{"id":"https://openalex.org/W2939637111","doi":"https://doi.org/10.3390/sym11040535","title":"Incomplete Fuzzy Soft Sets and Their Application to Decision-Making","display_name":"Incomplete Fuzzy Soft Sets and Their Application to Decision-Making","publication_year":2019,"publication_date":"2019-04-13","ids":{"openalex":"https://openalex.org/W2939637111","doi":"https://doi.org/10.3390/sym11040535","mag":"2939637111"},"language":"en","primary_location":{"id":"doi:10.3390/sym11040535","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11040535","pdf_url":"https://www.mdpi.com/2073-8994/11/4/535/pdf?version=1555668060","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/11/4/535/pdf?version=1555668060","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101562735","display_name":"Lu Wang","orcid":"https://orcid.org/0000-0003-1306-732X"},"institutions":[{"id":"https://openalex.org/I4800084","display_name":"Southwest Jiaotong University","ror":"https://ror.org/00hn7w693","country_code":"CN","type":"education","lineage":["https://openalex.org/I4800084"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lu Wang","raw_affiliation_strings":["College of Mathematics, Southwest Jiaotong University, Chengdu 610030, China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics, Southwest Jiaotong University, Chengdu 610030, China","institution_ids":["https://openalex.org/I4800084"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110365678","display_name":"Keyun Qin","orcid":null},"institutions":[{"id":"https://openalex.org/I4800084","display_name":"Southwest Jiaotong University","ror":"https://ror.org/00hn7w693","country_code":"CN","type":"education","lineage":["https://openalex.org/I4800084"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Keyun Qin","raw_affiliation_strings":["College of Mathematics, Southwest Jiaotong University, Chengdu 610030, China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics, Southwest Jiaotong University, Chengdu 610030, China","institution_ids":["https://openalex.org/I4800084"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5110365678"],"corresponding_institution_ids":["https://openalex.org/I4800084"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":2.2685,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.88424099,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"11","issue":"4","first_page":"535","last_page":"535"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","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/T11671","display_name":"Fuzzy and Soft Set Theory","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/T10050","display_name":"Multi-Criteria Decision Making","score":0.955299973487854,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9510999917984009,"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/soft-set","display_name":"Soft set","score":0.5415982604026794},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5352184772491455},{"id":"https://openalex.org/keywords/type-2-fuzzy-sets-and-systems","display_name":"Type-2 fuzzy sets and systems","score":0.5213155150413513},{"id":"https://openalex.org/keywords/fuzzy-set-operations","display_name":"Fuzzy set operations","score":0.5183883309364319},{"id":"https://openalex.org/keywords/complete-information","display_name":"Complete information","score":0.5148812532424927},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5118185877799988},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.5023758411407471},{"id":"https://openalex.org/keywords/ambiguity","display_name":"Ambiguity","score":0.49653154611587524},{"id":"https://openalex.org/keywords/membership-function","display_name":"Membership function","score":0.49569475650787354},{"id":"https://openalex.org/keywords/fuzzy-classification","display_name":"Fuzzy classification","score":0.4876788854598999},{"id":"https://openalex.org/keywords/defuzzification","display_name":"Defuzzification","score":0.4487709105014801},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.43177396059036255},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3938072621822357},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.36511483788490295},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.36007121205329895},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.07150289416313171}],"concepts":[{"id":"https://openalex.org/C2777037408","wikidata":"https://www.wikidata.org/wiki/Q4310193","display_name":"Soft set","level":3,"score":0.5415982604026794},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5352184772491455},{"id":"https://openalex.org/C17350324","wikidata":"https://www.wikidata.org/wiki/Q7860605","display_name":"Type-2 fuzzy sets and systems","level":5,"score":0.5213155150413513},{"id":"https://openalex.org/C148671577","wikidata":"https://www.wikidata.org/wiki/Q5511133","display_name":"Fuzzy set operations","level":4,"score":0.5183883309364319},{"id":"https://openalex.org/C113336015","wikidata":"https://www.wikidata.org/wiki/Q574010","display_name":"Complete information","level":2,"score":0.5148812532424927},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5118185877799988},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.5023758411407471},{"id":"https://openalex.org/C2780522230","wikidata":"https://www.wikidata.org/wiki/Q1140419","display_name":"Ambiguity","level":2,"score":0.49653154611587524},{"id":"https://openalex.org/C5263885","wikidata":"https://www.wikidata.org/wiki/Q1967302","display_name":"Membership