{"id":"https://openalex.org/W4307549405","doi":"https://doi.org/10.3390/axioms11110593","title":"Pseudo Overlap Functions, Fuzzy Implications and Pseudo Grouping Functions with Applications","display_name":"Pseudo Overlap Functions, Fuzzy Implications and Pseudo Grouping Functions with Applications","publication_year":2022,"publication_date":"2022-10-26","ids":{"openalex":"https://openalex.org/W4307549405","doi":"https://doi.org/10.3390/axioms11110593"},"language":"en","primary_location":{"id":"doi:10.3390/axioms11110593","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11110593","pdf_url":"https://www.mdpi.com/2075-1680/11/11/593/pdf?version=1668688249","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/2075-1680/11/11/593/pdf?version=1668688249","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":["Department of Mathematics, Shaanxi University of Science & Technology, Xi\u2019an 710021, China","Shaanxi Joint Laboratory of Artificial Intelligence, Shaanxi University of Science & Technology, Xi\u2019an 710021, China","Shaanxi Joint Laboratory of Artificial Intelligence, Shaanxi University of Science & Technology, Xi'an 710021, China","Department of Mathematics, Shaanxi University of Science & Technology, Xi'an 710021, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shaanxi University of Science & Technology, Xi\u2019an 710021, China","institution_ids":["https://openalex.org/I51622183"]},{"raw_affiliation_string":"Shaanxi Joint Laboratory of Artificial Intelligence, Shaanxi University of Science & Technology, Xi\u2019an 710021, China","institution_ids":["https://openalex.org/I51622183"]},{"raw_affiliation_string":"Shaanxi Joint Laboratory of Artificial Intelligence, Shaanxi University of Science & Technology, Xi'an 710021, China","institution_ids":["https://openalex.org/I51622183"]},{"raw_affiliation_string":"Department of Mathematics, Shaanxi University of Science & Technology, Xi'an 710021, China","institution_ids":["https://openalex.org/I51622183"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035633704","display_name":"Rong Liang","orcid":"https://orcid.org/0000-0001-9336-437X"},"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":"Rong Liang","raw_affiliation_strings":["Department of Mathematics, Shaanxi University of Science & Technology, Xi\u2019an 710021, China","Department of Mathematics, Shaanxi University of Science & Technology, Xi'an 710021, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shaanxi University of Science & Technology, Xi\u2019an 710021, China","institution_ids":["https://openalex.org/I51622183"]},{"raw_affiliation_string":"Department of Mathematics, Shaanxi University of Science & Technology, Xi'an 710021, China","institution_ids":["https://openalex.org/I51622183"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049375194","display_name":"Humberto Bustince","orcid":"https://orcid.org/0000-0002-1279-6195"},"institutions":[{"id":"https://openalex.org/I175051016","display_name":"Universidad Publica de Navarra","ror":"https://ror.org/02z0cah89","country_code":"ES","type":"education","lineage":["https://openalex.org/I175051016"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Humberto Bustince","raw_affiliation_strings":["Departamento de Estadistica, Matematicas e Informatica, Universidad Publica de Navarra, Campus Arrosadia s/n, 31006 Pamplona, Spain"],"affiliations":[{"raw_affiliation_string":"Departamento de Estadistica, Matematicas e Informatica, Universidad Publica de Navarra, Campus Arrosadia s/n, 31006 Pamplona, Spain","institution_ids":["https://openalex.org/I175051016"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004002970","display_name":"Benjam\u00edn Bedregal","orcid":"https://orcid.org/0000-0002-6757-7934"},"institutions":[{"id":"https://openalex.org/I35046152","display_name":"Universidade Federal do Rio Grande do Norte","ror":"https://ror.org/04wn09761","country_code":"BR","type":"education","lineage":["https://openalex.org/I35046152"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Benjamin Bedregal","raw_affiliation_strings":["Departamento de Informatica e Matematica Aplicada, Universidade Federal do Rio Grande do Norte, Natal 59078-970, Brazil"],"affiliations":[{"raw_affiliation_string":"Departamento de Informatica e Matematica Aplicada, Universidade Federal do Rio Grande do Norte, Natal 59078-970, Brazil","institution_ids":["https://openalex.org/I35046152"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085226753","display_name":"Javier Fern\u00e1ndez","orcid":"https://orcid.org/0000-0003-4427-3935"},"institutions":[{"id":"https://openalex.org/I175051016","display_name":"Universidad Publica de Navarra","ror":"https://ror.org/02z0cah89","country_code":"ES","type":"education","lineage":["https://openalex.org/I175051016"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Javier Fernandez","raw_affiliation_strings":["Departamento de Estadistica, Matematicas e Informatica, Universidad Publica de Navarra, Campus Arrosadia s/n, 31006 Pamplona, Spain"],"affiliations":[{"raw_affiliation_string":"Departamento de Estadistica, Matematicas e Informatica, Universidad Publica de Navarra, Campus Arrosadia s/n, 31006 Pamplona, Spain","institution_ids":["https://openalex.org/I175051016"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100415401","display_name":"Mengyuan