{"id":"https://openalex.org/W4313894088","doi":"https://doi.org/10.3390/axioms12010063","title":"Partial Residuated Implications Induced by Partial Triangular Norms and Partial Residuated Lattices","display_name":"Partial Residuated Implications Induced by Partial Triangular Norms and Partial Residuated Lattices","publication_year":2023,"publication_date":"2023-01-06","ids":{"openalex":"https://openalex.org/W4313894088","doi":"https://doi.org/10.3390/axioms12010063"},"language":"en","primary_location":{"id":"doi:10.3390/axioms12010063","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12010063","pdf_url":"https://www.mdpi.com/2075-1680/12/1/63/pdf?version=1673017432","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/12/1/63/pdf?version=1673017432","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100330121","display_name":"Xiaohong Zhang","orcid":"https://orcid.org/0000-0003-2320-0884"},"institutions":[{"id":"https://openalex.org/I51622183","display_name":"Shaanxi University of Science and Technology","ror":"https://ror.org/034t3zs45","country_code":"CN","type":"education","lineage":["https://openalex.org/I51622183"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiaohong Zhang","raw_affiliation_strings":["School of Mathematics and Data Science, Shaanxi University of Science & Technology, Xi\u2019an 710021, China","School of Mathematics and Data Science, Shaanxi University of Science & Technology, Xi'an 710021, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Data Science, Shaanxi University of Science & Technology, Xi\u2019an 710021, China","institution_ids":["https://openalex.org/I51622183"]},{"raw_affiliation_string":"School of Mathematics and Data Science, Shaanxi University of Science & Technology, Xi'an 710021, China","institution_ids":["https://openalex.org/I51622183"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060599484","display_name":"Nan Sheng","orcid":null},"institutions":[{"id":"https://openalex.org/I51622183","display_name":"Shaanxi University of Science and Technology","ror":"https://ror.org/034t3zs45","country_code":"CN","type":"education","lineage":["https://openalex.org/I51622183"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Nan Sheng","raw_affiliation_strings":["School of Mathematics and Data Science, Shaanxi University of Science & Technology, Xi\u2019an 710021, China","School of Mathematics and Data Science, Shaanxi University of Science & Technology, Xi'an 710021, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Data Science, Shaanxi University of Science & Technology, Xi\u2019an 710021, China","institution_ids":["https://openalex.org/I51622183"]},{"raw_affiliation_string":"School of Mathematics and Data Science, Shaanxi University of Science & Technology, Xi'an 710021, China","institution_ids":["https://openalex.org/I51622183"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072356626","display_name":"R. A. Borzooei","orcid":"https://orcid.org/0000-0001-7538-7885"},"institutions":[{"id":"https://openalex.org/I48379061","display_name":"Shahid Beheshti University","ror":"https://ror.org/0091vmj44","country_code":"IR","type":"education","lineage":["https://openalex.org/I48379061"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Rajab Ali Borzooei","raw_affiliation_strings":["Department of Mathematics, Faculty at Mathematical Sciences, Shahid Beheshti University, Tehran 1983963113, Iran"],"raw_orcid":"https://orcid.org/0000-0001-7538-7885","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty at Mathematical Sciences, Shahid Beheshti University, Tehran 1983963113, Iran","institution_ids":["https://openalex.org/I48379061"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100330121"],"corresponding_institution_ids":["https://openalex.org/I51622183"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1782},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1782},"fwci":2.0107,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.88062322,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"12","issue":"1","first_page":"63","last_page":"63"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9998999834060669,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9998999834060669,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9988999962806702,"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":0.9932000041007996,"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/residuated-lattice","display_name":"Residuated lattice","score":0.8929521441459656},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6879269480705261},{"id":"https://openalex.org/keywords/partial-agonist","display_name":"Partial agonist","score":0.6201070547103882},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5698306560516357},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5492562651634216},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.4516073167324066},{"id":"https://openalex.org/keywords/monoidal-t-norm-logic","display_name":"Monoidal t-norm logic","score":0.4220900535583496},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.41595470905303955},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32573753595352173},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16413718461990356},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.12389346957206726},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0762816071510315},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06459221243858337},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.06338703632354736},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.04479187726974487}],"concepts":[{"id":"https://openalex.org/C2781278839","wikidata":"https://www.wikidata.org/wiki/Q9462417","display_name":"Residuated lattice","level":3,"score":0.8929521441459656},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6879269480705261},{"id":"https://openalex.org/C58732023","wikidata":"https://www.wikidata.org/wiki/Q770260","display_name":"Partial