function","level":4,"score":0.49569475650787354},{"id":"https://openalex.org/C127385683","wikidata":"https://www.wikidata.org/wiki/Q1475696","display_name":"Fuzzy classification","level":4,"score":0.4876788854598999},{"id":"https://openalex.org/C170260401","wikidata":"https://www.wikidata.org/wiki/Q5251735","display_name":"Defuzzification","level":5,"score":0.4487709105014801},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.43177396059036255},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3938072621822357},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36511483788490295},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.36007121205329895},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.07150289416313171},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym11040535","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11040535","pdf_url":"https://www.mdpi.com/2073-8994/11/4/535/pdf?version=1555668060","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:e5d3fd75febb4e718379d8e3b525008f","is_oa":true,"landing_page_url":"https://doaj.org/article/e5d3fd75febb4e718379d8e3b525008f","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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 11, Iss 4, p 535 (2019)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/11/4/535/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym11040535","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym11040535","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11040535","pdf_url":"https://www.mdpi.com/2073-8994/11/4/535/pdf?version=1555668060","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.8299999833106995,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3085993365","display_name":null,"funder_award_id":"(Grant No.","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5249178904","display_name":null,"funder_award_id":"Grant No. 6","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7365172496","display_name":null,"funder_award_id":"61473239","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7726157001","display_name":null,"funder_award_id":"Grant No.","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2939637111.pdf","grobid_xml":"https://content.openalex.org/works/W2939637111.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W81357781","https://openalex.org/W1225501595","https://openalex.org/W1978352585","https://openalex.org/W1979152784","https://openalex.org/W1982907249","https://openalex.org/W1989832241","https://openalex.org/W1990975338","https://openalex.org/W2007620983","https://openalex.org/W2010699311","https://openalex.org/W2016485564","https://openalex.org/W2052949124","https://openalex.org/W2071761363","https://openalex.org/W2093595945","https://openalex.org/W2520155300","https://openalex.org/W2565148426","https://openalex.org/W2604253847","https://openalex.org/W2939637111","https://openalex.org/W4211007335","https://openalex.org/W4234423219","https://openalex.org/W4255833381","https://openalex.org/W6639019343","https://openalex.org/W6652303923","https://openalex.org/W6693091319"],"related_works":["https://openalex.org/W2674573885","https://openalex.org/W2781808531","https://openalex.org/W2145270521","https://openalex.org/W2166637398","https://openalex.org/W1486684451","https://openalex.org/W2066929655","https://openalex.org/W2025902904","https://openalex.org/W1487720066","https://openalex.org/W2791187250","https://openalex.org/W2890798884"],"abstract_inverted_index":{"The":[0,44],"research":[1],"of":[2,8,18,27,46,53,66,74,106,139],"incomplete":[3,19,61,76,81,91,107,118,149],"fuzzy":[4,12,20,33,54,82,92,109,120,132,150],"soft":[5,13,21,34,55,77,83,93,110,121,133,151],"sets":[6,35,78,94,111,122,134],"is":[7,26,112],"paramount":[9],"importance":[10],"in":[11,32,42],"sets,":[14,84],"where":[15],"the":[16,64,67,72,100,104,117,125],"combination":[17],"set":[22,56,152],"and":[23,40,79,85,157,167],"decision-making":[24,58,126,156],"problem":[25],"great":[28],"significance.":[29],"Incomplete":[30],"information":[31],"leads":[36],"to":[37,49,89,123,153,162],"more":[38,165],"uncertainty":[39],"ambiguity":[41],"decision-making.":[43,98],"focus":[45],"this":[47],"paper":[48],"propose":[50,158],"an":[51,87],"algorithm":[52,161],"based":[57],"problems":[59],"under":[60],"information.":[62],"On":[63],"basis":[65],"weighted":[68,75,80,90,108,119],"function,":[69,103],"we":[70,115,144],"introduce":[71],"notions":[73],"show":[86],"approach":[88],"for":[95,131,148],"dealing":[96],"with":[97,155],"Considering":[99],"missing":[101],"weight":[102],"concept":[105],"presented.":[113],"Meanwhile,":[114],"apply":[116,145],"solve":[124],"problem.":[127],"As":[128],"modal-style":[129,146],"operators":[130],"have":[135],"a":[136,159],"precise":[137],"description":[138],"attributes":[140],"possessed":[141],"by":[142],"objects,":[143],"operator":[147],"deal":[154],"new":[160],"make":[163],"it":[164],"accurate":[166],"simple.":[168]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":1}],"updated_date":"2026-04-13T07:58:08.660418","created_date":"2025-10-10T00:00:00"}