{"id":"https://openalex.org/W7223293106","doi":"https://doi.org/10.48550/arxiv.2610.30138","title":"On the formal definition of average function for interval data","display_name":"On the formal definition of average function for interval data","publication_year":2026,"publication_date":"2026-07-29","ids":{"openalex":"https://openalex.org/W7223293106","doi":"https://doi.org/10.48550/arxiv.2610.30138"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.30138","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.30138","pdf_url":"https://arxiv.org/pdf/2610.30138","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.30138","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5159368952","display_name":"Sergio F. Alonso","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I165339363","display_name":"Universidad de Oviedo","ror":"https://ror.org/006gksa02","country_code":"ES","type":"education","lineage":["https://openalex.org/I165339363"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Alonso, Sergio F.","raw_affiliation_strings":["Dept. Statistics and O. R. and M. T. , University of Oviedo , Federico Garcia Lorca , 18 , Oviedo , 33007 , Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dept. Statistics and O. R. and M. T. , University of Oviedo , Federico Garcia Lorca , 18 , Oviedo , 33007 , Spain","institution_ids":["https://openalex.org/I165339363"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5159326513","display_name":"Susana Montes","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I165339363","display_name":"Universidad de Oviedo","ror":"https://ror.org/006gksa02","country_code":"ES","type":"education","lineage":["https://openalex.org/I165339363"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Montes, Susana","raw_affiliation_strings":["Dept. Statistics and O. R. and M. T. , University of Oviedo , Federico Garcia Lorca , 18 , Oviedo , 33007 , Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dept. Statistics and O. R. and M. T. , University of Oviedo , Federico Garcia Lorca , 18 , Oviedo , 33007 , Spain","institution_ids":["https://openalex.org/I165339363"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071710752","display_name":"Susana D\u00edaz","orcid":"https://orcid.org/0000-0002-7510-9858","observed_orcids":["https://orcid.org/0000-0002-7510-9858"]},"institutions":[{"id":"https://openalex.org/I165339363","display_name":"Universidad de Oviedo","ror":"https://ror.org/006gksa02","country_code":"ES","type":"education","lineage":["https://openalex.org/I165339363"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Diaz-Vazquez, Susana","raw_affiliation_strings":["Dept. Statistics and O. R. and M. T. , University of Oviedo , Federico Garcia Lorca , 18 , Oviedo , 33007 , Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dept. Statistics and O. R. and M. T. , University of Oviedo , Federico Garcia Lorca , 18 , Oviedo , 33007 , Spain","institution_ids":["https://openalex.org/I165339363"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I165339363"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.8579000234603882,"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":0.8579000234603882,"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":0.07289999723434448,"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/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.009700000286102295,"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/interval-valued-data","display_name":"interval data","score":0.8610000014305115},{"id":"https://openalex.org/keywords/aggregation-operators","display_name":"aggregation operators","score":0.9200000166893005},{"id":"https://openalex.org/keywords/idempotence","display_name":"idempotency","score":0.8270000219345093},{"id":"https://openalex.org/keywords/monotonicity","display_name":"monotonicity","score":0.9919999837875366},{"id":"https://openalex.org/keywords/lattice-order","display_name":"lattice order","score":0.6700000166893005},{"id":"https://openalex.org/keywords/power-means","display_name":"power means","score":0.9750000238418579},{"id":"https://openalex.org/keywords/median","display_name":"median","score":0.7049999833106995},{"id":"https://openalex.org/keywords/imprecise-data","display_name":"imprecise data","score":0.7300000190734863}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6917999982833862},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.5777999758720398},{"id":"https://openalex.org/C128394911","wikidata":"https://www.wikidata.org/wiki/Q1987578","display_name":"Unit interval","level":2,"score":0.44130000472068787},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3982999920845032},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.38600000739097595},{"id":"https://openalex.org/C172252984","wikidata":"https://www.wikidata.org/wiki/Q368988","display_name":"Idempotence","level":2,"score":0.3596000075340271},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.35600000619888306},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.30489999055862427},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.2957000136375427},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.28940001130104065},{"id":"https://openalex.org/C112799922","wikidata":"https://www.wikidata.org/wiki/Q5104911","display_name":"Choquet