{"id":"https://openalex.org/W4408053794","doi":"https://doi.org/10.3390/sym17030369","title":"Fuzzy Reasoning Symmetric Quintuple-Implication Method for Mixed Information and Its Application","display_name":"Fuzzy Reasoning Symmetric Quintuple-Implication Method for Mixed Information and Its Application","publication_year":2025,"publication_date":"2025-02-28","ids":{"openalex":"https://openalex.org/W4408053794","doi":"https://doi.org/10.3390/sym17030369"},"language":"en","primary_location":{"id":"doi:10.3390/sym17030369","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17030369","pdf_url":"https://www.mdpi.com/2073-8994/17/3/369/pdf?version=1740749273","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"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/17/3/369/pdf?version=1740749273","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101932063","display_name":"Ning Yao","orcid":null},"institutions":[{"id":"https://openalex.org/I55538621","display_name":"China Jiliang University","ror":"https://ror.org/05v1y0t93","country_code":"CN","type":"education","lineage":["https://openalex.org/I55538621"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ning Yao","raw_affiliation_strings":["Department of Information and Computing Science, China Jiliang University, Hangzhou 310018, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Information and Computing Science, China Jiliang University, Hangzhou 310018, China","institution_ids":["https://openalex.org/I55538621"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100353673","display_name":"Hao Chen","orcid":"https://orcid.org/0009-0001-6480-7976"},"institutions":[{"id":"https://openalex.org/I55538621","display_name":"China Jiliang University","ror":"https://ror.org/05v1y0t93","country_code":"CN","type":"education","lineage":["https://openalex.org/I55538621"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hao Chen","raw_affiliation_strings":["Department of Information and Computing Science, China Jiliang University, Hangzhou 310018, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Information and Computing Science, China Jiliang University, Hangzhou 310018, China","institution_ids":["https://openalex.org/I55538621"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103044194","display_name":"Ruirui Zhao","orcid":"https://orcid.org/0000-0002-5337-5813"},"institutions":[{"id":"https://openalex.org/I55538621","display_name":"China Jiliang University","ror":"https://ror.org/05v1y0t93","country_code":"CN","type":"education","lineage":["https://openalex.org/I55538621"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ruirui Zhao","raw_affiliation_strings":["Department of Information and Computing Science, China Jiliang University, Hangzhou 310018, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Information and Computing Science, China Jiliang University, Hangzhou 310018, China","institution_ids":["https://openalex.org/I55538621"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006235641","display_name":"Minxia Luo","orcid":"https://orcid.org/0000-0001-9400-3533"},"institutions":[{"id":"https://openalex.org/I55538621","display_name":"China Jiliang University","ror":"https://ror.org/05v1y0t93","country_code":"CN","type":"education","lineage":["https://openalex.org/I55538621"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Minxia Luo","raw_affiliation_strings":["Department of Information and Computing Science, China Jiliang University, Hangzhou 310018, China"],"raw_orcid":"https://orcid.org/0000-0001-9400-3533","affiliations":[{"raw_affiliation_string":"Department of Information and Computing Science, China Jiliang University, Hangzhou 310018, China","institution_ids":["https://openalex.org/I55538621"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I55538621"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.0268,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.76545993,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"17","issue":"3","first_page":"369","last_page":"369"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9997000098228455,"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":0.9987000226974487,"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":0.9976000189781189,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6302247643470764},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.52266925573349},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3432391881942749},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33047330379486084},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2870408892631531}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6302247643470764},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.52266925573349},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3432391881942749},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33047330379486084},