{"id":"https://openalex.org/W3136750270","doi":"https://doi.org/10.3233/jifs-202725","title":"Approximations of pythagorean fuzzy sets over dual universes by soft binary relations","display_name":"Approximations of pythagorean fuzzy sets over dual universes by soft binary relations","publication_year":2021,"publication_date":"2021-03-23","ids":{"openalex":"https://openalex.org/W3136750270","doi":"https://doi.org/10.3233/jifs-202725","mag":"3136750270"},"language":"en","primary_location":{"id":"doi:10.3233/jifs-202725","is_oa":false,"landing_page_url":"https://doi.org/10.3233/jifs-202725","pdf_url":null,"source":{"id":"https://openalex.org/S179157397","display_name":"Journal of Intelligent & Fuzzy Systems","issn_l":"1064-1246","issn":["1064-1246","1875-8967"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Intelligent &amp; Fuzzy Systems","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/A5014456358","display_name":"Muhammad Bilal","orcid":"https://orcid.org/0000-0002-6788-0909"},"institutions":[{"id":"https://openalex.org/I12469534","display_name":"Quaid-i-Azam University","ror":"https://ror.org/04s9hft57","country_code":"PK","type":"education","lineage":["https://openalex.org/I12469534"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Muhammad Asim Bilal","raw_affiliation_strings":["Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan","institution_ids":["https://openalex.org/I12469534"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078902055","display_name":"Muhammad Shabir","orcid":"https://orcid.org/0000-0002-3161-8482"},"institutions":[{"id":"https://openalex.org/I12469534","display_name":"Quaid-i-Azam University","ror":"https://ror.org/04s9hft57","country_code":"PK","type":"education","lineage":["https://openalex.org/I12469534"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Shabir","raw_affiliation_strings":["Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan","institution_ids":["https://openalex.org/I12469534"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5014456358"],"corresponding_institution_ids":["https://openalex.org/I12469534"],"apc_list":null,"apc_paid":null,"fwci":2.7884,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.90178488,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":"41","issue":"1","first_page":"2495","last_page":"2511"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9995999932289124,"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":0.9995999932289124,"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/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9993000030517578,"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":0.998199999332428,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/pythagorean-theorem","display_name":"Pythagorean theorem","score":0.7359921932220459},{"id":"https://openalex.org/keywords/ranking","display_name":"Ranking (information retrieval)","score":0.6311852335929871},{"id":"https://openalex.org/keywords/binary-relation","display_name":"Binary relation","score":0.572085976600647},{"id":"https://openalex.org/keywords/soft-set","display_name":"Soft set","score":0.5672812461853027},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.5472327470779419},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5171434283256531},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.48993128538131714},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.46743789315223694},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.4658454656600952},{"id":"https://openalex.org/keywords/multiple-criteria-decision-analysis","display_name":"Multiple-criteria decision analysis","score":0.4354557991027832},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.4245375692844391},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.41816988587379456},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3920844793319702},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.33152204751968384},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2837957739830017},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.14282935857772827}],"concepts":[{"id":"https://openalex.org/C100461760","wikidata":"https://www.wikidata.org/wiki/Q11518","display_name":"Pythagorean theorem","level":2,"score":0.7359921932220459},{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.6311852335929871},{"id":"https://openalex.org/C65180967","wikidata":"https://www.wikidata.org/wiki/Q130901","display_name":"Binary relation","level":2,"score":0.572085976600647},{"id":"https://openalex.org/C2777037408","wikidata":"https://www.wikidata.org/wiki/Q4310193","display_name":"Soft set","level":3,"score":0.5672812461853027},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5472327470779419},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5171434283256531},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.48993128538131714},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.46743789315223694},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.4658454656600952},{"id":"https://openalex.org/C11105738","wikidata":"https://www.wikidata.org/wiki/Q1895805","display_name":"Multiple-criteria