{"id":"https://openalex.org/W4213334693","doi":"https://doi.org/10.3390/axioms11030089","title":"Modification of the Logarithm Methodology of Additive Weights (LMAW) by a Triangular Fuzzy Number and Its Application in Multi-Criteria Decision Making","display_name":"Modification of the Logarithm Methodology of Additive Weights (LMAW) by a Triangular Fuzzy Number and Its Application in Multi-Criteria Decision Making","publication_year":2022,"publication_date":"2022-02-23","ids":{"openalex":"https://openalex.org/W4213334693","doi":"https://doi.org/10.3390/axioms11030089"},"language":"en","primary_location":{"id":"doi:10.3390/axioms11030089","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11030089","pdf_url":"https://www.mdpi.com/2075-1680/11/3/89/pdf?version=1645761512","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"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":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/11/3/89/pdf?version=1645761512","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078330420","display_name":"Darko Bo\u017eani\u0107","orcid":"https://orcid.org/0000-0002-9657-0889"},"institutions":[{"id":"https://openalex.org/I4210153194","display_name":"University of Defence","ror":"https://ror.org/04mmq3h75","country_code":"RS","type":"education","lineage":["https://openalex.org/I4210153194"]}],"countries":["RS"],"is_corresponding":false,"raw_author_name":"Darko Bo\u017eani\u0107","raw_affiliation_strings":["Military Academy, University of Defence in Belgrade, 11000 Belgrade, Serbia"],"affiliations":[{"raw_affiliation_string":"Military Academy, University of Defence in Belgrade, 11000 Belgrade, Serbia","institution_ids":["https://openalex.org/I4210153194"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018974025","display_name":"Dragan Pamu\u010dar","orcid":"https://orcid.org/0000-0001-8522-1942"},"institutions":[{"id":"https://openalex.org/I4210153194","display_name":"University of Defence","ror":"https://ror.org/04mmq3h75","country_code":"RS","type":"education","lineage":["https://openalex.org/I4210153194"]}],"countries":["RS"],"is_corresponding":false,"raw_author_name":"Dragan Pamu\u010dar","raw_affiliation_strings":["Military Academy, University of Defence in Belgrade, 11000 Belgrade, Serbia"],"affiliations":[{"raw_affiliation_string":"Military Academy, University of Defence in Belgrade, 11000 Belgrade, Serbia","institution_ids":["https://openalex.org/I4210153194"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072015722","display_name":"Aleksandar Mili\u0107","orcid":"https://orcid.org/0000-0002-2642-0340"},"institutions":[{"id":"https://openalex.org/I4210153194","display_name":"University of Defence","ror":"https://ror.org/04mmq3h75","country_code":"RS","type":"education","lineage":["https://openalex.org/I4210153194"]}],"countries":["RS"],"is_corresponding":false,"raw_author_name":"Aleksandar Mili\u0107","raw_affiliation_strings":["Military Academy, University of Defence in Belgrade, 11000 Belgrade, Serbia"],"affiliations":[{"raw_affiliation_string":"Military Academy, University of Defence in Belgrade, 11000 Belgrade, Serbia","institution_ids":["https://openalex.org/I4210153194"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022372409","display_name":"Dragan Marinkovi\u0107","orcid":"https://orcid.org/0000-0002-3583-9434"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Dragan Marinkovi\u0107","raw_affiliation_strings":["Department of Structural Analysis, Technical University of Berlin, 10623 Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Structural Analysis, Technical University of Berlin, 10623 Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075599345","display_name":"Nenad Komazec","orcid":"https://orcid.org/0000-0001-9227-118X"},"institutions":[{"id":"https://openalex.org/I4210153194","display_name":"University of Defence","ror":"https://ror.org/04mmq3h75","country_code":"RS","type":"education","lineage":["https://openalex.org/I4210153194"]}],"countries":["RS"],"is_corresponding":false,"raw_author_name":"Nenad Komazec","raw_affiliation_strings":["Military Academy, University of Defence in Belgrade, 11000 Belgrade, Serbia"],"affiliations":[{"raw_affiliation_string":"Military Academy, University of Defence in Belgrade, 11000 