{"id":"https://openalex.org/W3204921395","doi":"https://doi.org/10.1007/s44196-021-00008-x","title":"Multi-criteria Optimization Technique with Complex Pythagorean Fuzzy N-soft Information","display_name":"Multi-criteria Optimization Technique with Complex Pythagorean Fuzzy N-soft Information","publication_year":2021,"publication_date":"2021-09-27","ids":{"openalex":"https://openalex.org/W3204921395","doi":"https://doi.org/10.1007/s44196-021-00008-x","mag":"3204921395"},"language":"en","primary_location":{"id":"doi:10.1007/s44196-021-00008-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s44196-021-00008-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s44196-021-00008-x.pdf","source":{"id":"https://openalex.org/S190680769","display_name":"International Journal of Computational Intelligence Systems","issn_l":"1875-6883","issn":["1875-6883","1875-6891"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["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":"International Journal of Computational Intelligence 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/s44196-021-00008-x.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001270995","display_name":"Muhammad Akram","orcid":"https://orcid.org/0000-0001-7217-7962"},"institutions":[{"id":"https://openalex.org/I172780181","display_name":"University of the Punjab","ror":"https://ror.org/011maz450","country_code":"PK","type":"education","lineage":["https://openalex.org/I172780181"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Akram","raw_affiliation_strings":["Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan"],"raw_orcid":"https://orcid.org/0000-0001-7217-7962","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan","institution_ids":["https://openalex.org/I172780181"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005184441","display_name":"Faiza Wasim","orcid":null},"institutions":[{"id":"https://openalex.org/I172780181","display_name":"University of the Punjab","ror":"https://ror.org/011maz450","country_code":"PK","type":"education","lineage":["https://openalex.org/I172780181"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Faiza Wasim","raw_affiliation_strings":["Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan","institution_ids":["https://openalex.org/I172780181"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024802129","display_name":"Jos\u00e9 Carlos R. Alcantud","orcid":"https://orcid.org/0000-0002-4533-9281"},"institutions":[{"id":"https://openalex.org/I184999862","display_name":"Universidad de Salamanca","ror":"https://ror.org/02f40zc51","country_code":"ES","type":"education","lineage":["https://openalex.org/I184999862"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Jos\u00e9 Carlos R. Alcantud","raw_affiliation_strings":["BORDA Research Unit and IME, University of Salamanca, 37007, Salamanca, Spain"],"raw_orcid":"https://orcid.org/0000-0002-4533-9281","affiliations":[{"raw_affiliation_string":"BORDA Research Unit and IME, University of Salamanca, 37007, Salamanca, Spain","institution_ids":["https://openalex.org/I184999862"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009981956","display_name":"Ahmad N. Al\u2010Kenani","orcid":null},"institutions":[{"id":"https://openalex.org/I185163786","display_name":"King Abdulaziz University","ror":"https://ror.org/02ma4wv74","country_code":"SA","type":"education","lineage":["https://openalex.org/I185163786"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Ahmad N. Al-Kenani","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0001-5559-5951","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia","institution_ids":["https://openalex.org/I185163786"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5024802129"],"corresponding_institution_ids":["https://openalex.org/I184999862"],"apc_list":{"value":1390,"currency":"GBP","value_usd":1704},"apc_paid":{"value":1390,"currency":"GBP","value_usd":1704},"fwci":1.4328,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.82737969,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"14","issue":"1","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":0.9998999834060669,"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":0.9998999834060669,"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":0.9955000281333923,"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/T12709","display_name":"Optimization and Mathematical Programming","score":0.9914000034332275,"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/vikor-method","display_name":"VIKOR method","score":0.8223378658294678},{"id":"https://openalex.org/keywords/regret","display_name":"Regret","score":0.6758419275283813},{"id":"https://openalex.org/keywords/pythagorean-theorem","display_name":"Pythagorean theorem","score":0.6756569743156433},{"id":"https://openalex.org/keywords/ranking","display_name":"Ranking (information retrieval)","score":0.6669594049453735},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6328423023223877},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5576561689376831},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.5158950090408325},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.44459185004234314},{"id":"https://openalex.org/keywords/vagueness","display_name":"Vagueness","score":0.4250241219997406},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3494570851325989},{"id":"https://openalex.org/keywords/operations-research","display_name":"Operations