decision analysis","level":2,"score":0.4354557991027832},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.4245375692844391},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.41816988587379456},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3920844793319702},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.33152204751968384},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2837957739830017},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.14282935857772827},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","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/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/jifs-202725","is_oa":false,"landing_page_url":"https://doi.org/10.3233/jifs-202725","pdf_url":null,"source":{"id":"https://openalex.org/S179157397","display_name":"Journal of Intelligent & Fuzzy Systems","issn_l":"1064-1246","issn":["1064-1246","1875-8967"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Intelligent &amp; Fuzzy Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.8199999928474426,"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":26,"referenced_works":["https://openalex.org/W1829951598","https://openalex.org/W1978352585","https://openalex.org/W1980564456","https://openalex.org/W1982907249","https://openalex.org/W1989832241","https://openalex.org/W1990975338","https://openalex.org/W1999420420","https://openalex.org/W1999693983","https://openalex.org/W2002541167","https://openalex.org/W2007620983","https://openalex.org/W2013932252","https://openalex.org/W2027654459","https://openalex.org/W2069754181","https://openalex.org/W2083267403","https://openalex.org/W2093456061","https://openalex.org/W2156982617","https://openalex.org/W2374072881","https://openalex.org/W2885877913","https://openalex.org/W2922129843","https://openalex.org/W2935807176","https://openalex.org/W2988347501","https://openalex.org/W2997198052","https://openalex.org/W3040745443","https://openalex.org/W4211007335","https://openalex.org/W4255833381","https://openalex.org/W6693091319"],"related_works":["https://openalex.org/W2934833842","https://openalex.org/W2095099707","https://openalex.org/W2490388779","https://openalex.org/W4288375230","https://openalex.org/W2990643015","https://openalex.org/W4313031743","https://openalex.org/W2087816839","https://openalex.org/W2953564685","https://openalex.org/W2116017123","https://openalex.org/W2337818413"],"abstract_inverted_index":{"Yager":[0],"introduced":[1],"the":[2,59,65,93,110,151,158,178,197],"Pythagorean":[3,71],"Fuzzy":[4,72],"Set":[5],"(PFS)":[6],"to":[7,58,64,195],"deal":[8],"with":[9,56,62,139,192],"uncertainty":[10],"in":[11,21,26,126,150,199],"real-world":[12],"decision-making":[13,111],"problems.":[14],"Binary":[15],"relations":[16,31,53,78],"play":[17],"an":[18,82,101],"important":[19],"role":[20],"mathematics":[22],"as":[23,25],"well":[24],"information":[27],"sciences.":[28],"Soft":[29,51,76],"binary":[30,38,52],"give":[32],"us":[33],"a":[34,86,135,140,171,185,190,201],"parameterized":[35],"collection":[36],"of":[37,47,70,85,99,109,130,173,181,204],"relations.":[39],"In":[40],"this":[41],"paper,":[42],"lower":[43],"and":[44,61,81,96,107,168,183],"upper":[45],"approximations":[46,98],"PFSs":[48,122],"based":[49,91,187],"on":[50,92,166,177],"are":[54,79],"given":[55],"respect":[57,63],"aftersets":[60],"foresets.":[66],"Further,":[67],"two":[68],"kinds":[69],"Topologies":[73],"induced":[74],"by":[75],"reflexive":[77],"investigated":[80],"accuracy":[83],"measure":[84],"PFS":[87],"is":[88,103,137,148],"provided.":[89],"Besides,":[90],"score":[94],"function":[95],"these":[97],"PFSs,":[100],"algorithm":[102],"constructed":[104],"for":[105,121,189],"ranking":[106,169,186],"selection":[108],"alternatives.":[112],"Although":[113],"many":[114],"MCDM":[115,143],"(multiple":[116],"criteria":[117,194],"decision":[118],"making)":[119],"methods":[120],"have":[123],"been":[124],"proposed":[125,146,155,163],"previous":[127],"studies,":[128],"some":[129],"those":[131],"cannot":[132],"solve":[133],"when":[134],"person":[136],"encountered":[138],"two-sided":[141,179],"matching":[142,180],"problem.":[144],"The":[145,162],"method":[147,164],"new":[149],"literature.":[152],"This":[153],"newly":[154],"model":[156],"solved":[157],"problem":[159,191],"more":[160],"accurately.":[161],"focuses":[165],"selecting":[167],"from":[170],"set":[172],"feasible":[174],"alternatives":[175],"depending":[176],"attributes":[182],"determines":[184],"solution":[188],"conflicting":[193],"help":[196],"decision-maker":[198],"reaching":[200],"final":[202],"course":[203],"action.":[205]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
