003-3260-7280"},"institutions":[{"id":"https://openalex.org/I236232284","display_name":"Karakoram International University","ror":"https://ror.org/0324r4e56","country_code":"PK","type":"education","lineage":["https://openalex.org/I236232284"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Rashid Hussain","raw_affiliation_strings":["Department of Mathematical Science, Karakoram International University, Gilgit-Baltistan, 15100, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Science, Karakoram International University, Gilgit-Baltistan, 15100, Pakistan","institution_ids":["https://openalex.org/I236232284"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5107874994","display_name":"NasimUllah","orcid":null},"institutions":[{"id":"https://openalex.org/I236232284","display_name":"Karakoram International University","ror":"https://ror.org/0324r4e56","country_code":"PK","type":"education","lineage":["https://openalex.org/I236232284"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Nasimullah","raw_affiliation_strings":["Department of Mathematical Science, Karakoram International University, Gilgit-Baltistan, 15100, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Science, Karakoram International University, Gilgit-Baltistan, 15100, Pakistan","institution_ids":["https://openalex.org/I236232284"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5046124406"],"corresponding_institution_ids":["https://openalex.org/I236232284"],"apc_list":{"value":3090,"currency":"USD","value_usd":3090},"apc_paid":null,"fwci":1.5479,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.83391103,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"42","issue":"7","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":0.996999979019165,"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":0.996999979019165,"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":0.9944000244140625,"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/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.970300018787384,"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/pythagorean-theorem","display_name":"Pythagorean theorem","score":0.7059794664382935},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.5947847962379456},{"id":"https://openalex.org/keywords/similarity","display_name":"Similarity (geometry)","score":0.5786709189414978},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5048485398292542},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.474346786737442},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.4530661702156067},{"id":"https://openalex.org/keywords/similarity-measure","display_name":"Similarity measure","score":0.43654438853263855},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4208359718322754},{"id":"https://openalex.org/keywords/fuzzy-clustering","display_name":"Fuzzy clustering","score":0.41657736897468567},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.41164273023605347},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4052850604057312},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.4046779274940491},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36605778336524963},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.1060592532157898}],"concepts":[{"id":"https://openalex.org/C100461760","wikidata":"https://www.wikidata.org/wiki/Q11518","display_name":"Pythagorean theorem","level":2,"score":0.7059794664382935},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.5947847962379456},{"id":"https://openalex.org/C103278499","wikidata":"https://www.wikidata.org/wiki/Q254465","display_name":"Similarity (geometry)","level":3,"score":0.5786709189414978},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5048485398292542},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.474346786737442},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.4530661702156067},{"id":"https://openalex.org/C2776517306","wikidata":"https://www.wikidata.org/wiki/Q29017317","display_name":"Similarity measure","level":2,"score":0.43654438853263855},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4208359718322754},{"id":"https://openalex.org/C17212007","wikidata":"https://www.wikidata.org/wiki/Q5511111","display_name":"Fuzzy clustering","level":3,"score":0.41657736897468567},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.41164273023605347},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4052850604057312},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.4046779274940491},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36605778336524963},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.1060592532157898},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"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:10.1007/s40314-023-02420-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-023-02420-9","pdf_url":null,"source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"0101-8205","issn":["0101-8205","1807-0302","2238-3603"],"is_oa":false,"is_in_doaj":false,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational and Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7599999904632568,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W66917582","https://openalex.org/W202198668","https://openalex.org/W1515034838","https://openalex.org/W1668569279","https://openalex.org/W1829951598","https://openalex.org/W1980564456","https://openalex.org/W2004232496","https://openalex.org/W2039791408","https://openalex.org/W2058080862","https://openalex.org/W2079457935","https://openalex.org/W2079767857","https://openalex.org/W2104077967","https://openalex.org/W2117849675","https://openalex.org/W2125906479","https://openalex.org/W2315521424","https://openalex.org/W2414387118","https://openalex.org/W2790677216","https://openalex.org/W2791638390","https://openalex.org/W2799466028","https://openalex.org/W2804105936","https://openalex.org/W2884482861","https://openalex.org/W2899511870","https://openalex.org/W2902751867","https://openalex.org/W2904891763","https://openalex.org/W2923182347","https://openalex.org/W2969852833","https://openalex.org/W3048846577","https://openalex.org/W3084978713","https://openalex.org/W3178705801","https://openalex.org/W3179100250","https://openalex.org/W4211007335","https://openalex.org/W4211196307","https://openalex.org/W4229040362","https://openalex.org/W4283215232","https://openalex.org/W4295074053","https://openalex.org/W4309474360","https://openalex.org/W4309710940","https://openalex.org/W4375948421","https://openalex.org/W4379260611"],"related_works":["https://openalex.org/W2995447873","https://openalex.org/W2319693127","https://openalex.org/W2474567666","https://openalex.org/W2072263576","https://openalex.org/W2790658443","https://openalex.org/W1940044583","https://openalex.org/W2056226831","https://openalex.org/W2806903871","https://openalex.org/W4320802053","https://openalex.org/W1498655127"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3}],"updated_date":"2026-08-11T07:18:39.950985","created_date":"2025-10-10T00:00:00"}