{"id":"https://openalex.org/W3102095490","doi":"https://doi.org/10.1115/1.4048743","title":"Design Variety Measurement Using Sharma\u2013Mittal Entropy","display_name":"Design Variety Measurement Using Sharma\u2013Mittal Entropy","publication_year":2020,"publication_date":"2020-10-12","ids":{"openalex":"https://openalex.org/W3102095490","doi":"https://doi.org/10.1115/1.4048743","mag":"3102095490"},"language":"en","primary_location":{"id":"doi:10.1115/1.4048743","doi":"https://doi.org/10.1115/1.4048743","is_oa":false,"landing_page_url":"https://doi.org/10.1115/1.4048743","pdf_url":null,"source":{"id":"https://openalex.org/S88457320","display_name":"Journal of Mechanical Design","issn_l":"0161-8458","issn":["0161-8458","1050-0472","1528-9001"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-1"],"host_organization":"https://openalex.org/P4310321320","host_organization_name":"American Society of Mechanical Engineers","host_organization_lineage":["https://openalex.org/P4310321320"],"host_organization_lineage_names":["American Society of Mechanical Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mechanical Design","raw_type":"journal-article"},"volume":null,"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/A5040705509","display_name":"Faez Ahmed","orcid":"https://orcid.org/0000-0002-5227-2628","observed_orcids":["https://orcid.org/0000-0002-5227-2628"]},"institutions":[{"id":"https://openalex.org/I111979921","display_name":"Northwestern University","ror":"https://ror.org/000e0be47","country_code":"US","type":"education","lineage":["https://openalex.org/I111979921"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Faez Ahmed","raw_affiliation_strings":["Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208","institution_ids":["https://openalex.org/I111979921"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112395324","display_name":"Sharath Kumar Ramachandran","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sharath Kumar Ramachandran","raw_affiliation_strings":["School of Engineering Design, Technology and Professional Programs, The Pennsylvania State University, University Park, PA 16802"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Engineering Design, Technology and Professional Programs, The Pennsylvania State University, University Park, PA 16802","institution_ids":["https://openalex.org/I130769515"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036788329","display_name":"Mark Fuge","orcid":"https://orcid.org/0000-0003-3819-8895","observed_orcids":["https://orcid.org/0000-0003-3819-8895"]},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mark Fuge","raw_affiliation_strings":["Department of Mechanical Engineering, University of Maryland, College Park, MD 20742"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, University of Maryland, College Park, MD 20742","institution_ids":["https://openalex.org/I66946132"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018009125","display_name":"Samuel T. Hunter","orcid":"https://orcid.org/0000-0002-2036-7681","observed_orcids":["https://orcid.org/0000-0002-2036-7681"]},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sam Hunter","raw_affiliation_strings":["Industrial and Organizational Psychology, The Pennsylvania State University, University Park, PA 16802"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Industrial and Organizational Psychology, The Pennsylvania State University, University Park, PA 16802","institution_ids":["https://openalex.org/I130769515"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046296081","display_name":"Scarlett R. Miller","orcid":"https://orcid.org/0000-0002-5854-8314","observed_orcids":["https://orcid.org/0000-0002-5854-8314"]},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Scarlett Miller","raw_affiliation_strings":["School of Engineering Design, Technology and Professional Programs, The Pennsylvania State University, University Park, PA 16802"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Engineering Design, Technology and Professional Programs, The Pennsylvania State University, University Park, PA 16802","institution_ids":["https://openalex.org/I130769515"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.1427,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.83611867,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":98},"biblio":{"volume":"143","issue":"6","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11729","display_name":"Product Development and Customization","score":0.2468000054359436,"subfield":{"id":"https://openalex.org/subfields/1405","display_name":"Management of Technology and