Li","orcid":"https://orcid.org/0000-0002-9135-0641"},"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":"Mengyuan Li","raw_affiliation_strings":["Department of Mathematics, Shaanxi University of Science & Technology, Xi\u2019an 710021, China","Department of Mathematics, Shaanxi University of Science & Technology, Xi'an 710021, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shaanxi University of Science & Technology, Xi\u2019an 710021, China","institution_ids":["https://openalex.org/I51622183"]},{"raw_affiliation_string":"Department of Mathematics, Shaanxi University of Science & Technology, Xi'an 710021, China","institution_ids":["https://openalex.org/I51622183"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103093184","display_name":"Qiqi Ou","orcid":"https://orcid.org/0009-0005-6885-7427"},"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":"Qiqi Ou","raw_affiliation_strings":["Department of Mathematics, Shaanxi University of Science & Technology, Xi\u2019an 710021, China","Department of Mathematics, Shaanxi University of Science & Technology, Xi'an 710021, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shaanxi University of Science & Technology, Xi\u2019an 710021, China","institution_ids":["https://openalex.org/I51622183"]},{"raw_affiliation_string":"Department of Mathematics, Shaanxi University of Science & Technology, Xi'an 710021, China","institution_ids":["https://openalex.org/I51622183"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5100330121"],"corresponding_institution_ids":["https://openalex.org/I51622183"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":5.2545,"has_fulltext":true,"cited_by_count":32,"citation_normalized_percentile":{"value":0.96186522,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"11","issue":"11","first_page":"593","last_page":"593"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9977999925613403,"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":0.9977999925613403,"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":0.9973000288009644,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9696000218391418,"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/commutative-property","display_name":"Commutative property","score":0.715065598487854},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5916052460670471},{"id":"https://openalex.org/keywords/flexibility","display_name":"Flexibility (engineering)","score":0.5673933625221252},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5287095308303833},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5139200687408447},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4466031491756439},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44493240118026733},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37842434644699097},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3612978458404541},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3209221065044403},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.18870809674263}],"concepts":[{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.715065598487854},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5916052460670471},{"id":"https://openalex.org/C2780598303","wikidata":"https://www.wikidata.org/wiki/Q65921492","display_name":"Flexibility (engineering)","level":2,"score":0.5673933625221252},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5287095308303833},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5139200687408447},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4466031491756439},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44493240118026733},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37842434644699097},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3612978458404541},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3209221065044403},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.18870809674263},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/axioms11110593","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11110593","pdf_url":"https://www.mdpi.com/2075-1680/11/11/593/pdf?version=1668688249","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:academica-e.unavarra.es:2454/45196","is_oa":true,"landing_page_url":"https://hdl.handle.net/2454/45196","pdf_url":null,"source":{"id":"https://openalex.org/S4306402560","display_name":"Academica-e (Universidad P\u00fablica de Navarra)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I175051016","host_organization_name":"Universidad Publica de Navarra","host_organization_lineage":["https://openalex.org/I175051016"],"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":null,"raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:doaj.org/article:01b3373c176549a5af04d5e4e8052789","is_oa":true,"landing_page_url":"https://doaj.org/article/01b3373c176549a5af04d5e4e8052789","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 11, Iss 11, p 593 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/11/11/593/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms11110593","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 11; Issue 11; Pages: 593","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms11110593","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11110593","pdf_url":"https://www.mdpi.com/2075-1680/11/11/593/pdf?version=1668688249","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":[{"display_name":"Peace, Justice