{"id":"https://openalex.org/W4311846917","doi":"https://doi.org/10.1007/s40747-022-00913-4","title":"The differential measure for Pythagorean fuzzy multiple criteria group decision-making","display_name":"The differential measure for Pythagorean fuzzy multiple criteria group decision-making","publication_year":2022,"publication_date":"2022-12-07","ids":{"openalex":"https://openalex.org/W4311846917","doi":"https://doi.org/10.1007/s40747-022-00913-4","pmid":"https://pubmed.ncbi.nlm.nih.gov/36530758"},"language":"en","primary_location":{"id":"doi:10.1007/s40747-022-00913-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40747-022-00913-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40747-022-00913-4.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","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complex & Intelligent Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://link.springer.com/content/pdf/10.1007/s40747-022-00913-4.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060460021","display_name":"Iman Mohamad Sharaf","orcid":"https://orcid.org/0000-0002-0878-5696"},"institutions":[{"id":"https://openalex.org/I160419504","display_name":"Higher Technological Institute","ror":"https://ror.org/051q8jk17","country_code":"EG","type":"education","lineage":["https://openalex.org/I160419504"]}],"countries":["EG"],"is_corresponding":true,"raw_author_name":"Iman Mohamad Sharaf","raw_affiliation_strings":["Department of Basic Sciences, Higher Technological Institute, Tenth of Ramadan City, Egypt"],"affiliations":[{"raw_affiliation_string":"Department of Basic Sciences, Higher Technological Institute, Tenth of Ramadan City, Egypt","institution_ids":["https://openalex.org/I160419504"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5060460021"],"corresponding_institution_ids":["https://openalex.org/I160419504"],"apc_list":{"value":1320,"currency":"GBP","value_usd":1619},"apc_paid":{"value":1320,"currency":"GBP","value_usd":1619},"fwci":0.6766,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.73552972,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"9","issue":"3","first_page":"3333","last_page":"3354"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9988999962806702,"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":0.9988999962806702,"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":0.9843000173568726,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9690999984741211,"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/pythagorean-theorem","display_name":"Pythagorean theorem","score":0.8165848851203918},{"id":"https://openalex.org/keywords/computational-intelligence","display_name":"Computational intelligence","score":0.7298126220703125},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.7245639562606812},{"id":"https://openalex.org/keywords/group-decision-making","display_name":"Group decision-making","score":0.5498712658882141},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5212460160255432},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.5046354532241821},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.4780293405056},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44704607129096985},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3645789623260498},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.32335278391838074},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.253883957862854},{"id":"https://openalex.org/keywords/psychology","display_name":"Psychology","score":0.16048943996429443},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.1488960087299347},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11999046802520752},{"id":"https://openalex.org/keywords/social-psychology","display_name":"Social psychology","score":0.08719196915626526}],"concepts":[{"id":"https://openalex.org/C100461760","wikidata":"https://www.wikidata.org/wiki/Q11518","display_name":"Pythagorean theorem","level":2,"score":0.8165848851203918},{"id":"https://openalex.org/C139502532","wikidata":"https://www.wikidata.org/wiki/Q1122090","display_name":"Computational intelligence","level":2,"score":0.7298126220703125},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.7245639562606812},{"id":"https://openalex.org/C20701700","wikidata":"https://www.wikidata.org/wiki/Q388791","display_name":"Group