{"id":"https://openalex.org/W2176394242","doi":"https://doi.org/10.1109/fuzz-ieee.2015.7338097","title":"Heavy weighted geometric aggregation operators in analytic hierarchy process-group decision making","display_name":"Heavy weighted geometric aggregation operators in analytic hierarchy process-group decision making","publication_year":2015,"publication_date":"2015-08-01","ids":{"openalex":"https://openalex.org/W2176394242","doi":"https://doi.org/10.1109/fuzz-ieee.2015.7338097","mag":"2176394242"},"language":"en","primary_location":{"id":"doi:10.1109/fuzz-ieee.2015.7338097","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fuzz-ieee.2015.7338097","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)","raw_type":"proceedings-article"},"type":"conference-paper","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/A5084859378","display_name":"Binyamin Yusoff","orcid":"https://orcid.org/0000-0002-3899-1474"},"institutions":[{"id":"https://openalex.org/I42134832","display_name":"Barcelona School of Economics","ror":"https://ror.org/02k09n368","country_code":"ES","type":"education","lineage":["https://openalex.org/I42134832"]},{"id":"https://openalex.org/I71999127","display_name":"Universitat de Barcelona","ror":"https://ror.org/021018s57","country_code":"ES","type":"education","lineage":["https://openalex.org/I71999127"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Binyamin Yusoff","raw_affiliation_strings":["Department of Mathematical Economics & Finance, University of Barcelona, Barcelona, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Economics & Finance, University of Barcelona, Barcelona, Spain","institution_ids":["https://openalex.org/I42134832","https://openalex.org/I71999127"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076412373","display_name":"Jos\u00e9 M. Merig\u00f3","orcid":"https://orcid.org/0000-0002-4672-6961"},"institutions":[{"id":"https://openalex.org/I69737025","display_name":"University of Chile","ror":"https://ror.org/047gc3g35","country_code":"CL","type":"education","lineage":["https://openalex.org/I69737025"]}],"countries":["CL"],"is_corresponding":false,"raw_author_name":"Jose M. Merigo Lindahl","raw_affiliation_strings":["Department of Management Control & Information Systems, University of Chile, Santiago de Chile, CL"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Management Control & Information Systems, University of Chile, Santiago de Chile, CL","institution_ids":["https://openalex.org/I69737025"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"7","issue":null,"first_page":"1","last_page":"6"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9997000098228455,"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":0.9997000098228455,"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/T13955","display_name":"Evaluation Methods in Various Fields","score":0.9746999740600586,"subfield":{"id":"https://openalex.org/subfields/2302","display_name":"Ecological Modeling"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9620000123977661,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/analytic-hierarchy-process","display_name":"Analytic hierarchy process","score":0.8158893585205078},{"id":"https://openalex.org/keywords/weighted-geometric-mean","display_name":"Weighted geometric mean","score":0.7903429269790649},{"id":"https://openalex.org/keywords/weighting","display_name":"Weighting","score":0.7257896661758423},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.6622484922409058},{"id":"https://openalex.org/keywords/geometric-mean","display_name":"Geometric mean","score":0.6065936088562012},{"id":"https://openalex.org/keywords/reciprocal","display_name":"Reciprocal","score":0.6023606061935425},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5487540364265442},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5417000651359558},{"id":"https://openalex.org/keywords/weighted-arithmetic-mean","display_name":"Weighted arithmetic mean","score":0.4904591739177704},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.44568973779678345},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.4418216347694397},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.4310220777988434},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41471320390701294},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14011558890342712},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.13050246238708496},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12133750319480896},{"id":"https://openalex.org/keywords/operations-research","display_name":"Operations research","score":0.08517181873321533}],"concepts":[{"id":"https://openalex.org/C87345402","wikidata":"https://www.wikidata.org/wiki/Q485202","display_name":"Analytic hierarchy process","level":2,"score":0.8158893585205078},{"id":"https://openalex.org/C117656884","wikidata":"https://www.wikidata.org/wiki/Q2625569","display_name":"Weighted