{"id":"https://openalex.org/W2120454538","doi":"https://doi.org/10.1109/fuzzy.2005.1452551","title":"Exact solving for a class of second order fuzzy equation","display_name":"Exact solving for a class of second order fuzzy equation","publication_year":2005,"publication_date":"2005-07-27","ids":{"openalex":"https://openalex.org/W2120454538","doi":"https://doi.org/10.1109/fuzzy.2005.1452551","mag":"2120454538"},"language":"en","primary_location":{"id":"doi:10.1109/fuzzy.2005.1452551","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fuzzy.2005.1452551","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The 14th IEEE International Conference on Fuzzy Systems, 2005. FUZZ '05.","raw_type":"proceedings-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/A5046741202","display_name":"Reda Boukezzoula","orcid":"https://orcid.org/0000-0002-0451-8945"},"institutions":[{"id":"https://openalex.org/I70900168","display_name":"Universit\u00e9 Savoie Mont Blanc","ror":"https://ror.org/04gqg1a07","country_code":"FR","type":"education","lineage":["https://openalex.org/I70900168"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"R. Boukezzoula","raw_affiliation_strings":["LISTIC, University of Savoie, Annecy-le-vieux, France","LISTIC, Univ. of Savoie, Annecy"],"affiliations":[{"raw_affiliation_string":"LISTIC, University of Savoie, Annecy-le-vieux, France","institution_ids":["https://openalex.org/I70900168"]},{"raw_affiliation_string":"LISTIC, Univ. of Savoie, Annecy","institution_ids":["https://openalex.org/I70900168"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000285051","display_name":"S. Marteau","orcid":null},"institutions":[{"id":"https://openalex.org/I70900168","display_name":"Universit\u00e9 Savoie Mont Blanc","ror":"https://ror.org/04gqg1a07","country_code":"FR","type":"education","lineage":["https://openalex.org/I70900168"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"S. Marteau","raw_affiliation_strings":["LISTIC, University of Savoie, Annecy-le-vieux, France","LISTIC, Univ. of Savoie, Annecy"],"affiliations":[{"raw_affiliation_string":"LISTIC, University of Savoie, Annecy-le-vieux, France","institution_ids":["https://openalex.org/I70900168"]},{"raw_affiliation_string":"LISTIC, Univ. of Savoie, Annecy","institution_ids":["https://openalex.org/I70900168"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5046741202"],"corresponding_institution_ids":["https://openalex.org/I70900168"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.17800023,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"7","issue":null,"first_page":"1116","last_page":"1121"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9990000128746033,"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"}},"topics":[{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9990000128746033,"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/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9980000257492065,"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/T10320","display_name":"Neural Networks and Applications","score":0.9886000156402588,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6634615659713745},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.6268222332000732},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.6048776507377625},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5482407808303833},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5441076159477234},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45796114206314087},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.41707950830459595},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.40368738770484924},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3871638774871826},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.130121111869812},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.07188922166824341}],"concepts":[{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6634615659713745},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.6268222332000732},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.6048776507377625},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5482407808303833},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5441076159477234},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45796114206314087},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.41707950830459595},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40368738770484924},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3871638774871826},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.130121111869812},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.07188922166824341},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/fuzzy.2005.1452551","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fuzzy.2005.1452551","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The 14th IEEE International Conference on Fuzzy Systems, 2005. FUZZ '05.","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W218974552","https://openalex.org/W1580809199","https://openalex.org/W2006319249","https://openalex.org/W2037142859","https://openalex.org/W2044770310","https://openalex.org/W2047440354","https://openalex.org/W2049785322","https://openalex.org/W2065397160","https://openalex.org/W2069069851","https://openalex.org/W2072204236","https://openalex.org/W2093261176","https://openalex.org/W2109046578","https://openalex.org/W2133056736","https://openalex.org/W2912565176","https://openalex.org/W2970857329","https://openalex.org/W4211007335","https://openalex.org/W4249936906","https://openalex.org/W6643765341"],"related_works":["https://openalex.org/W3086618278","https://openalex.org/W2006100586","https://openalex.org/W4300809132","https://openalex.org/W2103373899","https://openalex.org/W2367223136","https://openalex.org/W3111373190","https://openalex.org/W2039972010","https://openalex.org/W2796568981","https://openalex.org/W2368454205","https://openalex.org/W2348093013"],"abstract_inverted_index":{"This":[0],"paper":[1],"aims":[2],"at":[3],"solving":[4,51],"the":[5,30,33,40,50,59],"second":[6],"order":[7],"fuzzy":[8],"interval":[9],"equation":[10],"A.X2":[11],"+":[12],"B=C.":[13],"The":[14,36,56],"general":[15],"solution":[16,34,47],"is":[17,25,62],"expressed":[18],"in":[19],"an":[20,44],"analytical":[21,46],"compact":[22],"form":[23],"which":[24],"directly":[26],"used":[27],"for":[28,53],"deriving":[29],"condition":[31],"of":[32,58],"existence.":[35],"proposed":[37,60],"method":[38,61],"has":[39],"advantage":[41],"to":[42],"give":[43],"exact":[45],"without":[48],"runing":[49],"algorithm":[52],"every":[54],"alpha-cut.":[55],"validity":[57],"illustrated":[63],"by":[64],"a":[65],"simulation":[66],"example":[67]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}