{"id":"https://openalex.org/W3048011900","doi":"https://doi.org/10.3390/math8081319","title":"A Piecewise Linear FGM Approach for Efficient and Accurate FAHP Analysis: Smart Backpack Design as an Example","display_name":"A Piecewise Linear FGM Approach for Efficient and Accurate FAHP Analysis: Smart Backpack Design as an Example","publication_year":2020,"publication_date":"2020-08-08","ids":{"openalex":"https://openalex.org/W3048011900","doi":"https://doi.org/10.3390/math8081319","mag":"3048011900"},"language":"en","primary_location":{"id":"doi:10.3390/math8081319","doi":"https://doi.org/10.3390/math8081319","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math8081319","pdf_url":"https://www.mdpi.com/2227-7390/8/8/1319/pdf?version=1596877341","source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2227-7390/8/8/1319/pdf?version=1596877341","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111974309","display_name":"Hsin-Chieh Wu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I126145234","display_name":"Chaoyang University of Technology","ror":"https://ror.org/04xwksx09","country_code":"TW","type":"education","lineage":["https://openalex.org/I126145234"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Hsin-Chieh Wu","raw_affiliation_strings":["Department of Industrial Engineering and Management, Chaoyang University of Technology, Taichung 41349, Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering and Management, Chaoyang University of Technology, Taichung 41349, Taiwan","institution_ids":["https://openalex.org/I126145234"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037831741","display_name":"Toly Chen","orcid":"https://orcid.org/0000-0002-5608-5176","observed_orcids":["https://orcid.org/0000-0002-5608-5176","https://orcid.org/0000-0003-1466-6519"]},"institutions":[{"id":"https://openalex.org/I148366613","display_name":"National Yang Ming Chiao Tung University","ror":"https://ror.org/00se2k293","country_code":"TW","type":"education","lineage":["https://openalex.org/I148366613"]}],"countries":["TW"],"is_corresponding":true,"raw_author_name":"Toly Chen","raw_affiliation_strings":["Department of Industrial Engineering and Management, National Chiao Tung University, 1001, University Road, Hsinchu 300, Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering and Management, National Chiao Tung University, 1001, University Road, Hsinchu 300, Taiwan","institution_ids":["https://openalex.org/I148366613"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110703379","display_name":"Chin-Hau Huang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I148366613","display_name":"National Yang Ming Chiao Tung University","ror":"https://ror.org/00se2k293","country_code":"TW","type":"education","lineage":["https://openalex.org/I148366613"]},{"id":"https://openalex.org/I207776796","display_name":"Overseas Chinese University","ror":"https://ror.org/01j9jq089","country_code":"TW","type":"education","lineage":["https://openalex.org/I207776796"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Chin-Hau Huang","raw_affiliation_strings":["Department of Computer-Aided Industrial Design, Overseas Chinese University, 100, Chiao Kwang Road, Seatwen, Taichung City 407, Taiwan","Department of Industrial Engineering and Management, National Chiao Tung University, 1001, University Road, Hsinchu 300, Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer-Aided Industrial Design, Overseas Chinese University, 100, Chiao Kwang Road, Seatwen, Taichung City 407, Taiwan","institution_ids":["https://openalex.org/I207776796"]},{"raw_affiliation_string":"Department of Industrial Engineering and Management, National Chiao Tung University, 1001, University Road, Hsinchu 300, Taiwan","institution_ids":["https://openalex.org/I148366613"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5037831741"],"corresponding_institution_ids":["https://openalex.org/I148366613"],"apc_list":{"value":1200,"currency":"CHF","value_usd":1267},"apc_paid":{"value":1200,"currency":"CHF","value_usd":1267},"fwci":3.4991,"has_fulltext":true,"cited_by_count":28,"citation_normalized_percentile":{"value":0.93166813,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"8","issue":"8","first_page":"1319","last_page":"1319"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9990000128746033,"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":0.9990000128746033,"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":0.00019999999494757503,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":9.999999747378752e-05,"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/fuzzy-analytic-hierarchy-process","display_name":"fuzzy analytic hierarchy process","score":0.8119999766349792},{"id":"https://openalex.org/keywords/triangular-fuzzy-numbers","display_name":"triangular fuzzy numbers","score":0.9150000214576721},{"id":"https://openalex.org/keywords/membership-functions","display_name":"membership functions","score":0.6790000200271606},{"id":"https://openalex.org/keywords/multi-criteria-decision-making","display_name":"multi-criteria decision making","score":0.8849999904632568}],"concepts":[{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.6859605312347412},{"id":"https://openalex.org/C2780345887","wikidata":"https://www.wikidata.org/wiki/Q5843","display_name":"Backpack","level":2,"score":0.66408371925354},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6256818175315857},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.6017839312553406},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5836189389228821},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.5777292251586914},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5225833654403687},{"id":"https://openalex.org/C170260401","wikidata":"https://www.wikidata.org/wiki/Q5251735","display_name":"Defuzzification","level":5,"score":0.4757532775402069},{"id":"https://openalex.org/C127385683","wikidata":"https://www.wikidata.org/wiki/Q1475696","display_name":"Fuzzy