Innovation"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11729","display_name":"Product Development and Customization","score":0.2468000054359436,"subfield":{"id":"https://openalex.org/subfields/1405","display_name":"Management of Technology and Innovation"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10672","display_name":"Design Education and Practice","score":0.1429000049829483,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/T11798","display_name":"Optimal Experimental Design Methods","score":0.13850000500679016,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/sharma-mittal-entropy","display_name":"Sharma-Mittal entropy","score":0.949999988079071},{"id":"https://openalex.org/keywords/design-space-exploration","display_name":"design space exploration","score":0.8930000066757202},{"id":"https://openalex.org/keywords/entropy-measures","display_name":"entropy measures","score":0.4620000123977661},{"id":"https://openalex.org/keywords/submodularity","display_name":"submodular functions","score":0.8149999976158142},{"id":"https://openalex.org/keywords/greedy-optimization","display_name":"greedy optimization","score":0.746999979019165},{"id":"https://openalex.org/keywords/metric-comparison","display_name":"metric comparison","score":0.5609999895095825},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"pairwise comparison","score":0.5830000042915344},{"id":"https://openalex.org/keywords/human-ratings","display_name":"human ratings","score":0.5960000157356262}],"concepts":[{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.6734371185302734},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.6574402451515198},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.6142643094062805},{"id":"https://openalex.org/C178621042","wikidata":"https://www.wikidata.org/wiki/Q7631710","display_name":"Submodular set function","level":2,"score":0.5761090517044067},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.5627362728118896},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5230346918106079},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.4859067499637604},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.4439723789691925},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37301671504974365},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3508404791355133},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.22489586472511292},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.11821123957633972},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1115/1.4048743","doi":"https://doi.org/10.1115/1.4048743","is_oa":false,"landing_page_url":"https://doi.org/10.1115/1.4048743","pdf_url":null,"source":{"id":"https://openalex.org/S88457320","display_name":"Journal of Mechanical Design","issn_l":"0161-8458","issn":["0161-8458","1050-0472","1528-9001"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-1"],"host_organization":"https://openalex.org/P4310321320","host_organization_name":"American Society of Mechanical Engineers","host_organization_lineage":["https://openalex.org/P4310321320"],"host_organization_lineage_names":["American Society of Mechanical Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mechanical Design","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G7911332868","display_name":"Collaborative Research:  Improving the Validity and Reliability of  Creativity Ratings in Engineering Design","funder_award_id":"1728086","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":85,"referenced_works":["https://openalex.org/W378939584","https://openalex.org/W596263638","https://openalex.org/W627443184","https://openalex.org/W629241095","https://openalex.org/W1536984214","https://openalex.org/W1556662545","https://openalex.org/W1582768477","https://openalex.org/W1584162686","https://openalex.org/W1605977036","https://openalex.org/W1680189815","https://openalex.org/W1742272783","https://openalex.org/W1788836429","https://openalex.org/W1894926079","https://openalex.org/W1977967506","https://openalex.org/W1983874169","https://openalex.org/W1984652453","https://openalex.org/W1984914454","https://openalex.org/W1985126292","https://openalex.org/W1989792933","https://openalex.org/W1993310546","https://openalex.org/W1995875735","https://openalex.org/W1996779371","https://openalex.org/W2011632012","https://openalex.org/W2014205684","https://openalex.org/W2019443768","https://openalex.org/W2019516754","https://openalex.org/W2019998121","https://openalex.org/W2023435434","https://openalex.org/W2028994502","https://openalex.org/W2034607416","https://openalex.org/W2040127736","https://openalex.org/W2043318959