{"id":"https://openalex.org/W1980775764","doi":"https://doi.org/10.1109/tfuzz.2009.2031561","title":"Latticized Linear Optimization on the Unit Interval","display_name":"Latticized Linear Optimization on the Unit Interval","publication_year":2009,"publication_date":"2009-09-09","ids":{"openalex":"https://openalex.org/W1980775764","doi":"https://doi.org/10.1109/tfuzz.2009.2031561","mag":"1980775764"},"language":"en","primary_location":{"id":"doi:10.1109/tfuzz.2009.2031561","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2009.2031561","pdf_url":null,"source":{"id":"https://openalex.org/S134177497","display_name":"IEEE Transactions on Fuzzy Systems","issn_l":"1063-6706","issn":["1063-6706","1941-0034"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Fuzzy 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/A5013548183","display_name":"Pingke Li","orcid":"https://orcid.org/0000-0003-2244-3139"},"institutions":[{"id":"https://openalex.org/I137902535","display_name":"North Carolina State University","ror":"https://ror.org/04tj63d06","country_code":"US","type":"education","lineage":["https://openalex.org/I137902535"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Pingke Li","raw_affiliation_strings":["Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC, USA"],"affiliations":[{"raw_affiliation_string":"Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC, USA","institution_ids":["https://openalex.org/I137902535"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110625824","display_name":"Shu-Cherng Fang","orcid":null},"institutions":[{"id":"https://openalex.org/I137902535","display_name":"North Carolina State University","ror":"https://ror.org/04tj63d06","country_code":"US","type":"education","lineage":["https://openalex.org/I137902535"]},{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN","US"],"is_corresponding":false,"raw_author_name":"Shu-Cherng Fang","raw_affiliation_strings":["Department of Industrial Engineering, Tsinghua University, Beijing, China","Edward P. Fitts Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC, USA"],"affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"Edward P. Fitts Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC, USA","institution_ids":["https://openalex.org/I137902535"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5013548183"],"corresponding_institution_ids":["https://openalex.org/I137902535"],"apc_list":null,"apc_paid":null,"fwci":2.0567,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.85868341,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"17","issue":"6","first_page":"1353","last_page":"1365"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9987000226974487,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9987000226974487,"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/T10050","display_name":"Multi-Criteria Decision Making","score":0.9976000189781189,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9976000189781189,"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":0.7476791143417358},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.5903424620628357},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.5901613831520081},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.5844323635101318},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5736044645309448},{"id":"https://openalex.org/keywords/solution-set","display_name":"Solution set","score":0.48973512649536133},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.48847949504852295},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.45477670431137085},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.446128249168396},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37035682797431946},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.3562876582145691},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19710451364517212},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.11706596612930298},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08779889345169067}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7476791143417358},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.5903424620628357},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.5901613831520081},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.5844323635101318},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5736044645309448},{"id":"https://openalex.org/C60033838","wikidata":"https://www.wikidata.org/wiki/Q1751685","display_name":"Solution