{"id":"https://openalex.org/W3120301049","doi":"https://doi.org/10.1142/s0218488521500082","title":"Intuitionistic Fuzzy Calculus Based on Einstein Operations","display_name":"Intuitionistic Fuzzy Calculus Based on Einstein Operations","publication_year":2021,"publication_date":"2021-01-06","ids":{"openalex":"https://openalex.org/W3120301049","doi":"https://doi.org/10.1142/s0218488521500082","mag":"3120301049"},"language":"en","primary_location":{"id":"doi:10.1142/s0218488521500082","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218488521500082","pdf_url":null,"source":{"id":"https://openalex.org/S69518169","display_name":"International Journal of Uncertainty Fuzziness and Knowledge-Based Systems","issn_l":"0218-4885","issn":["0218-4885","1793-6411"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Uncertainty, Fuzziness and Knowledge-Based 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/A5112750655","display_name":"Changhong Guo","orcid":null},"institutions":[{"id":"https://openalex.org/I139024713","display_name":"Guangdong University of Technology","ror":"https://ror.org/04azbjn80","country_code":"CN","type":"education","lineage":["https://openalex.org/I139024713"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Changhong Guo","raw_affiliation_strings":["School of Management, Guangdong University of Technology, Guangzhou 510520, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Management, Guangdong University of Technology, Guangzhou 510520, P. R. China","institution_ids":["https://openalex.org/I139024713"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103196666","display_name":"Shaomei Fang","orcid":"https://orcid.org/0000-0002-7017-8168"},"institutions":[{"id":"https://openalex.org/I101479585","display_name":"South China Agricultural University","ror":"https://ror.org/05v9jqt67","country_code":"CN","type":"education","lineage":["https://openalex.org/I101479585"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Shaomei Fang","raw_affiliation_strings":["Department of Mathematics, South China Agricultural University, Guangzhou 510640, P. R. China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, South China Agricultural University, Guangzhou 510640, P. R. China","institution_ids":["https://openalex.org/I101479585"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5103196666"],"corresponding_institution_ids":["https://openalex.org/I101479585"],"apc_list":null,"apc_paid":null,"fwci":0.1743,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.49098184,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"29","issue":"01","first_page":"145","last_page":"178"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9896000027656555,"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":0.9896000027656555,"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/einstein","display_name":"Einstein","score":0.8409807682037354},{"id":"https://openalex.org/keywords/exponentiation","display_name":"Exponentiation","score":0.7142959237098694},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.520994246006012},{"id":"https://openalex.org/keywords/subtraction","display_name":"Subtraction","score":0.4692264497280121},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.43524807691574097},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3818829655647278},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.36260437965393066},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3492947220802307},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32404547929763794},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2937498092651367},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.18644747138023376},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.18388041853904724},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1693161427974701},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.10284441709518433}],"concepts":[{"id":"https://openalex.org/C146846114","wikidata":"https://www.wikidata.org/wiki/Q901448","display_name":"Einstein","level":2,"score":0.8409807682037354},{"id":"https://openalex.org/C81539297","wikidata":"https://www.wikidata.org/wiki/Q33456","display_name":"Exponentiation","level":2,"score":0.7142959237098694},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.520994246006012},{"id":"https://openalex.org/C68060419","wikidata":"https://www.wikidata.org/wiki/Q40754","display_name":"Subtraction","level":2,"score":0.4692264497280121},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.43524807691574097},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3818829655647278},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.36260437965393066},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3492947220802307},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32404547929763794},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2937498092651367},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.18644747138023376},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.18388041853904724},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1693161427974701},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.10284441709518433},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218488521500082","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218488521500082","pdf_url":null,"source":{"id":"https://openalex.org/S69518169","display_name":"International Journal of Uncertainty Fuzziness and Knowledge-Based Systems","issn_l":"0218-4885","issn":["0218-4885","1793-6411"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.8299999833106995}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1821857592","https://openalex.org/W2057474768","https://openalex.org/W3082721911","https://openalex.org/W4213010969","https://openalex.org/W4298965518","https://openalex.org/W3103765022","https://openalex.org/W2119606669","https://openalex.org/W2094893810","https://openalex.org/W4300883263","https://openalex.org/W2148968135"],"abstract_inverted_index":{"The":[0,17],"intuitionistic":[1,25,36,87],"fuzzy":[2,15,26,37,88],"set":[3,38],"(A-IFS)":[4],"was":[5,121],"introduced":[6,122],"by":[7],"Atanassov":[8],"to":[9,123],"generalize":[10],"the":[11,24,35,40,54,81,93,107,118,133],"concept":[12],"of":[13,20,42,50,86],"Zadeh\u2019s":[14],"set.":[16],"basic":[18],"elements":[19],"an":[21,113],"A-IFS":[22],"are":[23,109],"numbers":[27],"(IFNs).":[28],"In":[29],"this":[30],"paper,":[31],"we":[32,46,79],"deal":[33],"with":[34,39],"help":[41],"Einstein":[43,55,57,59,63,73,76,94],"operations.":[44,95],"First":[45],"introduce":[47],"some":[48,101,125],"operations":[49],"A-IFS,":[51],"such":[52],"as":[53,72],"sum,":[56],"product,":[58],"scalar":[60],"multiplication":[61],"and":[62,65,69,75,84,97,103,112,136],"exponentiation,":[64],"redefine":[66],"two":[67],"new":[68],"important":[70],"operation":[71],"subtraction":[74],"division.":[77],"Then":[78],"investigate":[80],"limit,":[82],"continuity":[83],"derivatives":[85],"functions":[89],"(IFFs)":[90],"based":[91,116],"on":[92,117,132],"Furthermore":[96],"what":[98],"is":[99],"more,":[100],"infinite":[102],"definite":[104,119],"integrals":[105],"for":[106],"IFFs":[108],"discussed":[110],"importantly,":[111],"aggregation":[114],"method":[115],"integral":[120],"solve":[124],"actual":[126],"decision":[127],"making":[128],"problems,":[129],"which":[130],"focus":[131],"original":[134],"data":[135],"obtain":[137],"better":[138],"overall":[139],"evaluations":[140],"in":[141],"information":[142],"aggregation.":[143]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}