Belgrade, Serbia","institution_ids":["https://openalex.org/I4210153194"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5022372409"],"corresponding_institution_ids":["https://openalex.org/I4577782"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":751,"currency":"EUR","value_usd":809},"fwci":11.6958,"has_fulltext":true,"cited_by_count":70,"citation_normalized_percentile":{"value":0.99047496,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"11","issue":"3","first_page":"89","last_page":"89"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9994000196456909,"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":0.9994000196456909,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9531999826431274,"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"}},{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9189000129699707,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6565055847167969},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.6359559893608093},{"id":"https://openalex.org/keywords/weighting","display_name":"Weighting","score":0.6016721725463867},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.5905880331993103},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.5734938979148865},{"id":"https://openalex.org/keywords/ranking","display_name":"Ranking (information retrieval)","score":0.5553250312805176},{"id":"https://openalex.org/keywords/defuzzification","display_name":"Defuzzification","score":0.5034536719322205},{"id":"https://openalex.org/keywords/sensitivity","display_name":"Sensitivity (control systems)","score":0.489018052816391},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4858352839946747},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.44191431999206543},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.29197922348976135},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.24597060680389404},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.181138277053833},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.07377421855926514}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6565055847167969},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.6359559893608093},{"id":"https://openalex.org/C183115368","wikidata":"https://www.wikidata.org/wiki/Q856577","display_name":"Weighting","level":2,"score":0.6016721725463867},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.5905880331993103},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5734938979148865},{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.5553250312805176},{"id":"https://openalex.org/C170260401","wikidata":"https://www.wikidata.org/wiki/Q5251735","display_name":"Defuzzification","level":5,"score":0.5034536719322205},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.489018052816391},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4858352839946747},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.44191431999206543},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29197922348976135},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.24597060680389404},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.181138277053833},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.07377421855926514},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C126838900","wikidata":"https://www.wikidata.org/wiki/Q77604","display_name":"Radiology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms11030089","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11030089","pdf_url":"https://www.mdpi.com/2075-1680/11/3/89/pdf?version=1645761512","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:41270626ed2f43c5843f9c329dd373b0","is_oa":true,"landing_page_url":"https://doaj.org/article/41270626ed2f43c5843f9c329dd373b0","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 11, Iss 3, p 89 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/11/3/89/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms11030089","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms; Volume 11; Issue 3; Pages: 89","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms11030089","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11030089","pdf_url":"https://www.mdpi.com/2075-1680/11/3/89/pdf?version=1645761512","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.8100000023841858,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[{"id":"https://openalex.org/G8330397625","display_name":null,"funder_award_id":"Funding","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320324094","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4213334693.pdf","grobid_xml":"https://content.openalex.org/works/W4213334693.grobid-xml"},"referenced_works_count":51,"referenced_works":["https://openalex.org/W38708963","https://openalex.org/W1524771255","https://openalex.org/W1748537427","https://openalex.org/W2002929769","https://openalex.org/W2022032472","https://openalex.org/W2033401964","https://openalex.org/W2041280856","https://openalex.org/W2056258586","https://openalex.org/W2066495914","https://openalex.org/W2073945238","https://openalex.org/W2083624225","https://openalex.org/W2096011273","https://openalex.org/W2144472000","https://openalex.org/W2327347366","https://openalex.org/W2332088957","https://openalex.org/W2334204898