integral","level":3,"score":0.2840000092983246},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.27799999713897705},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2732999920845032},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.272599995136261},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.25609999895095825},{"id":"https://openalex.org/C43994743","wikidata":"https://www.wikidata.org/wiki/Q516776","display_name":"Measurable function","level":3,"score":0.25369998812675476}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.30138","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.30138","pdf_url":"https://arxiv.org/pdf/2610.30138","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"doi:10.48550/arxiv.2610.30138","doi":"https://doi.org/10.48550/arxiv.2610.30138","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.30138","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.30138","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.30138","pdf_url":"https://arxiv.org/pdf/2610.30138","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1238650926","display_name":null,"funder_award_id":"PID2022- 139886NB-I00","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G745419941","display_name":null,"funder_award_id":"PID2023","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G8920660035","display_name":null,"funder_award_id":"PID2022","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"}],"funders":[{"id":"https://openalex.org/F4320322930","display_name":"Ministerio de Ciencia e Innovaci\u00f3n","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223293106.pdf","grobid_xml":"https://content.openalex.org/works/W7223293106.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W1981107087","https://openalex.org/W1988053196","https://openalex.org/W2000301175","https://openalex.org/W3105975110","https://openalex.org/W3125777971","https://openalex.org/W3204749642","https://openalex.org/W4252793191","https://openalex.org/W4389626079"],"related_works":["https://openalex.org/W4389626079","https://openalex.org/W2184109814","https://openalex.org/W2955603147","https://openalex.org/W1974300543","https://openalex.org/W4226397040","https://openalex.org/W1985130342","https://openalex.org/W47149522","https://openalex.org/W2979471077","https://openalex.org/W7095800447","https://openalex.org/W2551565194"],"abstract_inverted_index":{"This":[0,160],"paper":[1],"addresses":[2],"the":[3,21,55,63,69,75,86,124,132,144,153,166],"formal":[4],"definition":[5],"of":[6,25,46,77,97,112,135,146,157,169],"average":[7,136],"functions":[8,50,137],"for":[9,138,165],"interval":[10,30,125],"data,":[11],"extending":[12],"classical":[13,110],"aggregation":[14,49,113,168],"theory":[15],"beyond":[16],"precise":[17],"numerical":[18],"values":[19],"to":[20,62,123],"more":[22],"general":[23],"setting":[24],"real-valued":[26],"intervals.":[27,139],"Recognizing":[28],"that":[29,143],"data":[31,182],"nat-":[32],"urally":[33],"arise":[34],"in":[35,102,152,175],"contexts":[36],"involving":[37],"imprecision":[38,183],"or":[39],"uncertainty,":[40],"we":[41,106],"examine":[42],"how":[43],"established":[44],"notions":[45],"averages":[47],"and":[48,89,93,99,108,121,155,179],"can":[51],"be":[52],"generalized":[53],"when":[54,128],"underlying":[56],"domain":[57],"is":[58,184],"no":[59],"longer":[60],"restricted":[61],"unit":[64],"interval,":[65],"but":[66],"instead":[67],"encompasses":[68],"entire":[70],"real":[71],"line.":[72],"We":[73],"analyze":[74],"impact":[76],"different":[78],"admissible":[79],"orders":[80],"on":[81,85],"intervals,":[82],"particularly":[83],"focusing":[84],"lattice":[87],"order":[88,147],"several":[90],"total":[91],"orders,":[92],"provide":[94],"rigorous":[95],"definitions":[96],"idempotency":[98],"mono-":[100],"tonicity":[101],"this":[103],"context.":[104],"Furthermore,":[105],"adapt":[107],"study":[109],"families":[111],"operators":[114,130],"such":[115],"as":[116],"power":[117],"means,":[118],"minimum,":[119],"maximum,":[120],"median":[122],"setting,":[126],"characterizing":[127],"these":[129,158],"satisfy":[131],"properties":[133],"required":[134],"Our":[140],"results":[141],"highlight":[142],"choice":[145],"plays":[148],"a":[149,163],"crucial":[150],"role":[151],"behavior":[154],"suitability":[156],"operators.":[159],"work":[161],"lays":[162],"foundation":[164],"systematic":[167],"interval-valued":[170],"information,":[171],"with":[172],"potential":[173],"applications":[174],"statistics,":[176],"decision":[177],"making,":[178],"fields":[180],"where":[181],"inherent.":[185]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-24T00:00:00"}