{"id":"https://openalex.org/W3181048974","doi":"https://doi.org/10.3233/jifs-210527","title":"Pythagorean fuzzy full implication multiple I method and corresponding applications","display_name":"Pythagorean fuzzy full implication multiple I method and corresponding applications","publication_year":2021,"publication_date":"2021-07-13","ids":{"openalex":"https://openalex.org/W3181048974","doi":"https://doi.org/10.3233/jifs-210527","mag":"3181048974"},"language":"en","primary_location":{"id":"doi:10.3233/jifs-210527","is_oa":false,"landing_page_url":"https://doi.org/10.3233/jifs-210527","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 & 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/A5069926561","display_name":"TaiBen Nan","orcid":null},"institutions":[{"id":"https://openalex.org/I145897649","display_name":"Minzu University of China","ror":"https://ror.org/0044e2g62","country_code":"CN","type":"education","lineage":["https://openalex.org/I145897649"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"TaiBen Nan","raw_affiliation_strings":["School of Mathematics and Computer Science, Northwest MinZu University, Lanzhou, Gansu, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computer Science, Northwest MinZu University, Lanzhou, Gansu, P. R. China","institution_ids":["https://openalex.org/I145897649"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080814061","display_name":"Haidong Zhang","orcid":"https://orcid.org/0000-0003-0605-8265"},"institutions":[{"id":"https://openalex.org/I145897649","display_name":"Minzu University of China","ror":"https://ror.org/0044e2g62","country_code":"CN","type":"education","lineage":["https://openalex.org/I145897649"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Haidong Zhang","raw_affiliation_strings":["School of Mathematics and Computer Science, Northwest MinZu University, Lanzhou, Gansu, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computer Science, Northwest MinZu University, Lanzhou, Gansu, P. R. China","institution_ids":["https://openalex.org/I145897649"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111484874","display_name":"Yanping He","orcid":null},"institutions":[{"id":"https://openalex.org/I145897649","display_name":"Minzu University of China","ror":"https://ror.org/0044e2g62","country_code":"CN","type":"education","lineage":["https://openalex.org/I145897649"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yanping He","raw_affiliation_strings":["School of Electrical Engineering, Northwest MinZu University, Lanzhou, Gansu, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Electrical Engineering, Northwest MinZu University, Lanzhou, Gansu, P. R. China","institution_ids":["https://openalex.org/I145897649"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5080814061"],"corresponding_institution_ids":["https://openalex.org/I145897649"],"apc_list":null,"apc_paid":null,"fwci":0.3486,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.62176862,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"41","issue":"1","first_page":"1741","last_page":"1755"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9998999834060669,"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":0.9998999834060669,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9794999957084656,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9761000275611877,"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/pythagorean-theorem","display_name":"Pythagorean theorem","score":0.9578496217727661},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.519138753414154},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5004541873931885},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42341774702072144},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3549630641937256}],"concepts":[{"id":"https://openalex.org/C100461760","wikidata":"https://www.wikidata.org/wiki/Q11518","display_name":"Pythagorean theorem","level":2,"score":0.9578496217727661},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.519138753414154},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5004541873931885},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42341774702072144},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3549630641937256},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/jifs-210527","is_oa":false,"landing_page_url":"https://doi.org/10.3233/jifs-210527","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 & Fuzzy Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.8299999833106995,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W1829951598","https://openalex.org/W1963901723","https://openalex.org/W1980564456","https://openalex.org/W1997724331","https://openalex.org/W2013932252","https://openalex.org/W2024244056","https://openalex.org/W2036610495","https://openalex.org/W2041280856","https://openalex.org/W2046794773","https://openalex.org/W2083293441","https://openalex.org/W2166550958","https://openalex.org/W2292359941","https://openalex.org/W2347319959","https://openalex.org/W2375639571","https://openalex.org/W2412590235","https://openalex.org/W2549733045","https://openalex.org/W2589233777","https://openalex.org/W2755143840","https://openalex.org/W2790677216","https://openalex.org/W2902861753","https://openalex.org/W2962845237","https://openalex.org/W2982031253","https://openalex.org/W3014707988","https://openalex.org/W3036144362","https://openalex.org/W3039996349","https://openalex.org/W3084715339","https://openalex.org/W3088396459","https://openalex.org/W3115644321","https://openalex.org/W3118993451","https://openalex.org/W3126088291","https://openalex.org/W3136750270","https://openalex.org/W4206464249","https://openalex.org/W4211007335","https://openalex.org/W4234672050","https://openalex.org/W6656334979","https://openalex.org/W6662063049"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2995447873","https://openalex.org/W1802380781","https://openalex.org/W4378767041","https://openalex.org/W4210969441","https://openalex.org/W4313271080","https://openalex.org/W2050612014","https://openalex.org/W3166167233","https://openalex.org/W2387128994","https://openalex.org/W3093594498"],"abstract_inverted_index":{"The":[0,147],"overwhelming":[1],"majority":[2],"of":[3,48,64,81,113,120,134,149],"existing":[4,154],"decision-making":[5,31,145],"methods":[6,32,155,162],"combined":[7],"with":[8],"the":[9,35,46,49,57,62,79,87,93,108,114,132,135,150,160],"Pythagorean":[10,36,65,67,70,75,88,100,136],"fuzzy":[11,37,71,76,89,101,137],"set":[12],"(PFS)":[13],"are":[14,122,156,163],"based":[15,33,55,85,164],"on":[16,34,56,86,165],"aggregation":[17],"operators,":[18],"and":[19,78,107,110,173],"their":[20],"logical":[21,166],"foundation":[22],"is":[23,43,105,128],"imperfect.":[24],"Therefore,":[25],"we":[26],"attempt":[27],"to":[28,45,130],"establish":[29],"two":[30],"multiple":[38,52,96,117,140],"I":[39,53,97,118,141],"method.":[40],"This":[41],"paper":[42],"devoted":[44],"discussion":[47],"full":[50,94,115,138],"implication":[51,72,95,116,139],"method":[54,98,119,142,152],"PFS.":[58],"We":[59],"first":[60],"propose":[61],"concepts":[63],"t-norm,":[66],"t-conorm,":[68],"residual":[69],"operator":[73],"(RPFIO),":[74],"biresiduum,":[77],"degree":[80],"similarity":[82],"between":[83],"PFSs":[84],"biresiduum.":[90],"In":[91],"addition,":[92],"for":[99],"modus":[102],"ponens":[103],"(PFMP)":[104],"established,":[106],"reversibility":[109],"continuity":[111],"properties":[112],"PFMP":[121],"analyzed.":[123],"Finally,":[124],"a":[125,144],"practical":[126],"problem":[127],"discussed":[129],"demonstrate":[131],"effectiveness":[133],"in":[143],"problem.":[146],"advantages":[148],"new":[151],"over":[153],"also":[157],"explained.":[158],"Overall,":[159],"proposed":[161],"reasoning,":[167],"so":[168],"they":[169],"can":[170],"more":[171],"accurately":[172],"completely":[174],"express":[175],"decision":[176],"information.":[177]},"counts_by_year":[{"year":2022,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}