classification","level":4,"score":0.41622394323349},{"id":"https://openalex.org/C148671577","wikidata":"https://www.wikidata.org/wiki/Q5511133","display_name":"Fuzzy set operations","level":4,"score":0.41476526856422424},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38292425870895386},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.35913586616516113},{"id":"https://openalex.org/C195975749","wikidata":"https://www.wikidata.org/wiki/Q1475705","display_name":"Fuzzy control system","level":3,"score":0.3331141471862793},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.3325154781341553},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.17198503017425537},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.14480045437812805},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/math8081319","doi":"https://doi.org/10.3390/math8081319","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math8081319","pdf_url":"https://www.mdpi.com/2227-7390/8/8/1319/pdf?version=1596877341","source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:gam:jmathe:v:8:y:2020:i:8:p:1319-:d:396298","doi":null,"is_oa":false,"landing_page_url":"https://www.mdpi.com/2227-7390/8/8/1319/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:2748df06cdab4054bb76b474e08b0cdf","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/2748df06cdab4054bb76b474e08b0cdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics, Vol 8, Iss 8, p 1319 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/math8081319","doi":"https://doi.org/10.3390/math8081319","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math8081319","pdf_url":"https://www.mdpi.com/2227-7390/8/8/1319/pdf?version=1596877341","source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322795","display_name":"Ministry of Science and Technology, Taiwan","ror":"https://ror.org/02kv4zf79"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3048011900.pdf","grobid_xml":"https://content.openalex.org/works/W3048011900.grobid-xml"},"referenced_works_count":46,"referenced_works":["https://openalex.org/W1972494505","https://openalex.org/W1977955720","https://openalex.org/W1994119659","https://openalex.org/W2001468102","https://openalex.org/W2014720154","https://openalex.org/W2025874826","https://openalex.org/W2028983668","https://openalex.org/W2032711326","https://openalex.org/W2034767759","https://openalex.org/W2034960640","https://openalex.org/W2042510122","https://openalex.org/W2059536960","https://openalex.org/W2068123185","https://openalex.org/W2078728013","https://openalex.org/W2079259391","https://openalex.org/W2080151622","https://openalex.org/W2081331155","https://openalex.org/W2085599369","https://openalex.org/W2130505148","https://openalex.org/W2170866269","https://openalex.org/W2514651717","https://openalex.org/W2518733171","https://openalex.org/W2619238644","https://openalex.org/W2747385025","https://openalex.org/W2763125701","https://openalex.org/W2792598011","https://openalex.org/W2795626005","https://openalex.org/W2887760402","https://openalex.org/W2889331931","https://openalex.org/W2911454810","https://openalex.org/W2914386580","https://openalex.org/W2940306124","https://openalex.org/W2953417725","https://openalex.org/W2970677793","https://openalex.org/W2980793946","https://openalex.org/W2982331550","https://openalex.org/W2986110788","https://openalex.org/W2992003758","https://openalex.org/W2998163240","https://openalex.org/W3004264460","https://openalex.org/W3005116743","https://openalex.org/W3006436526","https://openalex.org/W3011915539","https://openalex.org/W3015965366","https://openalex.org/W4240253636","https://openalex.org/W4243985074"],"related_works":["https://openalex.org/W2905886997","https://openalex.org/W2033447266","https://openalex.org/W3048770278","https://openalex.org/W2077855710","https://openalex.org/W2351598539","https://openalex.org/W2070006564","https://openalex.org/W2607479150","https://openalex.org/W3023613191","https://openalex.org/W2041452260","https://openalex.org/W2980793946"],"abstract_inverted_index":{"Most":[0],"existing":[1],"fuzzy":[2,8,13,23,42,49,67,83,129],"AHP":[3],"(FAHP)":[4],"methods":[5],"use":[6],"triangular":[7],"numbers":[9],"to":[10,33,102,114],"approximate":[11],"the":[12,35,41,46,63,81,93,103,115,118,122,128],"priorities":[14,43,68,84,130],"of":[15,39,44,66,105,126,131],"criteria,":[16,45],"which":[17],"is":[18,54],"inaccurate.":[19],"To":[20],"obtain":[21],"accurate":[22],"priorities,":[24],"time-consuming":[25],"alpha-cut":[26],"operations":[27],"are":[28],"usually":[29],"required.":[30],"In":[31],"order":[32],"improve":[34],"accuracy":[36,123],"and":[37,69,124,137],"efficiency":[38,125],"estimating":[40,127],"piecewise":[47,87],"linear":[48,88],"geometric":[50],"mean":[51],"(PLFGM)":[52],"approach":[53,98,120],"proposed":[55],"in":[56],"this":[57],"study.":[58],"The":[59,96],"PLFGM":[60,97,119],"method":[61],"estimates":[62],"\u03b1":[64,73],"cuts":[65,74],"then":[70],"connects":[71],"these":[72,132],"with":[75],"straight":[76],"lines.":[77],"As":[78],"a":[79,109],"result,":[80],"estimated":[82],"will":[85],"have":[86],"membership":[89],"functions":[90],"that":[91],"resemble":[92],"real":[94],"shapes.":[95],"has":[99],"been":[100],"applied":[101],"identification":[104],"critical":[106,133],"features":[107,134],"for":[108],"smart":[110],"backpack":[111],"design.":[112],"According":[113],"experimental":[116],"results,":[117],"improved":[121],"by":[135],"33%":[136],"80%,":[138],"respectively.":[139]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":4}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2020-08-13T00:00:00"}