{"id":"https://openalex.org/W1965647950","doi":"https://doi.org/10.1142/s0218488504002837","title":"LINEAR COORDINATION METHOD FOR FUZZY MULTI-OBJECTIVE LINEAR PROGRAMMING PROBLEMS WITH CONVEX POLYHEDRAL MEMBERSHIP FUNCTIONS","display_name":"LINEAR COORDINATION METHOD FOR FUZZY MULTI-OBJECTIVE LINEAR PROGRAMMING PROBLEMS WITH CONVEX POLYHEDRAL MEMBERSHIP FUNCTIONS","publication_year":2004,"publication_date":"2004-06-01","ids":{"openalex":"https://openalex.org/W1965647950","doi":"https://doi.org/10.1142/s0218488504002837","mag":"1965647950"},"language":"en","primary_location":{"id":"doi:10.1142/s0218488504002837","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218488504002837","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/A5018204443","display_name":"Busaba Phruksaphanrat","orcid":"https://orcid.org/0000-0002-3600-2943"},"institutions":[{"id":"https://openalex.org/I108108428","display_name":"Thammasat University","ror":"https://ror.org/002yp7f20","country_code":"TH","type":"education","lineage":["https://openalex.org/I108108428"]}],"countries":["TH"],"is_corresponding":true,"raw_author_name":"BUSABA PHRUKSAPHANRAT","raw_affiliation_strings":["Industrial Engineering Department,  Faculty of Engineering, Thammasat University,  Kloang Luang, Pathumthani 12121, Thailand","Industrial Engineering Department, Faculty of Engineering, Thammasat University, Kloang Luang, Pathumthani 12121, Thailand"],"affiliations":[{"raw_affiliation_string":"Industrial Engineering Department,  Faculty of Engineering, Thammasat University,  Kloang Luang, Pathumthani 12121, Thailand","institution_ids":["https://openalex.org/I108108428"]},{"raw_affiliation_string":"Industrial Engineering Department, Faculty of Engineering, Thammasat University, Kloang Luang, Pathumthani 12121, Thailand","institution_ids":["https://openalex.org/I108108428"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043080785","display_name":"Ario Ohsato","orcid":null},"institutions":[{"id":"https://openalex.org/I85922643","display_name":"Nagaoka University of Technology","ror":"https://ror.org/00ys1hz88","country_code":"JP","type":"education","lineage":["https://openalex.org/I85922643"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"ARIO OHSATO","raw_affiliation_strings":["Department of Management and Information Systems Science, Nagaoka University of Technology,  1603-1, Kami-Tomioka, Nagaoka, Niigata 940-2188, Japan","Department of Management and Information Systems Science, Nagaoka University of Technology, 1603-1, Kami-Tomioka, Nagaoka, Niigata 940-2188, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Management and Information Systems Science, Nagaoka University of Technology,  1603-1, Kami-Tomioka, Nagaoka, Niigata 940-2188, Japan","institution_ids":["https://openalex.org/I85922643"]},{"raw_affiliation_string":"Department of Management and Information Systems Science, Nagaoka University of Technology, 1603-1, Kami-Tomioka, Nagaoka, Niigata 940-2188, Japan","institution_ids":["https://openalex.org/I85922643"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5018204443"],"corresponding_institution_ids":["https://openalex.org/I108108428"],"apc_list":null,"apc_paid":null,"fwci":1.7385,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.85658824,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"12","issue":"03","first_page":"269","last_page":"285"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9991000294685364,"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":0.9991000294685364,"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/T10050","display_name":"Multi-Criteria Decision Making","score":0.9970999956130981,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9879999756813049,"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":0.6836234927177429},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6588060259819031},{"id":"https://openalex.org/keywords/membership-function","display_name":"Membership function","score":0.6448174715042114},{"id":"https://openalex.org/keywords/proper-convex-function","display_name":"Proper convex function","score":0.5441551804542542},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.5197343826293945},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.5086556077003479},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.5016582012176514},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.49049633741378784},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.48111671209335327},{"id":"https://openalex.org/keywords/subderivative","display_name":"Subderivative","score":0.47962459921836853},{"id":"https://openalex.org/keywords/satisficing","display_name":"Satisficing","score":0.4758017957210541},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.43636026978492737},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.4143153429031372},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.38871458172798157},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.27444955706596375},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2309316098690033},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11299517750740051}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6836234927177429},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6588060259819031},{"id":"https://openalex.org/C5263885","wikidata":"https://www.wikidata.org/wiki/Q1967302","display_name":"Membership