{"id":"https://openalex.org/W3163808893","doi":"https://doi.org/10.1080/23307706.2021.1919229","title":"Characterisations of semigroups by the properties of their picture fuzzy bi-ideals","display_name":"Characterisations of semigroups by the properties of their picture fuzzy bi-ideals","publication_year":2021,"publication_date":"2021-05-11","ids":{"openalex":"https://openalex.org/W3163808893","doi":"https://doi.org/10.1080/23307706.2021.1919229","mag":"3163808893"},"language":"en","primary_location":{"id":"doi:10.1080/23307706.2021.1919229","is_oa":false,"landing_page_url":"https://doi.org/10.1080/23307706.2021.1919229","pdf_url":null,"source":{"id":"https://openalex.org/S2475925340","display_name":"Journal of Control and Decision","issn_l":"2330-7706","issn":["2330-7706","2330-7714"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Control and Decision","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/A5025212558","display_name":"Pairote Yiarayong","orcid":"https://orcid.org/0000-0003-1525-9536"},"institutions":[{"id":"https://openalex.org/I154381313","display_name":"Pibulsongkram Rajabhat University","ror":"https://ror.org/02x7w2961","country_code":"TH","type":"education","lineage":["https://openalex.org/I154381313"]}],"countries":["TH"],"is_corresponding":true,"raw_author_name":"Pairote Yiarayong","raw_affiliation_strings":["Department of Mathematics, Faculty of Science and Technology, Pibulsongkram Rajabhat University, Phitsanulok, Thailand"],"raw_orcid":"https://orcid.org/0000-0003-1525-9536","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science and Technology, Pibulsongkram Rajabhat University, Phitsanulok, Thailand","institution_ids":["https://openalex.org/I154381313"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5025212558"],"corresponding_institution_ids":["https://openalex.org/I154381313"],"apc_list":null,"apc_paid":null,"fwci":0.1581,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.49966627,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"9","issue":"1","first_page":"111","last_page":"116"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9994999766349792,"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/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9994999766349792,"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/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9934999942779541,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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":0.9769999980926514,"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/mathematics","display_name":"Mathematics","score":0.8455551862716675},{"id":"https://openalex.org/keywords/idempotence","display_name":"Idempotence","score":0.7445210218429565},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.7414274215698242},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.705141007900238},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.5500503778457642},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.5451239347457886},{"id":"https://openalex.org/keywords/algebraic-structure","display_name":"Algebraic structure","score":0.5274945497512817},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5065103769302368},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4533202350139618},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.45024749636650085},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4447745978832245},{"id":"https://openalex.org/keywords/special-classes-of-semigroups","display_name":"Special classes of semigroups","score":0.4369894564151764},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3848119080066681},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11666736006736755},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08293652534484863},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07121440768241882}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8455551862716675},{"id":"https://openalex.org/C172252984","wikidata":"https://www.wikidata.org/wiki/Q368988","display_name":"Idempotence","level":2,"score":0.7445210218429565},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.7414274215698242},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.705141007900238},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.5500503778457642},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.5451239347457886},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.5274945497512817},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5065103769302368},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4533202350139618},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.45024749636650085},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4447745978832245},{"id":"https://openalex.org/C46149467","wikidata":"https://www.wikidata.org/wiki/Q7574800","display_name":"Special classes of semigroups","level":3,"score":0.4369894564151764},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3848119080066681},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11666736006736755},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08293652534484863},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07121440768241882},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/23307706.2021.1919229","is_oa":false,"landing_page_url":"https://doi.org/10.1080/23307706.2021.1919229","pdf_url":null,"source":{"id":"https://openalex.org/S2475925340","display_name":"Journal of Control and Decision","issn_l":"2330-7706","issn":["2330-7706","2330-7714"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Control and Decision","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.6399999856948853,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1993397290","https://openalex.org/W1995347224","https://openalex.org/W2001185642","https://openalex.org/W2041688671","https://openalex.org/W2093457081","https://openalex.org/W2189316863","https://openalex.org/W2401611518","https://openalex.org/W2581375872","https://openalex.org/W2975255263","https://openalex.org/W2988300002","https://openalex.org/W3166997273"],"related_works":["https://openalex.org/W2523958388","https://openalex.org/W2791788839","https://openalex.org/W3010834671","https://openalex.org/W2386165414","https://openalex.org/W2696520184","https://openalex.org/W2031407199","https://openalex.org/W2418579592","https://openalex.org/W2388404726","https://openalex.org/W2605708488","https://openalex.org/W807853954"],"abstract_inverted_index":{"In":[0],"this":[1,49],"article,":[2],"a":[3,14,23,88],"new":[4],"generalisation":[5],"of":[6,13,44,48,58,69,75,81],"fuzzy":[7,11,20,63,83,101],"bi-ideals":[8,12,21],"and":[9,93,96],"intuitionsitic":[10],"semigroup":[15,89],"considered":[16],"so":[17],"called":[18],"picture":[19,62,82,100],"no":[22],"semigroup.":[24],"It":[25],"is":[26,51,90,105],"well":[27],"known":[28],"that":[29,87],"the":[30,39,42,55],"intra-regular":[31,76,94],"semigroups":[32,59,78],"play":[33],"an":[34,67],"essential":[35],"role":[36],"in":[37,79],"studying":[38],"structure,":[40],"especially":[41],"decomposition,":[43],"semigroups.":[45],"The":[46],"purpose":[47],"paper":[50],"to":[52],"deal":[53],"with":[54],"algebraic":[56],"structure":[57],"by":[60],"applying":[61],"set":[64],"theory.":[65],"As":[66],"application":[68],"our":[70],"results":[71],"we":[72],"get":[73],"characterisations":[74],"regular":[77,92],"terms":[80],"bi-ideals.":[84],"We":[85],"prove":[86],"both":[91],"if":[95,98],"only":[97],"every":[99],"bi-ideal":[102],"on":[103],"S":[104],"idempotent.":[106]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}