set","level":3,"score":0.48973512649536133},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.48847949504852295},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.45477670431137085},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.446128249168396},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37035682797431946},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3562876582145691},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19710451364517212},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.11706596612930298},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08779889345169067},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tfuzz.2009.2031561","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2009.2031561","pdf_url":null,"source":{"id":"https://openalex.org/S134177497","display_name":"IEEE Transactions on Fuzzy Systems","issn_l":"1063-6706","issn":["1063-6706","1941-0034"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Fuzzy Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":67,"referenced_works":["https://openalex.org/W16272443","https://openalex.org/W18454675","https://openalex.org/W127405698","https://openalex.org/W148896681","https://openalex.org/W170294950","https://openalex.org/W262427364","https://openalex.org/W294994052","https://openalex.org/W409549338","https://openalex.org/W657218221","https://openalex.org/W1492076504","https://openalex.org/W1531600119","https://openalex.org/W1557098843","https://openalex.org/W1557235141","https://openalex.org/W1670369968","https://openalex.org/W1883105143","https://openalex.org/W1898259180","https://openalex.org/W1970676534","https://openalex.org/W1975873416","https://openalex.org/W1976430007","https://openalex.org/W1982657605","https://openalex.org/W1982911645","https://openalex.org/W1991241876","https://openalex.org/W1991475392","https://openalex.org/W1992081763","https://openalex.org/W1997511955","https://openalex.org/W2006973411","https://openalex.org/W2012201562","https://openalex.org/W2012628629","https://openalex.org/W2017076901","https://openalex.org/W2017703673","https://openalex.org/W2017831479","https://openalex.org/W2018323950","https://openalex.org/W2019716713","https://openalex.org/W2021027318","https://openalex.org/W2022011877","https://openalex.org/W2029338278","https://openalex.org/W2033869664","https://openalex.org/W2035096056","https://openalex.org/W2039018525","https://openalex.org/W2044454580","https://openalex.org/W2044684553","https://openalex.org/W2045459931","https://openalex.org/W2046108253","https://openalex.org/W2048845413","https://openalex.org/W2049053995","https://openalex.org/W2050942211","https://openalex.org/W2054416947","https://openalex.org/W2059287801","https://openalex.org/W2061590216","https://openalex.org/W2061821032","https://openalex.org/W2066323671","https://openalex.org/W2075826824","https://openalex.org/W2080947358","https://openalex.org/W2090700466","https://openalex.org/W2094360224","https://openalex.org/W2107293082","https://openalex.org/W2113250809","https://openalex.org/W2149872567","https://openalex.org/W2150002615","https://openalex.org/W2159441390","https://openalex.org/W2159755457","https://openalex.org/W2476538616","https://openalex.org/W2496338429","https://openalex.org/W2969808124","https://openalex.org/W4234672050","https://openalex.org/W6609651869","https://openalex.org/W6767454909"],"related_works":["https://openalex.org/W2009525028","https://openalex.org/W4321064619","https://openalex.org/W4301895170","https://openalex.org/W2163760347","https://openalex.org/W2048118513","https://openalex.org/W1520530328","https://openalex.org/W2809086605","https://openalex.org/W4390789936","https://openalex.org/W2371647654","https://openalex.org/W2321794351"],"abstract_inverted_index":{"This":[0],"paper":[1],"considers":[2],"the":[3,46,61,94,101],"latticized":[4],"linear":[5],"optimization":[6,18,123],"(LLO)":[7],"problem":[8,36],"and":[9,75,121,124],"its":[10],"variants,":[11],"which":[12],"are":[13,127],"a":[14,35,50,76,114],"special":[15],"class":[16],"of":[17,63,79,103],"problems":[19],"constrained":[20],"by":[21,70],"fuzzy":[22],"relational":[23],"equations":[24],"or":[25],"inequalities.":[26],"We":[27,57],"show":[28,59],"that":[29,60],"an":[30,109],"optimal":[31,65,73,81,85,95,106],"solution":[32,74,86],"to":[33],"such":[34],"can":[37,87],"be":[38,88],"obtained":[39],"in":[40,90,108],"polynomial":[41,91],"time":[42,92],"as":[43,45,113],"long":[44],"objective":[47,96],"function":[48,52],"is":[49,67,98],"max-separable":[51,122],"with":[53],"continuous":[54],"monotone":[55],"components.":[56],"further":[58],"set":[62],"all":[64,104],"solutions":[66,107],"fully":[68],"determined":[69],"one":[71],"maximum":[72,84],"finite":[77],"number":[78],"minimal":[80,105],"solutions.":[82],"The":[83,117],"constructed":[89],"once":[93],"value":[97],"known,":[99],"while":[100],"detection":[102],"efficient":[110],"manner":[111],"remains":[112],"challenging":[115],"problem.":[116],"relation":[118],"between":[119],"LLO":[120],"related":[125],"issues":[126],"also":[128],"investigated.":[129]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":4},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}