{"id":"https://openalex.org/W2158662559","doi":"https://doi.org/10.3233/ifs-151765","title":"The restricted hull operator of <i>M</i> -fuzzifying convex structures","display_name":"The restricted hull operator of <i>M</i> -fuzzifying convex structures","publication_year":2015,"publication_date":"2015-08-31","ids":{"openalex":"https://openalex.org/W2158662559","doi":"https://doi.org/10.3233/ifs-151765","mag":"2158662559"},"language":"en","primary_location":{"id":"doi:10.3233/ifs-151765","is_oa":false,"landing_page_url":"https://doi.org/10.3233/ifs-151765","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/A5011541575","display_name":"Fu-Gui Shi","orcid":"https://orcid.org/0000-0001-8090-3872"},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fugui Shi","raw_affiliation_strings":["School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, P.R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, P.R. China","institution_ids":["https://openalex.org/I125839683"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103029824","display_name":"Er-Qiang Li","orcid":"https://orcid.org/0000-0002-3354-654X"},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]},{"id":"https://openalex.org/I167383011","display_name":"Henan University of Science and Technology","ror":"https://ror.org/05d80kz58","country_code":"CN","type":"education","lineage":["https://openalex.org/I167383011"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Erqiang Li","raw_affiliation_strings":["School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, P.R. China","School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, P.R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, P.R. China","institution_ids":["https://openalex.org/I125839683"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, P.R. China","institution_ids":["https://openalex.org/I167383011"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5103029824"],"corresponding_institution_ids":["https://openalex.org/I125839683","https://openalex.org/I167383011"],"apc_list":null,"apc_paid":null,"fwci":11.2171,"has_fulltext":false,"cited_by_count":72,"citation_normalized_percentile":{"value":0.98488897,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"30","issue":"1","first_page":"409","last_page":"421"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9994999766349792,"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":0.9994999766349792,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9976000189781189,"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/T10050","display_name":"Multi-Criteria Decision Making","score":0.9966999888420105,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.7799496650695801},{"id":"https://openalex.org/keywords/hull","display_name":"Hull","score":0.7148779034614563},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6018598079681396},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5957615375518799},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5396943092346191},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.5306512117385864},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3593415319919586},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3527827262878418},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.07708051800727844},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07580262422561646},{"id":"https://openalex.org/keywords/business","display_name":"Business","score":0.05986756086349487},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.058063775300979614}],"concepts":[{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.7799496650695801},{"id":"https://openalex.org/C37423430","wikidata":"https://www.wikidata.org/wiki/Q6750281","display_name":"Hull","level":2,"score":0.7148779034614563},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6018598079681396},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5957615375518799},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5396943092346191},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.5306512117385864},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3593415319919586},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3527827262878418},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.07708051800727844},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07580262422561646},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.05986756086349487},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.058063775300979614},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/ifs-151765","is_oa":false,"landing_page_url":"https://doi.org/10.3233/ifs-151765","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W577570849","https://openalex.org/W1503074869","https://openalex.org/W1576113015","https://openalex.org/W1912497050","https://openalex.org/W1988233222","https://openalex.org/W1991241698","https://openalex.org/W1999565247","https://openalex.org/W2002955940","https://openalex.org/W2007388400","https://openalex.org/W2022137179","https://openalex.org/W2065460951","https://openalex.org/W2072578205","https://openalex.org/W2093775920","https://openalex.org/W2124840911","https://openalex.org/W2150862113","https://openalex.org/W2319893799","https://openalex.org/W2579805205","https://openalex.org/W2735093391","https://openalex.org/W4205110272","https://openalex.org/W4230506867","https://openalex.org/W4235730211","https://openalex.org/W4235789167","https://openalex.org/W4249667877","https://openalex.org/W4293200472","https://openalex.org/W6634641092","https://openalex.org/W6740763111"],"related_works":["https://openalex.org/W2467926385","https://openalex.org/W161301265","https://openalex.org/W2483619716","https://openalex.org/W4246461909","https://openalex.org/W2377576908","https://openalex.org/W2025606465","https://openalex.org/W2912909874","https://openalex.org/W4288573727","https://openalex.org/W2768754015","https://openalex.org/W2981448761"],"abstract_inverted_index":{"In":[0,69],"this":[1],"paper,":[2],"the":[3,44],"notion":[4],"of":[5,43,48,55,62],"M":[6,29,35,50,56,63,72,78,85],"-fuzzifying":[7,30,36,51,57,64,73,79],"restricted":[8,31,74],"hull":[9,32,75],"operators":[10,33],"is":[11,20,24],"introduced":[12],"and":[13,34,54,61],"several":[14],"equivalent":[15],"characterizations":[16],"are":[17,67,81],"given.":[18],"It":[19],"shown":[21],"that":[22],"there":[23],"a":[25],"one-to-one":[26],"correspondence":[27],"between":[28],"convex":[37,46,52],"structures.":[38],"As":[39],"applications,":[40],"some":[41,77],"properties":[42],"cut":[45],"structures":[47],"an":[49],"structure":[53],"convexity":[58],"preserving":[59],"functions":[60,66],"convex-to-convex":[65],"derived.":[68],"addition,":[70],"using":[71],"operators,":[76],"convexities":[80],"naturally":[82],"constructed":[83],"from":[84],"-fuzzy":[86],"quasi-orders.":[87]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":16},{"year":2018,"cited_by_count":14},{"year":2017,"cited_by_count":12},{"year":2016,"cited_by_count":2}],"updated_date":"2026-02-11T14:41:00.668223","created_date":"2016-06-24T00:00:00"}