{"id":"https://openalex.org/W2107293082","doi":"https://doi.org/10.1109/fuzzy.2007.4295386","title":"Optimizing the Linear Fractional Programming Problem with Max-Archimedean t-norm Fuzzy Relational Equation Constraints","display_name":"Optimizing the Linear Fractional Programming Problem with Max-Archimedean t-norm Fuzzy Relational Equation Constraints","publication_year":2007,"publication_date":"2007-06-01","ids":{"openalex":"https://openalex.org/W2107293082","doi":"https://doi.org/10.1109/fuzzy.2007.4295386","mag":"2107293082"},"language":"en","primary_location":{"id":"doi:10.1109/fuzzy.2007.4295386","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fuzzy.2007.4295386","pdf_url":null,"source":{"id":"https://openalex.org/S4210187232","display_name":"Proceedings of ... IEEE International Conference on Fuzzy Systems","issn_l":"1098-7584","issn":["1098-7584"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 IEEE International Fuzzy Systems Conference","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/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":true,"raw_author_name":"Yan-Kuen Wu","raw_affiliation_strings":["Department of Industrial Management, Vanung University, Taoyuan, Taiwan","Vanung Univ., Taoyuan"],"affiliations":[{"raw_affiliation_string":"Department of Industrial Management, Vanung University, Taoyuan, Taiwan","institution_ids":["https://openalex.org/I42474999"]},{"raw_affiliation_string":"Vanung Univ., Taoyuan","institution_ids":["https://openalex.org/I42474999"]}]},{"author_position":"middle","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":false,"raw_author_name":"Sy-Ming Guu","raw_affiliation_strings":["Department of Business Administration, Yuan-Ze University, Taoyuan, Taiwan","Department of Business Administration, Yuan Ze University, Taoyuan, 320, Taiwan, R.O.C. email: iesmguu@saturn.yzu.edu.tw"],"affiliations":[{"raw_affiliation_string":"Department of Business Administration, Yuan-Ze University, Taoyuan, Taiwan","institution_ids":["https://openalex.org/I99908691"]},{"raw_affiliation_string":"Department of Business Administration, Yuan Ze University, Taoyuan, 320, Taiwan, R.O.C. email: iesmguu@saturn.yzu.edu.tw","institution_ids":["https://openalex.org/I99908691"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019379032","display_name":"Yu\u2010Chih Liu","orcid":"https://orcid.org/0000-0002-0456-2858"},"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":false,"raw_author_name":"Julie Yu-Chih Liu","raw_affiliation_strings":["Department of Information Management, Yuan-Ze University, Taoyuan, Taiwan","Department of Information Management, Yuan Ze University, Taoyuan, 320, Taiwan, R.O.C. email: imyuchih@saturn.yzu.tw"],"affiliations":[{"raw_affiliation_string":"Department of Information Management, Yuan-Ze University, Taoyuan, Taiwan","institution_ids":["https://openalex.org/I99908691"]},{"raw_affiliation_string":"Department of Information Management, Yuan Ze University, Taoyuan, 320, Taiwan, R.O.C. email: imyuchih@saturn.yzu.tw","institution_ids":["https://openalex.org/I99908691"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5082483976"],"corresponding_institution_ids":["https://openalex.org/I42474999"],"apc_list":null,"apc_paid":null,"fwci":3.295,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.91574074,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"6"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9926999807357788,"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"}},"topics":[{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9926999807357788,"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":0.9800000190734863,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9789000153541565,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6763028502464294},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5588353872299194},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5070276260375977},{"id":"https://openalex.org/keywords/linear-fractional-programming","display_name":"Linear-fractional programming","score":0.5053535103797913},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.49063625931739807},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4768601357936859},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.4642672538757324},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.45792609453201294},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.45180901885032654},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4290525019168854},{"id":"https://openalex.org/keywords/fractional-programming","display_name":"Fractional