research","score":0.34150785207748413},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.3262701630592346},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2545292377471924},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.24388712644577026}],"concepts":[{"id":"https://openalex.org/C172438850","wikidata":"https://www.wikidata.org/wiki/Q7907019","display_name":"VIKOR method","level":3,"score":0.8223378658294678},{"id":"https://openalex.org/C50817715","wikidata":"https://www.wikidata.org/wiki/Q79895177","display_name":"Regret","level":2,"score":0.6758419275283813},{"id":"https://openalex.org/C100461760","wikidata":"https://www.wikidata.org/wiki/Q11518","display_name":"Pythagorean theorem","level":2,"score":0.6756569743156433},{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.6669594049453735},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6328423023223877},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5576561689376831},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.5158950090408325},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.44459185004234314},{"id":"https://openalex.org/C2776825360","wikidata":"https://www.wikidata.org/wiki/Q1411921","display_name":"Vagueness","level":3,"score":0.4250241219997406},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3494570851325989},{"id":"https://openalex.org/C42475967","wikidata":"https://www.wikidata.org/wiki/Q194292","display_name":"Operations research","level":1,"score":0.34150785207748413},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.3262701630592346},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2545292377471924},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.24388712644577026},{"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/s44196-021-00008-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s44196-021-00008-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s44196-021-00008-x.pdf","source":{"id":"https://openalex.org/S190680769","display_name":"International Journal of Computational Intelligence Systems","issn_l":"1875-6883","issn":["1875-6883","1875-6891"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["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":"International Journal of Computational Intelligence Systems","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s44196-021-00008-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s44196-021-00008-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s44196-021-00008-x.pdf","source":{"id":"https://openalex.org/S190680769","display_name":"International Journal of Computational Intelligence Systems","issn_l":"1875-6883","issn":["1875-6883","1875-6891"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["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":"International Journal of Computational Intelligence Systems","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/9","score":0.46000000834465027,"display_name":"Industry, innovation and infrastructure"}],"awards":[{"id":"https://openalex.org/G2131971619","display_name":null,"funder_award_id":"CLU-2019-03","funder_id":"https://openalex.org/F4320328351","funder_display_name":"Junta de Castilla y Le\u00f3n"},{"id":"https://openalex.org/G2791971228","display_name":null,"funder_award_id":"RG-24-130-38","funder_id":"https://openalex.org/F4320322322","funder_display_name":"King Abdulaziz University"},{"id":"https://openalex.org/G3584929499","display_name":null,"funder_award_id":"Grant CLU-2019-03","funder_id":"https://openalex.org/F4320328351","funder_display_name":"Junta de Castilla y Le\u00f3n"},{"id":"https://openalex.org/G4708082320","display_name":null,"funder_award_id":"CLU-2019-03","funder_id":"https://openalex.org/F4320325114","funder_display_name":"Consejer\u00eda de Educaci\u00f3n, Junta de Castilla y Le\u00f3n"},{"id":"https://openalex.org/G7457857910","display_name":null,"funder_award_id":"CLU-2019-03","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G817937095","display_name":null,"funder_award_id":"Grant CLU-2019-03","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"}],"funders":[{"id":"https://openalex.org/F4320322322","display_name":"King Abdulaziz University","ror":"https://ror.org/02ma4wv74"},{"id":"https://openalex.org/F4320325114","display_name":"Consejer\u00eda de Educaci\u00f3n, Junta de Castilla y Le\u00f3n","ror":"https://ror.org/02s8dab97"},{"id":"https://openalex.org/F4320328351","display_name":"Junta de Castilla y Le\u00f3n","ror":"https://ror.org/02s8dab97"},{"id":"https://openalex.org/F4320335322","display_name":"European Regional Development Fund","ror":"https://ror.org/00k4n6c32"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3204921395.pdf","grobid_xml":"https://content.openalex.org/works/W3204921395.grobid-xml"},"referenced_works_count":67,"referenced_works":["https://openalex.org/W1552174551","https://openalex.org/W1748537427","https://openalex.org/W1968069774","https://openalex.org/W1978352585","https://openalex.org/W1980564456","https://openalex.org/W2002929769","https://openalex.org/W2012575173","https://openalex.org/W2053190248","https://openalex.org/W2056164867","https://openalex.org/W2065363019","https://openalex.org/W2079457935","https://openalex.org/W2081338955","https://openalex.org/W2097403045","https://openalex.org/W2153478942","https://openalex.org/W2170866269","https://openalex.org/W2263787491","https://openalex.org/W2374072881","https://openalex.org/W2488327324","https://openalex.org/W2506768821","https://openalex.org/W2760273722","https://openalex.org/W2766654731","https://openalex.org/W2769278513","https://openalex.org/W2885385239","https