","https://openalex.org/W2510799815","https://openalex.org/W2559560406","https://openalex.org/W2605207615","https://openalex.org/W2919574594","https://openalex.org/W2944037155","https://openalex.org/W2997546710","https://openalex.org/W3003452991","https://openalex.org/W3006730176","https://openalex.org/W3009462382","https://openalex.org/W3015393762","https://openalex.org/W3030459390","https://openalex.org/W3092427834","https://openalex.org/W3101857030","https://openalex.org/W3109308806","https://openalex.org/W3125705824","https://openalex.org/W3135978863","https://openalex.org/W3138299418","https://openalex.org/W3156565247","https://openalex.org/W3158073486","https://openalex.org/W3161270683","https://openalex.org/W3161894236","https://openalex.org/W3167828116","https://openalex.org/W3176573844","https://openalex.org/W3182846189","https://openalex.org/W3186816969","https://openalex.org/W3203399525","https://openalex.org/W3207660825","https://openalex.org/W3211959137","https://openalex.org/W4206573739","https://openalex.org/W4211007335","https://openalex.org/W4214624437","https://openalex.org/W6655805609","https://openalex.org/W6671553121","https://openalex.org/W6701162952","https://openalex.org/W6785567397"],"related_works":["https://openalex.org/W2773005380","https://openalex.org/W4388451300","https://openalex.org/W2060361571","https://openalex.org/W1879432897","https://openalex.org/W2256857057","https://openalex.org/W3167814444","https://openalex.org/W3176863924","https://openalex.org/W2023513928","https://openalex.org/W2182392910","https://openalex.org/W4361984403"],"abstract_inverted_index":{"The":[0,38,54,90,114,278],"Logarithm":[1],"Methodology":[2],"of":[3,44,57,81,98,111,116,125,167,175,189,192,202,210,235,239,254,264,270,284],"Additive":[4,131],"Weights":[5],"(LMAW)":[6],"method":[7,12,28,47,59,91,206],"is":[8,18,60,72],"a":[9,63,103],"very":[10],"young":[11],"and":[13,83,155,177,221,256],"in":[14,51,62,87,94,108,223,249],"its":[15],"basic":[16],"form":[17],"defined":[19],"for":[20,102],"crisp":[21],"values.":[22],"In":[23,182],"this":[24],"paper,":[25],"the":[26,42,45,58,96,99,112,117,128,135,143,149,156,172,187,190,199,203,215,226,229,233,236,243,251,262,268,274,282,285],"LMAW":[27,46,205],"was":[29,92,120,195],"improved":[30,41],"by":[31,123,165,170],"being":[32],"modified":[33,286],"with":[34,76,127,184,267],"triangular":[35],"fuzzy":[36,144,150,157,204],"numbers.":[37],"modification":[39],"significantly":[40],"capacity":[43],"to":[48,69,74,208],"consider":[49],"uncertainty":[50],"decision":[52],"making.":[53],"special":[55,200],"importance":[56,201],"reflected":[61],"relatively":[64],"simple":[65],"mathematical":[66],"apparatus":[67],"due":[68],"which":[70,197],"it":[71,257],"possible":[73],"define,":[75],"high":[77],"quality,":[78],"weight":[79,173,237,252],"coefficients":[80,174,238,253],"criteria":[82],"rank":[84],"alternative":[85,193],"solutions":[86,194],"uncertain":[88],"environments.":[89],"tested":[93],"solving":[95],"problem":[97],"location":[100],"selection":[101],"landing":[104],"operations":[105,110],"point":[106],"(LOP)":[107],"combat":[109],"army.":[113],"validation":[115,263],"obtained":[118,275],"results":[119,265,280],"performed:":[121],"(1)":[122],"means":[124,166],"comparison":[126,183],"Fuzzy":[129,136],"Simple":[130],"Weighting":[132],"(FSAW)":[133],"Method,":[134],"Multi-Attributive":[137],"Border":[138],"Approximation":[139],"area":[140],"Comparison":[141],"(FMABAC),":[142],"Vi\u0161ekriterijumsko":[145],"KOmpromisno":[146],"Rangiranje":[147],"(FVIKOR),":[148],"COmpressed":[151],"PRoportional":[152],"ASsessment":[153],"(FCOPRAS),":[154],"Multi":[158],"Attributive":[159],"Ideal-Real":[160],"Comparative":[161],"Analysis":[162],"(FMAIRCA);":[163],"(2)":[164],"sensitivity":[168,230],"analysis":[169],"changing":[171,234],"criteria;":[176],"(3)":[178],"using":[179],"simulation":[180,271],"software.":[181],"other":[185,227],"methods,":[186,213],"quality":[188,283],"ranking":[191],"confirmed,":[196],"highlighted":[198],"relative":[207],"that":[209,217,242],"certain":[211],"standard":[212],"respectively,":[214],"ones":[216],"are":[218],"often":[219],"used":[220],"confirmed":[222,273,281],"practice.":[224],"On":[225],"hand,":[228],"analysis,":[231],"including":[232],"criteria,":[240,255],"showed":[241],"model":[244],"could":[245],"tolerate":[246],"smaller":[247],"errors":[248],"defining":[250],"provided":[258],"stable":[259],"results.":[260,277],"Finally,":[261],"achieved":[266],"use":[269],"software":[272],"output":[276,279],"method.":[287]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":24},{"year":2024,"cited_by_count":18},{"year":2023,"cited_by_count":21},{"year":2022,"cited_by_count":6}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
