{"id":"https://openalex.org/W2080446903","doi":"https://doi.org/10.1142/s0218488597000300","title":"On Some Classes of Idempotent Operators","display_name":"On Some Classes of Idempotent Operators","publication_year":1997,"publication_date":"1997-08-01","ids":{"openalex":"https://openalex.org/W2080446903","doi":"https://doi.org/10.1142/s0218488597000300","mag":"2080446903"},"language":"en","primary_location":{"id":"doi:10.1142/s0218488597000300","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218488597000300","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/A5062266634","display_name":"Gaspar Mayor","orcid":null},"institutions":[{"id":"https://openalex.org/I50441567","display_name":"Universitat de les Illes Balears","ror":"https://ror.org/03e10x626","country_code":"ES","type":"education","lineage":["https://openalex.org/I50441567"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"G. Mayor","raw_affiliation_strings":["Dpt. de Ci\u00e8ncies Matem\u00e0tiques i Inform\u00e0tica, Universitat de les Illes Balears, 07071 Palma de Mallorca, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dpt. de Ci\u00e8ncies Matem\u00e0tiques i Inform\u00e0tica, Universitat de les Illes Balears, 07071 Palma de Mallorca, Spain","institution_ids":["https://openalex.org/I50441567"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010033209","display_name":"Joan Torrens","orcid":"https://orcid.org/0000-0002-5066-2913"},"institutions":[{"id":"https://openalex.org/I50441567","display_name":"Universitat de les Illes Balears","ror":"https://ror.org/03e10x626","country_code":"ES","type":"education","lineage":["https://openalex.org/I50441567"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"J. Torrens","raw_affiliation_strings":["Dpt. de Ci\u00e8ncies Matem\u00e0tiques i Inform\u00e0tica, Universitat de les Illes Balears, 07071 Palma de Mallorca, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dpt. de Ci\u00e8ncies Matem\u00e0tiques i Inform\u00e0tica, Universitat de les Illes Balears, 07071 Palma de Mallorca, Spain","institution_ids":["https://openalex.org/I50441567"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.5549,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.83371133,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"05","issue":"04","first_page":"401","last_page":"410"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9296000003814697,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9296000003814697,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9169999957084656,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.788196861743927},{"id":"https://openalex.org/keywords/idempotence","display_name":"Idempotence","score":0.7798882722854614},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5852828621864319},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5520631074905396},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5397506952285767},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.5124455094337463},{"id":"https://openalex.org/keywords/representation-theorem","display_name":"Representation theorem","score":0.5072193145751953},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.4761250615119934},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.44065847992897034},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3850415349006653},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35525089502334595}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.788196861743927},{"id":"https://openalex.org/C172252984","wikidata":"https://www.wikidata.org/wiki/Q368988","display_name":"Idempotence","level":2,"score":0.7798882722854614},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5852828621864319},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5520631074905396},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5397506952285767},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.5124455094337463},{"id":"https://openalex.org/C2776230367","wikidata":"https://www.wikidata.org/wiki/Q7314222","display_name":"Representation theorem","level":2,"score":0.5072193145751953},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.4761250615119934},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.44065847992897034},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3850415349006653},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35525089502334595},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218488597000300","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218488597000300","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1594270709","https://openalex.org/W2362786832","https://openalex.org/W2154958691","https://openalex.org/W2049944211","https://openalex.org/W2373496770","https://openalex.org/W2615385948","https://openalex.org/W2766427487","https://openalex.org/W219765222","https://openalex.org/W1819690510","https://openalex.org/W4387635768"],"abstract_inverted_index":{"In":[0,13],"this":[1],"paper":[2],"we":[3,15],"deal":[4],"with":[5],"the":[6,75],"idempotency":[7],"equation":[8],"H(x,x)=x":[9],"for":[10,18,79],"all":[11],"x\u2208[0,1].":[12],"particular":[14],"solve":[16],"it":[17],"two":[19],"special":[20,48],"cases.":[21],"First":[22],"when":[23,39],"H":[24,40],"is":[25,41],"a":[26,31,42,47,65,70],"convex":[27,43],"linear":[28,44],"combination":[29,45],"of":[30,46,50,67],"strict":[32,81],"t-norm":[33],"and":[34,37,54],"its":[35,55],"(1-j)-dual":[36],"second,":[38],"kind":[49,66],"aggregation":[51,59,63],"functions":[52,68],"F=<(f,N)>":[53],"N-dual,":[56],"being":[57],"these":[58],"functions,":[60,64],"called":[61],"L-representable":[62],"verifying":[69],"similar":[71],"representation":[72,77],"theorem":[73,78],"to":[74],"classical":[76],"non":[80],"Archimedean":[82],"t-norms.":[83]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}