://openalex.org/W2890943116","https://openalex.org/W2903616776","https://openalex.org/W2904219061","https://openalex.org/W2911458131","https://openalex.org/W2912565176","https://openalex.org/W2919513668","https://openalex.org/W2921729277","https://openalex.org/W2922136142","https://openalex.org/W2922545006","https://openalex.org/W2924706661","https://openalex.org/W2945144398","https://openalex.org/W2945404912","https://openalex.org/W2947577298","https://openalex.org/W2962753525","https://openalex.org/W2963497629","https://openalex.org/W2979296518","https://openalex.org/W2981142350","https://openalex.org/W2983194979","https://openalex.org/W2984993758","https://openalex.org/W2988347501","https://openalex.org/W2995844073","https://openalex.org/W2999405368","https://openalex.org/W3009690107","https://openalex.org/W3014664391","https://openalex.org/W3014707988","https://openalex.org/W3020648609","https://openalex.org/W3024056334","https://openalex.org/W3024482632","https://openalex.org/W3028372551","https://openalex.org/W3036144362","https://openalex.org/W3043329660","https://openalex.org/W3044292067","https://openalex.org/W3046108428","https://openalex.org/W3048070941","https://openalex.org/W3100717670","https://openalex.org/W3109432046","https://openalex.org/W3114984455","https://openalex.org/W3121700030","https://openalex.org/W3126088291","https://openalex.org/W3128951492","https://openalex.org/W3133089600","https://openalex.org/W3156270649","https://openalex.org/W3157456600","https://openalex.org/W4211007335"],"related_works":["https://openalex.org/W2971351794","https://openalex.org/W4376155396","https://openalex.org/W1947085858","https://openalex.org/W2174986909","https://openalex.org/W2527791220","https://openalex.org/W2101991911","https://openalex.org/W1543100750","https://openalex.org/W2009841438","https://openalex.org/W3092075709","https://openalex.org/W2332239209"],"abstract_inverted_index":{"Abstract":[0],"The":[1,62,117,271],"main":[2],"objective":[3],"of":[4,12,37,58,69,78,93,106,130,137,143,153,188,199,206,220,227,237,286,304],"this":[5,244],"article":[6],"is":[7,29,87,274],"to":[8,32,125,183,218,308],"lay":[9],"the":[10,19,54,66,70,74,79,91,107,127,131,135,138,141,144,155,158,170,185,189,194,200,204,225,234,238,251,284,287,302,305],"foundations":[11],"a":[13,34,49,94,228,247],"novel":[14],"multi-criteria":[15],"optimization":[16],"technique,":[17],"namely,":[18],"complex":[20,80,159,253,259],"Pythagorean":[21,81,160,254,260,266],"fuzzy":[22,56,82,161,255,261,267],"N":[23,83,162],"-soft":[24,84,163],"VIKOR":[25,71,262],"(CPFNS-VIKOR)":[26],"method":[27,64,72,202,264],"that":[28,281],"highly":[30,292],"proficient":[31],"express":[33],"great":[35],"deal":[36],"linguistic":[38,123],"imprecision":[39],"and":[40,102,140,178,197,265,294,312],"vagueness":[41],"inherent":[42],"in":[43,181],"human":[44],"assessments.":[45],"This":[46],"strategy":[47,119,307],"provides":[48],"versatile":[50],"decision-making":[51,132],"tool":[52],"for":[53,90,224],"ranking-based":[55],"modeling":[57],"two-dimensional":[59],"parameterized":[60],"data.":[61],"CPFNS-VIKOR":[63],"integrates":[65],"ground-breaking":[67],"specialities":[68],"with":[73,203,250,276],"outstanding":[75],"parametric":[76],"structure":[77],"model.":[85],"It":[86],"exclusively":[88],"designed":[89],"specification":[92],"compromise":[95],"optimal":[96],"solution":[97],"having":[98],"maximum":[99],"group":[100,175],"utility":[101,176],"minimum":[103],"individual":[104,128],"regret":[105,179],"opponent":[108],"by":[109,173,246,290],"analyzing":[110],"their":[111],"weighted":[112,164],"proximity":[113],"from":[114],"ideal":[115],"solutions.":[116],"developed":[118,306],"factually":[120],"permits":[121],"specific":[122],"terms":[124],"demystify":[126],"perspectives":[129],"experts":[133,156],"regarding":[134],"efficacy":[136],"alternatives":[139],"priorities":[142],"applicable":[145],"criteria.":[146],"We":[147,192,211],"comprehensively":[148],"assemble":[149],"these":[150],"independent":[151],"appraisals":[152],"all":[154],"using":[157],"averaging":[165],"operator.":[166],"Moreover,":[167],"we":[168,242,299],"calibrate":[169],"ranking":[171],"measure":[172,177,180],"utilizing":[174],"order":[182],"specify":[184],"hierarchical":[186],"outranking":[187],"feasible":[190],"alternatives.":[191],"demonstrate":[193],"systematic":[195],"methodology":[196,289],"framework":[198],"proposed":[201,239,288],"assistance":[205],"an":[207,214,277],"explicative":[208],"flow":[209],"chart.":[210],"skilfully":[212],"investigate":[213],"empirical":[215],"analysis":[216],"related":[217],"selection":[219],"constructive":[221],"industrial":[222],"robots":[223],"modernization":[226],"manufacturing":[229],"industry":[230],"which":[231],"really":[232],"justifies":[233],"remarkable":[235],"accountability":[236],"strategy.":[240],"Furthermore,":[241],"validate":[243],"technique":[245],"comparative":[248,272],"study":[249,273],"existing":[252],"TOPSIS":[256,268],"(CPF-TOPSIS)":[257],"method,":[258],"(CPF-VIKOR)":[263],"(PF-TOPSIS)":[269],"method.":[270],"exemplified":[275],"illustrative":[278],"bar":[279],"chart":[280],"visually":[282],"endorses":[283],"rationality":[285],"interpreting":[291],"compatible":[293],"accurate":[295],"final":[296],"outcomes.":[297],"Finally,":[298],"holistically":[300],"analyze":[301],"functionality":[303],"enlighten":[309],"its":[310],"merits":[311],"prominence":[313],"over":[314],"other":[315],"available":[316],"competent":[317],"approaches.":[318]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}