decision-making","level":2,"score":0.5498712658882141},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5212460160255432},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.5046354532241821},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4780293405056},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44704607129096985},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3645789623260498},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.32335278391838074},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.253883957862854},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.16048943996429443},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.1488960087299347},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11999046802520752},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.08719196915626526},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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":4,"locations":[{"id":"doi:10.1007/s40747-022-00913-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40747-022-00913-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40747-022-00913-4.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","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complex & Intelligent Systems","raw_type":"journal-article"},{"id":"pmid:36530758","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/36530758","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complex & intelligent systems","raw_type":null},{"id":"pmh:oai:doaj.org/article:519d9929ddd749b0bfd531e405110f83","is_oa":true,"landing_page_url":"https://doaj.org/article/519d9929ddd749b0bfd531e405110f83","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 9, Iss 3, Pp 3333-3354 (2022)","raw_type":"article"},{"id":"pmh:oai:pubmedcentral.nih.gov:9734832","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/9734832","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"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":"Complex Intell Systems","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1007/s40747-022-00913-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40747-022-00913-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40747-022-00913-4.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","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complex & Intelligent Systems","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.5899999737739563,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321655","display_name":"Science and Technology Development Fund","ror":"https://ror.org/044vr6g03"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4311846917.pdf","grobid_xml":"https://content.openalex.org/works/W4311846917.grobid-xml"},"referenced_works_count":92,"referenced_works":["https://openalex.org/W1505735190","https://openalex.org/W1587546457","https://openalex.org/W1668569279","https://openalex.org/W1829951598","https://openalex.org/W1980564456","https://openalex.org/W2013932252","https://openalex.org/W2026244788","https://openalex.org/W2029074979","https://openalex.org/W2038166912","https://openalex.org/W2062087879","https://openalex.org/W2069510845","https://openalex.org/W2073820580","https://openalex.org/W2104077967","https://openalex.org/W2106135161","https://openalex.org/W2116365436","https://openalex.org/W2292359941","https://openalex.org/W2311142332","https://openalex.org/W2396040005","https://openalex.org/W2412590235","https://openalex.org/W2414387118","https://openalex.org/W2514754342","https://openalex.org/W2562993244","https://openalex.org/W2587083986","https://openalex.org/W2589233777","https://openalex.org/W2593530789","https://openalex.org/W2753862205","https://openalex.org/W2756107921","https://openalex.org/W2765614740","https://openalex.org/W2771959654","https://openalex.org/W2790677216","https://openalex.org/W2800899235","https://openalex.org/W2804105936","https://openalex.org/W2811195812","https://openalex.org/W2883368008","https://openalex.org/W2899511870","https://openalex.org/W2901104715","https://openalex.org/W2903466805","https://openalex.org/W2904891763","https://openalex.org/W2909916858","https://openalex.org/W2912632080","https://openalex.org/W2913099936","https://openalex.org/W2918302114","https://openalex.org/W2919513668","https://openalex.org/W2934195809","https://openalex.org/W2936635606","https://openalex.org/W2944393183","https://openalex.org/W2952311754","https://openalex.org/W2952314276","https://openalex.org/W2953240374","https://openalex.org/W2957999460","https://openalex.org/W2959038458","https://openalex.org/W2969852833","https://openalex.org/W2984896269","https://openalex.org/W2999935177","https://openalex.org/W3006789142","https://openalex.org/W3012582342","https://openalex.org/W3048070941","https://openalex.org/W3091686397","https://openalex.org/W3097128494","https://openalex.org/W3118993451","https://openalex.org/W3120084192","https://openalex.org/W3121700030","https://openalex.org/W3123054758","https://openalex.org/W3161541711","https://openalex.org/W3162432343","https://openalex.org/W3170308824","https://openalex.org/W3183639688","https://openalex.org/W3202923289","https://openalex.org/W3203503599","https://openalex.org/W3203828355","https://openalex.org/W3209127401","https://openalex.org/W3214367067","https://openalex.org/W3214435916","https://openalex.org/W3217669713","https://openalex.org/W4205543335","https://openalex.org/W4210542188","https://openalex.org/W4210835717","https://openalex.org/W4210954013","https://openalex.org/W4211007335","https://openalex.org/W4220694800","https://openalex.org/W4220915829","https://openalex.org/W4221129481","https://openalex.org/W4225980591","https://openalex.org/W4229457423","https://openalex.org/W4239165868","https://openalex.org/W4254501931","https://openalex.org/W4281696218","https://openalex.org/W4283030009","https://openalex.org/W4285736300","https://openalex.org/W4286268327","https://openalex.org/W4288721483","https://openalex.org/W4291008812"],"related_works":["https://openalex.org/W2995447873","https://openalex.org/W1802380781","https://openalex.org/W4210969441","https://openalex.org/W4313271080","https://openalex.org/W4378767041","https://openalex.org/W2050612014","https://openalex.org/W3166167233","https://openalex.org/W2943864676","https://openalex.org/W2624109864","https://openalex.org/W2906568202"],"abstract_inverted_index":{"Pythagorean":[0],"fuzzy":[1],"sets":[2],"(PFSs)":[3],"proved":[4],"to":[5,95,130,149,200,228,242],"be":[6],"powerful":[7],"for":[8,31,85,171,186],"handling":[9],"uncertainty":[10],"and":[11,36,128,136,209,232,246],"vagueness":[12],"in":[13,57,124],"multi-criteria":[14],"group":[15,174],"decision-making":[16,175],"(MCGDM).":[17],"To":[18],"make":[19],"a":[20,71,82,110,114],"compromise":[21],"decision,":[22],"comparing":[23,86],"PFSs":[24,119,140],"is":[25,94,113,176,193,198,240],"essential.":[26],"Several":[27],"approaches":[28],"were":[29],"introduced":[30,181],"comparison,":[32],"e.g.,":[33],"distance":[34],"measures":[35,41],"similarity":[37],"measures.":[38],"Nevertheless,":[39],"extant":[40,226],"have":[42],"several":[43],"defects":[44],"that":[45],"can":[46],"produce":[47],"counter-intuitive":[48],"results,":[49],"since":[50],"they":[51],"treat":[52],"any":[53],"increase":[54],"or":[55,147,157],"decrease":[56],"the":[58,61,64,77,92,97,102,106,125,131,153,163,180,188,191,204,210,213,222,230,235],"membership":[59,135],"degree":[60,154],"same":[62],"as":[63,81,143],"non-membership":[65,137],"degree;":[66],"although":[67],"each":[68],"parameter":[69],"has":[70],"different":[72],"implication.":[73],"This":[74],"study":[75],"introduces":[76],"differential":[78],"measure":[79],"(DFM)":[80],"new":[83,184],"approach":[84],"PFSs.":[87],"The":[88,159,195,217],"main":[89],"purpose":[90],"of":[91,105,109,122,133,155,162,190,206,212,224,234],"DFM":[93,165],"eliminate":[96],"unfair":[98],"arguments":[99],"resulting":[100],"from":[101],"equal":[103],"treatment":[104],"contradicting":[107],"parameters":[108],"PFS.":[111],"It":[112],"preference":[115],"relation":[116],"between":[117],"two":[118,202],"by":[120],"virtue":[121],"position":[123],"attribute":[126],"space":[127],"according":[129],"closeness":[132],"their":[134],"degrees.":[138],"Two":[139],"are":[141,166,219],"classified":[142],"identical,":[144],"equivalent,":[145],"superior,":[146],"inferior":[148],"one":[150],"another":[151],"giving":[152],"superiority":[156],"inferiority.":[158],"basic":[160],"properties":[161],"proposed":[164,177,196],"given.":[167],"A":[168,183,237],"novel":[169],"method":[170,197],"multiple":[172],"criteria":[173],"based":[178],"on":[179],"DFM.":[182],"technique":[185],"computing":[187],"weights":[189],"experts":[192],"developed.":[194],"applied":[199],"solve":[201],"applications,":[203],"evaluation":[205],"solid-state":[207],"drives":[208],"selection":[211],"best":[214],"photovoltaic":[215],"cell.":[216],"results":[218,223],"compared":[220],"with":[221],"some":[225],"methods":[227],"illustrate":[229],"applicability":[231],"validity":[233],"method.":[236],"sensitivity":[238],"analysis":[239],"conducted":[241],"examine":[243],"its":[244],"stability":[245],"practicality.":[247]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}