{"id":"https://openalex.org/W3081691475","doi":"https://doi.org/10.1109/fuzz48607.2020.9177808","title":"Midpoint Representation of Fuzzy-Valued Functions and Applications","display_name":"Midpoint Representation of Fuzzy-Valued Functions and Applications","publication_year":2020,"publication_date":"2020-07-01","ids":{"openalex":"https://openalex.org/W3081691475","doi":"https://doi.org/10.1109/fuzz48607.2020.9177808","mag":"3081691475"},"language":"en","primary_location":{"id":"doi:10.1109/fuzz48607.2020.9177808","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fuzz48607.2020.9177808","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)","raw_type":"proceedings-article"},"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/A5079360809","display_name":"Benedetta Amicizia","orcid":"https://orcid.org/0000-0003-3003-8133"},"institutions":[{"id":"https://openalex.org/I190397597","display_name":"University of Urbino","ror":"https://ror.org/04q4kt073","country_code":"IT","type":"education","lineage":["https://openalex.org/I190397597"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Benedetta Amicizia","raw_affiliation_strings":["DiSPeA, University of Urbino Carlo Bo, Urbino, Italy"],"affiliations":[{"raw_affiliation_string":"DiSPeA, University of Urbino Carlo Bo, Urbino, Italy","institution_ids":["https://openalex.org/I190397597"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080629371","display_name":"Maria Letizia Guerra","orcid":"https://orcid.org/0000-0002-8944-2192"},"institutions":[{"id":"https://openalex.org/I9360294","display_name":"University of Bologna","ror":"https://ror.org/01111rn36","country_code":"IT","type":"education","lineage":["https://openalex.org/I9360294"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Maria Letizia Guerra","raw_affiliation_strings":["Department of Statistics P Fortunati, University of Bologna, Bologna, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Statistics P Fortunati, University of Bologna, Bologna, Italy","institution_ids":["https://openalex.org/I9360294"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024433740","display_name":"Mina Shahidi","orcid":"https://orcid.org/0000-0001-8185-403X"},"institutions":[{"id":"https://openalex.org/I161028277","display_name":"Institute for Advanced Studies in Basic Sciences","ror":"https://ror.org/00bzsst90","country_code":"IR","type":"education","lineage":["https://openalex.org/I161028277"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Mina Shahidi","raw_affiliation_strings":["Department of Mathematics, IASBS Institute, Zanjan, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, IASBS Institute, Zanjan, Iran","institution_ids":["https://openalex.org/I161028277"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056967799","display_name":"Laerte Sorini","orcid":"https://orcid.org/0000-0003-0088-4005"},"institutions":[{"id":"https://openalex.org/I190397597","display_name":"University of Urbino","ror":"https://ror.org/04q4kt073","country_code":"IT","type":"education","lineage":["https://openalex.org/I190397597"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Laerte Sorini","raw_affiliation_strings":["DESP, University of Urbino \"Carlo Bo\", Urbino, Italy"],"affiliations":[{"raw_affiliation_string":"DESP, University of Urbino \"Carlo Bo\", Urbino, Italy","institution_ids":["https://openalex.org/I190397597"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084200898","display_name":"Luciano Stefanini","orcid":"https://orcid.org/0000-0002-7367-8520"},"institutions":[{"id":"https://openalex.org/I190397597","display_name":"University of Urbino","ror":"https://ror.org/04q4kt073","country_code":"IT","type":"education","lineage":["https://openalex.org/I190397597"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Luciano Stefanini","raw_affiliation_strings":["DESP, University of Urbino \"Carlo Bo\", Urbino, Italy"],"affiliations":[{"raw_affiliation_string":"DESP, University of Urbino \"Carlo Bo\", Urbino, Italy","institution_ids":["https://openalex.org/I190397597"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5079360809"],"corresponding_institution_ids":["https://openalex.org/I190397597"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.1090316,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"8"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9998999834060669,"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/T10050","display_name":"Multi-Criteria Decision Making","score":0.9965000152587891,"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":0.9902999997138977,"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/midpoint","display_name":"Midpoint","score":0.8761609792709351},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6887007355690002},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.6719626784324646},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5310761332511902},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.5295109748840332},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.4698411822319031},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.45432108640670776},{"id":"https://openalex.org/keywords/defuzzification","display_name":"Defuzzification","score":0.4108947813510895},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