function","level":4,"score":0.6448174715042114},{"id":"https://openalex.org/C50862404","wikidata":"https://www.wikidata.org/wiki/Q3075259","display_name":"Proper convex function","level":5,"score":0.5441551804542542},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.5197343826293945},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.5086556077003479},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.5016582012176514},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.49049633741378784},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.48111671209335327},{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.47962459921836853},{"id":"https://openalex.org/C94822996","wikidata":"https://www.wikidata.org/wiki/Q1777902","display_name":"Satisficing","level":2,"score":0.4758017957210541},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.43636026978492737},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.4143153429031372},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.38871458172798157},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.27444955706596375},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2309316098690033},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11299517750740051},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218488504002837","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218488504002837","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":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.75}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W68537122","https://openalex.org/W1487465581","https://openalex.org/W1963652112","https://openalex.org/W1977310087","https://openalex.org/W1988131669","https://openalex.org/W1991564569","https://openalex.org/W1993841150","https://openalex.org/W1999571264","https://openalex.org/W2000191646","https://openalex.org/W2001368153","https://openalex.org/W2002531900","https://openalex.org/W2005108373","https://openalex.org/W2006092425","https://openalex.org/W2021341221","https://openalex.org/W2022822758","https://openalex.org/W2026033545","https://openalex.org/W2029244406","https://openalex.org/W2033591598","https://openalex.org/W2038564152","https://openalex.org/W2041210202","https://openalex.org/W2041442835","https://openalex.org/W2043453164","https://openalex.org/W2048808726","https://openalex.org/W2054111873","https://openalex.org/W2062366157","https://openalex.org/W2064141091","https://openalex.org/W2072994800","https://openalex.org/W2076994513","https://openalex.org/W2086646689","https://openalex.org/W2088240994","https://openalex.org/W2091120028","https://openalex.org/W2094476259","https://openalex.org/W2096768134","https://openalex.org/W2099867994","https://openalex.org/W2142159867","https://openalex.org/W2320115115","https://openalex.org/W2335677820","https://openalex.org/W4229859894","https://openalex.org/W4255037432","https://openalex.org/W4292158025"],"related_works":["https://openalex.org/W2007576447","https://openalex.org/W2026600343","https://openalex.org/W2356261519","https://openalex.org/W4382519084","https://openalex.org/W2045422358","https://openalex.org/W4361807553","https://openalex.org/W165488893","https://openalex.org/W2040676043","https://openalex.org/W1510770274","https://openalex.org/W2185500298"],"abstract_inverted_index":{"A":[0],"fuzzy":[1,21,28,172],"multi-objective":[2,173],"decision-making":[3],"with":[4,141,181],"nonlinear":[5],"membership":[6,36,70,77,84,91,147,155],"functions":[7,78,92,156],"is":[8,50],"proposed":[9,150],"in":[10,176],"this":[11],"paper":[12],"by":[13,33,41,113],"assuming":[14],"that":[15,93],"the":[16,47,98,101,121,125,142,146,162,167,182],"decision":[17,126,163],"maker":[18],"has":[19],"a":[20,54,67,177],"goal":[22],"for":[23,124,171],"each":[24],"objective":[25],"function.":[26,71],"The":[27,44,72,107,149],"goals":[29],"can":[30,61,94,110,119,129],"be":[31,63,82,95,111,130],"quantified":[32],"convex":[34,48,56,68,89,153,187],"polyhedral":[35,57,69,90,154],"functions,":[37],"which":[38,60,128],"are":[39,79],"expressed":[40],"linguistic":[42],"terms.":[43],"concept":[45],"of":[46,76,86,88,100,103,161],"cone":[49],"used":[51],"to":[52,81,157],"formulate":[53],"normalized":[55],"penalty":[58],"function,":[59],"also":[62],"considered":[64],"conversely":[65],"as":[66,97],"most":[73],"desirable":[74],"value":[75],"selected":[80],"reference":[83,104],"values":[85],"achievement":[87],"viewed":[96],"extension":[99],"idea":[102],"point":[105],"method.":[106],"formulated":[108],"model":[109,151],"solved":[112],"existing":[114,168],"linear":[115,174],"programming":[116,175],"solvers":[117],"and":[118],"find":[120],"satisficing":[122,169],"solution":[123,138],"maker,":[127],"derived":[131],"efficiently":[132],"from":[133],"among":[134],"an":[135],"M-Pareto":[136],"optimal":[137],"set":[139],"together":[140],"trade-off":[143],"rates":[144],"between":[145],"functions.":[148],"uses":[152],"represent":[158],"vague":[159],"aspirations":[160],"maker.":[164],"It":[165],"enriches":[166],"methods":[170],"more":[178],"practical":[179],"way":[180],"effective":[183],"method":[184],"based":[185],"on":[186],"cone.":[188]},"counts_by_year":[{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}