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2870408892631531}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3390/sym17030369","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17030369","pdf_url":"https://www.mdpi.com/2073-8994/17/3/369/pdf?version=1740749273","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"}],"best_oa_location":{"id":"doi:10.3390/sym17030369","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17030369","pdf_url":"https://www.mdpi.com/2073-8994/17/3/369/pdf?version=1740749273","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":[],"awards":[{"id":"https://openalex.org/G3352100827","display_name":null,"funder_award_id":"12171445","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":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4408053794.pdf"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W1966808269","https://openalex.org/W1971875039","https://openalex.org/W1980564456","https://openalex.org/W2006941110","https://openalex.org/W2007805591","https://openalex.org/W2014816111","https://openalex.org/W2041280856","https://openalex.org/W2041569651","https://openalex.org/W2053860555","https://openalex.org/W2083293441","https://openalex.org/W2087501680","https://openalex.org/W2091275864","https://openalex.org/W2793389633","https://openalex.org/W2807914813","https://openalex.org/W2945816468","https://openalex.org/W3192487278","https://openalex.org/W4211007335","https://openalex.org/W4234672050","https://openalex.org/W4285209116","https://openalex.org/W4306773040","https://openalex.org/W4388451403","https://openalex.org/W4396851248"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W4391913857","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W4396696052"],"abstract_inverted_index":{"Rule-based":[0],"reasoning":[1,19,106,128,159,254,273,284,306],"with":[2,36,191,208,276,285],"different":[3,193,203],"kinds":[4],"of":[5,39,81,102,117,133,201,234,238,250,268,279],"uncertain":[6],"information":[7,135,139,182,272,305],"has":[8],"been":[9,293],"identified":[10],"in":[11,115,259],"numerous":[12],"applications":[13],"within":[14],"the":[15,27,32,37,40,53,60,71,78,84,94,99,105,131,142,155,164,167,170,199,218,222,228,232,236,252,266,277,280,303,310,316,321],"real":[16],"world.":[17],"Any":[18],"method":[20,107],"must":[21],"be":[22,175,196],"able":[23],"to":[24,265,295,315],"coherently":[25],"obtain":[26],"inference":[28],"result":[29],"by":[30,49,109,220],"composing":[31],"given":[33,41,171,188,205],"if\u2013then":[34,172,189,206],"rule":[35,173,190,239,242],"assertion":[38],"input.":[42],"The":[43,248,288],"symmetric":[44,68,143],"quintuple-implication":[45,144,156,229,281,311],"principle":[46,111,145,230,282,312],"was":[47],"established":[48],"introducing":[50],"symmetry":[51,152],"into":[52,283],"five":[54,148],"implication":[55,65,73,88,96,149],"operators":[56,66,74,89,97,150,226],"included.":[57],"For":[58],"example,":[59],"first,":[61],"third":[62],"and":[63,83,86,121,126,136,169,224,227,241,298],"fifth":[64],"exhibit":[67,184],"properties,":[69],"i.e.,":[70],"three":[72],"are":[75,161,313],"taken":[76],"as":[77,198],"same":[79,100],"kind":[80,101],"operator":[82],"second":[85],"fourth":[87],"satisfy":[90,151],"symmetry,":[91],"that":[92,166,302],"is,":[93],"two":[95,192,202],"take":[98],"operator.":[103],"So,":[104],"induced":[108],"this":[110],"possesses":[112],"significant":[113],"advantages":[114],"terms":[116],"its":[118],"logical":[119],"foundation":[120],"reductivity.":[122],"This":[123,213,261],"paper":[124,214,262],"derives":[125],"studies":[127],"methods":[129,160,219,255,290,307,318],"for":[130,177],"mixture":[132],"fuzzy":[134,138],"intuitionistic":[137],"based":[140,162,308,319],"on":[141,163,217,309,320],"where":[146],"all":[147,251],"(also":[153],"called":[154],"principle).":[157],"Such":[158],"ideas":[165],"input":[168],"can":[174],"combined":[176],"calculation":[178],"only":[179],"when":[180],"their":[181,209],"representations":[183,194],"consistency.":[185],"An":[186],"inconsistent":[187],"should":[195],"regarded":[197],"composition":[200],"consistent":[204,245],"rules":[207],"own":[210],"unique":[211],"representations.":[212],"then":[215],"elaborates":[216],"employing":[221],"possibility":[223],"necessity":[225],"from":[231],"perspective":[233],"whether":[235],"representation":[237],"antecedent":[240],"consequent":[243],"is":[244,256],"or":[246],"not.":[247],"reductivity":[249],"proposed":[253,289],"also":[257,292],"analyzed":[258],"detail.":[260],"mainly":[263],"contributes":[264],"development":[267],"a":[269],"novel":[270],"mixed":[271,286,304],"framework,":[274],"along":[275],"introduction":[278],"information.":[287],"have":[291],"applied":[294],"pattern":[296],"recognition,":[297],"several":[299],"experiments":[300],"demonstrate":[301],"superior":[314],"corresponding":[317],"triple":[322],"I":[323],"principle.":[324]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}