","https://openalex.org/W2051021140","https://openalex.org/W2053381548","https://openalex.org/W2056146479","https://openalex.org/W2067906953","https://openalex.org/W2071836643","https://openalex.org/W2076717460","https://openalex.org/W2082652812","https://openalex.org/W2087189381","https://openalex.org/W2090933635","https://openalex.org/W2101658911","https://openalex.org/W2104767862","https://openalex.org/W2116104206","https://openalex.org/W2118544668","https://openalex.org/W2119049305","https://openalex.org/W2120474334","https://openalex.org/W2124379907","https://openalex.org/W2125524641","https://openalex.org/W2126135370","https://openalex.org/W2136317303","https://openalex.org/W2138895711","https://openalex.org/W2144999175","https://openalex.org/W2145300789","https://openalex.org/W2163989766","https://openalex.org/W2168697680","https://openalex.org/W2184980188","https://openalex.org/W2255704654","https://openalex.org/W2262250234","https://openalex.org/W2285368144","https://openalex.org/W2318516124","https://openalex.org/W2327506841","https://openalex.org/W2402713938","https://openalex.org/W2488766709","https://openalex.org/W2500139799","https://openalex.org/W2520731239","https://openalex.org/W2540929915","https://openalex.org/W2560413501","https://openalex.org/W2753574082","https://openalex.org/W2765842531","https://openalex.org/W2787151490","https://openalex.org/W2888481622","https://openalex.org/W2898964810","https://openalex.org/W2951355742","https://openalex.org/W2990601365","https://openalex.org/W3041149780","https://openalex.org/W3114913914","https://openalex.org/W3165828102","https://openalex.org/W4206448857","https://openalex.org/W4206653364","https://openalex.org/W4213051584","https://openalex.org/W4249591233","https://openalex.org/W4251723820","https://openalex.org/W4301108176","https://openalex.org/W4301891957"],"related_works":["https://openalex.org/W2990601365","https://openalex.org/W2765842531","https://openalex.org/W4401307617","https://openalex.org/W1984914454","https://openalex.org/W7214205551","https://openalex.org/W2325128113","https://openalex.org/W3145909771","https://openalex.org/W2043318959","https://openalex.org/W2129335383","https://openalex.org/W2582697653"],"abstract_inverted_index":{"Abstract":[0],"Design":[1],"variety":[2,95,113,150,166,186],"metrics":[3,21,75,128,162,187],"measure":[4,32,165,201],"how":[5],"much":[6],"a":[7,16,104,115,141,158],"design":[8,33,49,112,185],"space":[9],"is":[10,103],"explored.":[11],"This":[12,154],"article":[13,155],"proposes":[14],"that":[15,37,183],"generalized":[17],"class":[18],"of":[19,96,136],"entropy":[20,25],"based":[22],"on":[23,180],"Sharma\u2013Mittal":[24,42],"offers":[26],"advantages":[27,55],"over":[28,56],"existing":[29,57,70,89,127],"methods":[30,90],"to":[31,69,88,110,123,143,147,164,200],"variety.":[34],"We":[35],"show":[36],"an":[38],"exemplar":[39],"metric":[40,146],"from":[41,172],"entropy,":[43],"namely,":[44],"the":[45,52,94,134,145,191,197],"Herfindahl\u2013Hirschman":[46],"index":[47],"for":[48,76,151,160],"(HHID)":[50],"has":[51,84],"following":[53],"desirable":[54],"metrics:":[58,125],"(a)":[59],"more":[60],"accuracy:":[61],"it":[62,83,102],"better":[63,148],"aligns":[64],"with":[65,195],"human":[66],"ratings":[67],"compared":[68,87],"and":[71,120,190],"commonly":[72],"used":[73,163],"tree-based":[74],"two":[77],"new":[78,152],"datasets;":[79],"(b)":[80],"higher":[81,85],"sensitivity:":[82],"sensitivity":[86],"when":[91],"distinguishing":[92],"between":[93],"sets;":[97],"(c)":[98],"allows":[99,140],"efficient":[100],"optimization:":[101],"submodular":[105],"function,":[106],"which":[107,139],"enables":[108],"one":[109],"optimize":[111],"using":[114],"polynomial":[116],"time":[117],"greedy":[118],"algorithm;":[119],"(d)":[121],"generalizes":[122],"multiple":[124],"many":[126],"can":[129],"be":[130],"derived":[131],"by":[132],"changing":[133],"parameters":[135],"this":[137],"metric,":[138],"researcher":[142],"fit":[144],"represent":[149],"domains.":[153],"also":[156],"contributes":[157],"procedure":[159],"comparing":[161],"via":[167],"constructing":[168],"ground":[169],"truth":[170],"datasets":[171],"pairwise":[173],"comparisons.":[174],"Overall,":[175],"our":[176],"results":[177],"shed":[178],"light":[179],"some":[181],"qualities":[182],"good":[184],"should":[188],"possess":[189],"nontrivial":[192],"challenges":[193],"associated":[194],"collecting":[196],"data":[198],"needed":[199],"those":[202],"qualities.":[203]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2021,"cited_by_count":2}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2020-11-23T00:00:00"}