{"id":"https://openalex.org/W2013083232","doi":"https://doi.org/10.1109/fuzzy.2006.1681922","title":"Minimizing a Linear Objective Function under a Max-t-norm Fuzzy Relational Equation Constraint","display_name":"Minimizing a Linear Objective Function under a Max-t-norm Fuzzy Relational Equation Constraint","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2013083232","doi":"https://doi.org/10.1109/fuzzy.2006.1681922","mag":"2013083232"},"language":"en","primary_location":{"id":"doi:10.1109/fuzzy.2006.1681922","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fuzzy.2006.1681922","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2006 IEEE International Conference on Fuzzy Systems","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/A5111717695","display_name":"Sy\u2010Ming Guu","orcid":null},"institutions":[{"id":"https://openalex.org/I99908691","display_name":"Yuan Ze University","ror":"https://ror.org/01fv1ds98","country_code":"TW","type":"education","lineage":["https://openalex.org/I99908691"]}],"countries":["TW"],"is_corresponding":true,"raw_author_name":"Sy-Ming Guu","raw_affiliation_strings":["Department of Business Administration, Yuan-Ze University, Taoyuan, Taiwan","Yuan-Ze Univ., Taoyuan"],"affiliations":[{"raw_affiliation_string":"Department of Business Administration, Yuan-Ze University, Taoyuan, Taiwan","institution_ids":["https://openalex.org/I99908691"]},{"raw_affiliation_string":"Yuan-Ze Univ., Taoyuan","institution_ids":["https://openalex.org/I99908691"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082483976","display_name":"Yan-Kuen Wu","orcid":"https://orcid.org/0000-0001-7788-8157"},"institutions":[{"id":"https://openalex.org/I42474999","display_name":"Vanung University","ror":"https://ror.org/04r3dny05","country_code":"TW","type":"education","lineage":["https://openalex.org/I42474999"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Yan-Kuen Wu","raw_affiliation_strings":["Department of Industrial Management, Vanung University, Taoyuan, Taiwan","Department of Industrial Management, Vanung University, Taoyuan, 320, Taiwan, ROC"],"affiliations":[{"raw_affiliation_string":"Department of Industrial Management, Vanung University, Taoyuan, Taiwan","institution_ids":["https://openalex.org/I42474999"]},{"raw_affiliation_string":"Department of Industrial Management, Vanung University, Taoyuan, 320, Taiwan, ROC","institution_ids":["https://openalex.org/I42474999"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5111717695"],"corresponding_institution_ids":["https://openalex.org/I99908691"],"apc_list":null,"apc_paid":null,"fwci":0.4212,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.66917655,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"2","issue":null,"first_page":"1604","last_page":"1610"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9988999962806702,"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":0.9988999962806702,"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/T12709","display_name":"Optimization and Mathematical Programming","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9968000054359436,"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/mathematics","display_name":"Mathematics","score":0.6645713448524475},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6085747480392456},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5481572151184082},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.5039920210838318},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.45411112904548645},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.4527937173843384},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.4437715709209442},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.43548017740249634},{"id":"https://openalex.org/keywords/t-norm","display_name":"T-norm","score":0.42429715394973755},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.39015835523605347},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.3846518397331238},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3718714714050293},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32567617297172546},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2764543294906616},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09509414434432983}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6645713448524475},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6085747480392456},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5481572151184082},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5039920210838318},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.45411112904548645},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.4527937173843384},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.4437715709209442},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.43548017740249634},{"id":"https://openalex.org/C2721081","wikidata":"https://www.wikidata.org/wiki/Q2383161","display_name":"T-norm","level":5,"score":0.42429715394973755},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.39015835523605347},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.3846518397331238},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3718714714050293},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32567617297172546},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2764543294906616},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09509414434432983},{"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/fuzzy.2006.1681922","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fuzzy.2006.1681922","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2006 IEEE International Conference on Fuzzy Systems","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.7799999713897705,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W49782344","https://openalex.org/W157049284","https://openalex.org/W1531600119","https://openalex.org/W1967864090","https://openalex.org/W1970676534","https://openalex.org/W1971016194","https://openalex.org/W1990673965","https://openalex.org/W1994525828","https://openalex.org/W2006973411","https://openalex.org/W2012201562","https://openalex.org/W2020391927","https://openalex.org/W2033517995","https://openalex.org/W2034208803","https://openalex.org/W2036338807","https://openalex.org/W2039018525","https://openalex.org/W2042960352","https://openalex.org/W2050942211","https://openalex.org/W2061482204","https://openalex.org/W2061590216","https://openalex.org/W2062633196","https://openalex.org/W2068883966","https://openalex.org/W2087564856","https://openalex.org/W2135949973","https://openalex.org/W2146682692","https://openalex.org/W2149872567","https://openalex.org/W2578456536","https://openalex.org/W3213572188","https://openalex.org/W4234672050"],"related_works":["https://openalex.org/W2983685817","https://openalex.org/W4285278887","https://openalex.org/W2995925505","https://openalex.org/W134783735","https://openalex.org/W2365237642","https://openalex.org/W3116484972","https://openalex.org/W2941986668","https://openalex.org/W4232431455","https://openalex.org/W1486684451","https://openalex.org/W4361273540"],"abstract_inverted_index":{"In":[0],"this":[1,27],"paper":[2],"minimizing":[3],"a":[4,10,78,91],"linear":[5],"objective":[6,49],"function":[7],"subject":[8],"to":[9,71,105],"continuous":[11],"max-i-norm":[12],"fuzzy":[13],"relational":[14],"equation":[15],"is":[16,70,90,98],"considered.":[17],"Our":[18,67],"contributions":[19],"are":[20,103],"two":[21,34],"folds.":[22],"First,":[23],"We":[24],"show":[25],"that":[26],"optimization":[28,83],"problem":[29,55],"can":[30,60],"be":[31,61],"divided":[32],"into":[33],"subproblems":[35],"by":[36],"separating":[37],"the":[38,48,81,87,95,107],"decision":[39],"variables":[40],"associated":[41],"with":[42],"negative":[43],"and":[44],"nonnegative":[45],"coefficients":[46],"in":[47,85],"function.":[50],"A":[51],"0-1":[52],"integer":[53],"programming":[54],"as":[56],"an":[57,73],"equivalent":[58],"model":[59],"derived":[62],"for":[63,76],"our":[64],"current":[65],"study.":[66],"second":[68],"contribution":[69],"present":[72],"efficient":[74],"procedure":[75],"solving":[77],"subclass":[79],"of":[80],"max-t-norm-type":[82],"problems":[84],"which":[86],"max-product-type":[88],"one":[89,97],"special":[92],"case,":[93],"yet,":[94],"max-min-type":[96],"not":[99],"included.":[100],"Numerical":[101],"examples":[102],"provided":[104],"illustrate":[106],"procedure.":[108]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}