agonist","level":4,"score":0.6201070547103882},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5698306560516357},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5492562651634216},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.4516073167324066},{"id":"https://openalex.org/C98224912","wikidata":"https://www.wikidata.org/wiki/Q6901647","display_name":"Monoidal t-norm logic","level":5,"score":0.4220900535583496},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.41595470905303955},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32573753595352173},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16413718461990356},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.12389346957206726},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0762816071510315},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06459221243858337},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.06338703632354736},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.04479187726974487},{"id":"https://openalex.org/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","level":1,"score":0.0},{"id":"https://openalex.org/C2776885963","wikidata":"https://www.wikidata.org/wiki/Q245204","display_name":"Antagonist","level":3,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C170493617","wikidata":"https://www.wikidata.org/wiki/Q208467","display_name":"Receptor","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms12010063","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12010063","pdf_url":"https://www.mdpi.com/2075-1680/12/1/63/pdf?version=1673017432","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:0fae0441c9de4c30be27641efa4fb2ed","is_oa":true,"landing_page_url":"https://doaj.org/article/0fae0441c9de4c30be27641efa4fb2ed","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 12, Iss 1, p 63 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/12/1/63/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms12010063","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":"Axioms; Volume 12; Issue 1; Pages: 63","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms12010063","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12010063","pdf_url":"https://www.mdpi.com/2075-1680/12/1/63/pdf?version=1673017432","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G290929947","display_name":null,"funder_award_id":"61976130","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5794512001","display_name":null,"funder_award_id":"12271319","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":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4313894088.pdf"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W131822301","https://openalex.org/W146940927","https://openalex.org/W1551861123","https://openalex.org/W1981832097","https://openalex.org/W1996451158","https://openalex.org/W2040690525","https://openalex.org/W2080412456","https://openalex.org/W2083028880","https://openalex.org/W2094027511","https://openalex.org/W2124620155","https://openalex.org/W2362204274","https://openalex.org/W2576031330","https://openalex.org/W2578456536","https://openalex.org/W2616791547","https://openalex.org/W2777785099","https://openalex.org/W2890423038","https://openalex.org/W2899629775","https://openalex.org/W2932931752","https://openalex.org/W2990999098","https://openalex.org/W3023069276","https://openalex.org/W3044266563","https://openalex.org/W4206252197","https://openalex.org/W4211007335","https://openalex.org/W4211138484","https://openalex.org/W4220685328","https://openalex.org/W4285091555","https://openalex.org/W4292566538","https://openalex.org/W4293103410","https://openalex.org/W4294845633","https://openalex.org/W4303614006","https://openalex.org/W4307549405","https://openalex.org/W6761384680"],"related_works":["https://openalex.org/W1783029874","https://openalex.org/W1595640337","https://openalex.org/W169137922","https://openalex.org/W1968222062","https://openalex.org/W1487361824","https://openalex.org/W2103602076","https://openalex.org/W171102060","https://openalex.org/W1818045261","https://openalex.org/W4205339083","https://openalex.org/W1511669762"],"abstract_inverted_index":{"This":[0],"paper":[1],"reveals":[2],"some":[3],"relations":[4],"between":[5,45,123,135],"fuzzy":[6,90,102],"logic":[7,10],"and":[8,28,49,85,104,125,130,137,159,186],"quantum":[9],"on":[11,167],"partial":[12,18,24,29,35,50,57,67,75,89,97,139,147,154,161,168,174,183],"residuated":[13,25,30,98,138,169,175,184],"implications":[14],"(PRIs)":[15],"induced":[16],"by":[17,33,60],"t-norms":[19,51,58],"as":[20,22],"well":[21,173,182],"proposes":[23],"monoids":[26],"(PRMs)":[27],"lattices":[31,163,176],"(PRLs)":[32],"defining":[34],"adjoint":[36],"pairs.":[37],"First":[38],"of":[39,56,83,88,146,153,181,191],"all,":[40],"we":[41,78,113,149,171],"introduce":[42],"the":[43,54,64,80,86,94,121,133,144,151,179],"connection":[44],"lattice":[46,73,126],"effect":[47,127],"algebra":[48],"according":[52],"to":[53],"concept":[55],"given":[59],"Borzooei,":[61],"together":[62],"with":[63],"proof":[65],"that":[66,96,106],"operation":[68],"in":[69],"any":[70],"commutative":[71],"quasiresiduated":[72],"is":[74,100,109],"t-norm.":[76],"Then,":[77],"offer":[79],"general":[81],"form":[82],"PRI":[84,108],"definition":[87,145],"implication":[91,99],"(PFI),":[92],"give":[93],"condition":[95],"a":[101,110],"implication,":[103],"prove":[105],"each":[107],"PFI.":[111],"Next,":[112],"propose":[114],"PRLs,":[115],"study":[116,178],"their":[117],"basic":[118],"characteristics,":[119],"discuss":[120],"correspondence":[122],"PRLs":[124],"algebras":[128],"(LEAs),":[129],"point":[131],"out":[132],"relationship":[134],"LEAs":[136],"algebras.":[140],"In":[141],"addition,":[142],"like":[143],"t-norms,":[148],"provide":[150],"notions":[152],"triangular":[155],"conorms":[156],"(partial":[157],"t-conorms)":[158],"corresponding":[160],"co-residuated":[162],"(PcRLs).":[164],"Lastly,":[165],"based":[166],"lattices,":[170,185],"define":[172],"(wPRLs),":[177],"filter":[180],"then":[187],"construct":[188],"quotient":[189],"structure":[190],"PRMs.":[192]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2023-01-10T00:00:00"}