programming","score":0.42789018154144287},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.42595523595809937},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.40763574838638306},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.28684067726135254},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14999157190322876}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6763028502464294},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5588353872299194},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5070276260375977},{"id":"https://openalex.org/C205658194","wikidata":"https://www.wikidata.org/wiki/Q4168281","display_name":"Linear-fractional programming","level":3,"score":0.5053535103797913},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.49063625931739807},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4768601357936859},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.4642672538757324},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.45792609453201294},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.45180901885032654},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4290525019168854},{"id":"https://openalex.org/C169069869","wikidata":"https://www.wikidata.org/wiki/Q5477546","display_name":"Fractional programming","level":4,"score":0.42789018154144287},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.42595523595809937},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.40763574838638306},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28684067726135254},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14999157190322876},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/fuzzy.2007.4295386","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fuzzy.2007.4295386","pdf_url":null,"source":{"id":"https://openalex.org/S4210187232","display_name":"Proceedings of ... IEEE International Conference on Fuzzy Systems","issn_l":"1098-7584","issn":["1098-7584"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 IEEE International Fuzzy Systems Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W49782344","https://openalex.org/W657218221","https://openalex.org/W1531600119","https://openalex.org/W1970676534","https://openalex.org/W1971016194","https://openalex.org/W1976430007","https://openalex.org/W1990673965","https://openalex.org/W2006973411","https://openalex.org/W2012201562","https://openalex.org/W2021027318","https://openalex.org/W2029338278","https://openalex.org/W2033517995","https://openalex.org/W2034208803","https://openalex.org/W2036338807","https://openalex.org/W2049053995","https://openalex.org/W2050942211","https://openalex.org/W2061482204","https://openalex.org/W2061590216","https://openalex.org/W2061821032","https://openalex.org/W2068883966","https://openalex.org/W2087564856","https://openalex.org/W2135949973","https://openalex.org/W2146682692","https://openalex.org/W2150002615","https://openalex.org/W2156577211"],"related_works":["https://openalex.org/W4205348974","https://openalex.org/W2182614003","https://openalex.org/W175643398","https://openalex.org/W2514233839","https://openalex.org/W3180876591","https://openalex.org/W2518557062","https://openalex.org/W4366124562","https://openalex.org/W3161442234","https://openalex.org/W4205896566","https://openalex.org/W2080462934"],"abstract_inverted_index":{"In":[0,51],"the":[1,5,24,28,42,56,88,93,104],"literature,":[2],"one":[3],"of":[4,12,58,61,95],"minimal":[6],"solutions":[7],"is":[8,31,120],"an":[9,77,97],"optimal":[10,98],"solution":[11,99],"solving":[13],"a":[14,46,117,125],"linear":[15,47,112],"objective":[16,29,49],"function":[17,30],"subject":[18],"to":[19,41,55,85],"fuzzy":[20,62],"relational":[21,63],"equations":[22,64],"with":[23,45,65],"max-Archimedean":[25,66],"composition.":[26],"Since":[27],"nonlinear":[32],"so":[33],"that":[34],"this":[35,52],"characteristic":[36],"can't":[37],"be":[38,83,101,108],"employed":[39,84],"again":[40],"optimization":[43,78],"problem":[44,106],"fractional":[48,113],"function.":[50],"paper,":[53],"according":[54],"characteristics":[57],"feasible":[59,89],"domain":[60,90],"t-norm":[67],"composition,":[68],"some":[69],"theoretical":[70],"results":[71,81],"are":[72],"presented":[73],"for":[74,122],"exploring":[75],"such":[76,124],"problem.":[79,126],"These":[80],"can":[82,100,107],"cut":[86],"down":[87],"first.":[91],"Hence,":[92],"work":[94],"computing":[96],"simplified.":[102],"Then":[103],"simplified":[105],"converted":[109],"into":[110],"traditional":[111],"programming":[114],"problems":[115],"and":[116],"simple":[118],"procedure":[119],"proposed":[121],"optimizing":[123]},"counts_by_year":[{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}