.40504971146583557},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.39127397537231445},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.3896678686141968},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3227333426475525},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.24570363759994507},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23888850212097168},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.196171373128891},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1745316982269287}],"concepts":[{"id":"https://openalex.org/C34130140","wikidata":"https://www.wikidata.org/wiki/Q1645406","display_name":"Midpoint","level":2,"score":0.8761609792709351},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6887007355690002},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.6719626784324646},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5310761332511902},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.5295109748840332},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.4698411822319031},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.45432108640670776},{"id":"https://openalex.org/C170260401","wikidata":"https://www.wikidata.org/wiki/Q5251735","display_name":"Defuzzification","level":5,"score":0.4108947813510895},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.40504971146583557},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.39127397537231445},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.3896678686141968},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3227333426475525},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.24570363759994507},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23888850212097168},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.196171373128891},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1745316982269287},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/fuzz48607.2020.9177808","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fuzz48607.2020.9177808","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)","raw_type":"proceedings-article"},{"id":"pmh:oai:cris.unibo.it:11585/771855","is_oa":false,"landing_page_url":"https://hdl.handle.net/11585/771855","pdf_url":null,"source":{"id":"https://openalex.org/S4306402579","display_name":"Archivio istituzionale della ricerca (Alma Mater Studiorum Universit\u00e0 di Bologna)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210117483","host_organization_name":"Istituto di Ematologia di Bologna","host_organization_lineage":["https://openalex.org/I4210117483"],"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":"info:eu-repo/semantics/conferenceObject"},{"id":"pmh:oai:ora.uniurb.it:11576/2299372","is_oa":false,"landing_page_url":"http://hdl.handle.net/11576/2299372","pdf_url":null,"source":{"id":"https://openalex.org/S4377196377","display_name":"CINECA IRIS Institutional Research information system (University of Urbino)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I190397597","host_organization_name":"University of Urbino","host_organization_lineage":["https://openalex.org/I190397597"],"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":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.4300000071525574}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W565587792","https://openalex.org/W1507872748","https://openalex.org/W1542253753","https://openalex.org/W1551251595","https://openalex.org/W1580809199","https://openalex.org/W1995123739","https://openalex.org/W2006748591","https://openalex.org/W2034038007","https://openalex.org/W2038354216","https://openalex.org/W2050501209","https://openalex.org/W2059728681","https://openalex.org/W2060924166","https://openalex.org/W2099025530","https://openalex.org/W2801266866","https://openalex.org/W2941585389","https://openalex.org/W2979416550","https://openalex.org/W2979728612"],"related_works":["https://openalex.org/W4285988348","https://openalex.org/W4207006390","https://openalex.org/W1969361911","https://openalex.org/W2773005380","https://openalex.org/W4388451300","https://openalex.org/W2060361571","https://openalex.org/W4298646752","https://openalex.org/W1879432897","https://openalex.org/W2256857057","https://openalex.org/W4361984403"],"abstract_inverted_index":{"We":[0,15],"present":[1],"new":[2],"results":[3],"in":[4,23,31,72],"the":[5,18,24,79],"calculus":[6],"for":[7,51,60],"fuzzy-valued":[8],"functions":[9,62],"of":[10,21],"a":[11,65],"single":[12],"real":[13,25],"variable.":[14],"adopt":[16],"extensively":[17],"midpoint-radius":[19],"representation":[20],"intervals":[22],"half-plane":[26],"and":[27,38,45,54,58,70,76],"show":[28],"its":[29],"usefulness":[30],"fuzzy":[32,52,61],"calculus.":[33],"Concepts":[34],"related":[35],"to":[36,64],"convergence":[37],"limits,":[39],"continuity,":[40],"level-wise":[41],"gH-differentiability":[42],"have":[43],"interesting":[44],"useful":[46],"midpoint":[47],"expressions.":[48],"Partial":[49],"orders":[50],"numbers":[53],"extremal":[55],"points":[56],"(min":[57],"max)":[59],"associated":[63],"partial":[66],"order":[67],"are":[68],"discussed":[69],"analysed":[71],"detail.":[73],"Graphical":[74],"examples":[75],"pictures":[77],"accompany":[78],"presentation.":[80]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