and strong institutions","score":0.800000011920929,"id":"https://metadata.un.org/sdg/16"}],"awards":[{"id":"https://openalex.org/G3103453383","display_name":null,"funder_award_id":"20&ZD047","funder_id":"https://openalex.org/F4320335869","funder_display_name":"National Social Science Fund of China"},{"id":"https://openalex.org/G3206108213","display_name":null,"funder_award_id":"20&ZD047","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G391041541","display_name":null,"funder_award_id":"PID2019-108392GB-I00 (AEI/10.13039/501100011033)","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"},{"id":"https://openalex.org/G7026752651","display_name":null,"funder_award_id":"PID2019-108392GB-I00 (AEI/10.13039/501100011033)","funder_id":"https://openalex.org/F4320335869","funder_display_name":"National Social Science Fund of China"},{"id":"https://openalex.org/G985811546","display_name":null,"funder_award_id":"12271319","funder_id":"https://openalex.org/F4320335869","funder_display_name":"National Social Science Fund of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335869","display_name":"National Social Science Fund of China","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4307549405.pdf","grobid_xml":"https://content.openalex.org/works/W4307549405.grobid-xml"},"referenced_works_count":49,"referenced_works":["https://openalex.org/W20708483","https://openalex.org/W60357591","https://openalex.org/W189069394","https://openalex.org/W869044725","https://openalex.org/W1521729143","https://openalex.org/W1799460310","https://openalex.org/W1974361517","https://openalex.org/W1974543752","https://openalex.org/W1982776174","https://openalex.org/W1987898498","https://openalex.org/W1995828530","https://openalex.org/W2012797621","https://openalex.org/W2026485666","https://openalex.org/W2033994334","https://openalex.org/W2038675095","https://openalex.org/W2046701989","https://openalex.org/W2076379790","https://openalex.org/W2078572874","https://openalex.org/W2087424102","https://openalex.org/W2119737461","https://openalex.org/W2123529398","https://openalex.org/W2133059825","https://openalex.org/W2183383516","https://openalex.org/W2496338429","https://openalex.org/W2559077843","https://openalex.org/W2582267605","https://openalex.org/W2805694183","https://openalex.org/W2890847761","https://openalex.org/W2902712943","https://openalex.org/W2911650086","https://openalex.org/W2941627582","https://openalex.org/W2990652536","https://openalex.org/W3019914216","https://openalex.org/W3042706678","https://openalex.org/W3048868661","https://openalex.org/W3111342656","https://openalex.org/W3128742773","https://openalex.org/W3194813552","https://openalex.org/W4213427446","https://openalex.org/W4229068072","https://openalex.org/W4242872809","https://openalex.org/W4252793191","https://openalex.org/W4285091555","https://openalex.org/W4292547476","https://openalex.org/W4292566538","https://openalex.org/W4294845633","https://openalex.org/W4296482401","https://openalex.org/W6680508521","https://openalex.org/W6686212614"],"related_works":["https://openalex.org/W4236696095","https://openalex.org/W3143779693","https://openalex.org/W2626808643","https://openalex.org/W2004064826","https://openalex.org/W3103727510","https://openalex.org/W97045569","https://openalex.org/W1527069879","https://openalex.org/W2946179579","https://openalex.org/W2348021072","https://openalex.org/W1990776425"],"abstract_inverted_index":{"Overlap":[0],"and":[1,13,33,70,73,81,100,107,113,141,157,164],"grouping":[2,43,71,83,109,159],"functions":[3,39,44,69,80,84,106,110,133,156,160],"are":[4,45,85,111,122,144],"important":[5],"aggregation":[6],"operators,":[7],"especially":[8],"in":[9,134,150],"information":[10],"fusion,":[11],"classification":[12],"decision-making":[14],"problems.":[15],"However,":[16],"when":[17],"we":[18,36],"do":[19],"more":[20],"in-depth":[21],"application":[22,152],"research":[23],"(for":[24],"example,":[25],"non-commutative":[26],"fuzzy":[27,138],"reasoning,":[28],"complex":[29],"multi-attribute":[30,135],"decision":[31],"making":[32],"image":[34,142],"processing),":[35],"find":[37],"overlap":[38,68,79,105,131,155],"as":[40,42],"well":[41],"required":[46],"to":[47],"be":[48],"commutative":[49],"(or":[50],"symmetric),":[51],"which":[52],"limit":[53],"their":[54],"wide":[55],"applications.":[56],"For":[57],"the":[58,64,74,88,92,95,114],"above":[59],"reasons,":[60],"this":[61],"paper":[62],"expands":[63],"original":[65,96],"notions":[66],"of":[67,77,90,94,103,129],"functions,":[72],"new":[75],"concepts":[76],"pseudo":[78,82,104,108,130,154,158],"proposed":[86],"on":[87],"basis":[89],"removing":[91],"commutativity":[93],"functions.":[97],"Some":[98],"examples":[99],"construction":[101],"methods":[102],"presented,":[112],"residuated":[115],"implication":[116],"(co-implication)":[117],"operators":[118],"derived":[119],"from":[120],"them":[121],"investigated.":[123],"Not":[124],"only":[125],"that,":[126,149],"some":[127],"applications":[128],"(grouping)":[132],"(group)":[136],"decision-making,":[137],"mathematical":[139],"morphology":[140],"processing":[143],"discussed.":[145],"Experimental":[146],"results":[147],"show":[148],"many":[151],"fields,":[153],"have":[161],"greater":[162],"flexibility":[163],"practicability.":[165]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":6}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}