geometric mean","level":3,"score":0.7903429269790649},{"id":"https://openalex.org/C183115368","wikidata":"https://www.wikidata.org/wiki/Q856577","display_name":"Weighting","level":2,"score":0.7257896661758423},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.6622484922409058},{"id":"https://openalex.org/C40222840","wikidata":"https://www.wikidata.org/wiki/Q185049","display_name":"Geometric mean","level":2,"score":0.6065936088562012},{"id":"https://openalex.org/C2777742833","wikidata":"https://www.wikidata.org/wiki/Q1964083","display_name":"Reciprocal","level":2,"score":0.6023606061935425},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5487540364265442},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5417000651359558},{"id":"https://openalex.org/C9490382","wikidata":"https://www.wikidata.org/wiki/Q729113","display_name":"Weighted arithmetic mean","level":2,"score":0.4904591739177704},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.44568973779678345},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4418216347694397},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.4310220777988434},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41471320390701294},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14011558890342712},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.13050246238708496},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12133750319480896},{"id":"https://openalex.org/C42475967","wikidata":"https://www.wikidata.org/wiki/Q194292","display_name":"Operations research","level":1,"score":0.08517181873321533},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"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/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/fuzz-ieee.2015.7338097","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fuzz-ieee.2015.7338097","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.6700000166893005}],"awards":[],"funders":[{"id":"https://openalex.org/F4320327340","display_name":"Universiti Malaysia Terengganu","ror":"https://ror.org/02474f074"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W234991755","https://openalex.org/W801424931","https://openalex.org/W1616765759","https://openalex.org/W1822004825","https://openalex.org/W1988442031","https://openalex.org/W1997911001","https://openalex.org/W2011962431","https://openalex.org/W2012955605","https://openalex.org/W2014286416","https://openalex.org/W2020407132","https://openalex.org/W2026622914","https://openalex.org/W2036234778","https://openalex.org/W2039572875","https://openalex.org/W2047833440","https://openalex.org/W2060907774","https://openalex.org/W2074115763","https://openalex.org/W2163955621","https://openalex.org/W2170493368","https://openalex.org/W2460693936","https://openalex.org/W4230614082","https://openalex.org/W6684119003","https://openalex.org/W6718665846"],"related_works":["https://openalex.org/W2128177177","https://openalex.org/W2288790715","https://openalex.org/W2096851309","https://openalex.org/W3151496173","https://openalex.org/W2883092990","https://openalex.org/W2387425158","https://openalex.org/W2149623705","https://openalex.org/W2063484644","https://openalex.org/W4286890531","https://openalex.org/W4381516374"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"some":[3],"heavy":[4,25,31,36],"weighted":[5,27,32,38,49,55],"geometric":[6,33,39,50,56],"aggregation":[7,75,89],"operators":[8,41],"in":[9,21,73,107,120,134],"analytic":[10],"hierarchy":[11],"process":[12,76],"under":[13],"group":[14],"decision":[15],"making":[16],"(AHP-GDM)":[17],"are":[18,42,71],"proposed.":[19],"First,":[20],"the":[22,30,47,53,59,62,74,82,88,98,101,121,125,128],"sense":[23],"of":[24,46,77,90,97,104,127],"ordered":[26,37,54],"averaging":[28],"operator,":[29],"(HWG)":[34],"and":[35,52,68,117],"(HOWG)":[40],"introduced":[43],"as":[44,79],"extensions":[45],"normal":[48],"mean":[51],"by":[57],"relaxing":[58],"constraints":[60],"on":[61,87],"associated":[63],"weighting":[64],"vector.":[65],"These":[66],"HWG":[67],"HOWG":[69],"then":[70],"utilized":[72],"AHP-GDM":[78],"to":[80],"maintain":[81],"multiplicative":[83],"reciprocal":[84],"property,":[85],"specifically":[86],"individual":[91],"judgments":[92],"procedure.":[93],"The":[94],"main":[95],"advantage":[96],"model,":[99],"besides":[100],"complete":[102],"overlapping":[103],"information":[105,119],"such":[106],"classical":[108],"methods,":[109],"is":[110,139],"that":[111],"it":[112],"can":[113],"also":[114],"accommodate":[115],"partial":[116],"non-overlapping":[118],"formulation.":[122],"To":[123],"show":[124],"applicability":[126],"proposed":[129],"method,":[130],"a":[131],"numerical":[132],"example":[133],"an":[135],"investment":[136],"selection":[137],"problem":[138],"provided.":[140]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
