{"id":"https://openalex.org/W2561332882","doi":"https://doi.org/10.1155/2016/8127215","title":"Cardinal Basis Piecewise Hermite Interpolation on Fuzzy Data","display_name":"Cardinal Basis Piecewise Hermite Interpolation on Fuzzy Data","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2561332882","doi":"https://doi.org/10.1155/2016/8127215","mag":"2561332882"},"language":"en","primary_location":{"id":"doi:10.1155/2016/8127215","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2016/8127215","pdf_url":"http://downloads.hindawi.com/journals/afs/2016/8127215.pdf","source":{"id":"https://openalex.org/S117816480","display_name":"Advances in Fuzzy Systems","issn_l":"1687-7101","issn":["1687-7101","1687-711X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Fuzzy Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"http://downloads.hindawi.com/journals/afs/2016/8127215.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047404938","display_name":"H. Vosoughi","orcid":null},"institutions":[{"id":"https://openalex.org/I155419210","display_name":"Islamic Azad University, Science and Research Branch","ror":"https://ror.org/03187yj51","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I155419210"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"H. Vosoughi","raw_affiliation_strings":["Department of Mathematics, Islamic Azad University, Science and Research Branch, Tehran, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Islamic Azad University, Science and Research Branch, Tehran, Iran","institution_ids":["https://openalex.org/I155419210"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056670112","display_name":"S. Abbasbandy","orcid":"https://orcid.org/0000-0003-3385-4152"},"institutions":[{"id":"https://openalex.org/I155419210","display_name":"Islamic Azad University, Science and Research Branch","ror":"https://ror.org/03187yj51","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I155419210"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"S. Abbasbandy","raw_affiliation_strings":["Department of Mathematics, Islamic Azad University, Science and Research Branch, Tehran, Iran"],"raw_orcid":"https://orcid.org/0000-0003-3385-4152","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Islamic Azad University, Science and Research Branch, Tehran, Iran","institution_ids":["https://openalex.org/I155419210"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5056670112"],"corresponding_institution_ids":["https://openalex.org/I155419210"],"apc_list":{"value":900,"currency":"USD","value_usd":900},"apc_paid":{"value":900,"currency":"USD","value_usd":900},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.14183213,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2016","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":0.9988999962806702,"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":0.9988999962806702,"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/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9933000206947327,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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":0.9768999814987183,"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/hermite-interpolation","display_name":"Hermite interpolation","score":0.9199613332748413},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6874884366989136},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.595565140247345},{"id":"https://openalex.org/keywords/quintic-function","display_name":"Quintic function","score":0.5884734392166138},{"id":"https://openalex.org/keywords/hermite-polynomials","display_name":"Hermite polynomials","score":0.579933226108551},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.5736345648765564},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5568535923957825},{"id":"https://openalex.org/keywords/monotone-cubic-interpolation","display_name":"Monotone cubic interpolation","score":0.5366591215133667},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5215475559234619},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5127964615821838},{"id":"https://openalex.org/keywords/cubic-hermite-spline","display_name":"Cubic Hermite spline","score":0.5068352818489075},{"id":"https://openalex.org/keywords/hermite-spline","display_name":"Hermite spline","score":0.4457835257053375},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.44534415006637573},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.4125860929489136},{"id":"https://openalex.org/keywords/polynomial-interpolation","display_name":"Polynomial interpolation","score":0.36788880825042725},{"id":"https://openalex.org/keywords/spline-interpolation","display_name":"Spline interpolation","score":0.3446650505065918},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.32498621940612793},{"id":"https://openalex.org/keywords/linear-interpolation","display_name":"Linear interpolation","score":0.3063219487667084},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29646167159080505},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.22470638155937195},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19574150443077087},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.11456865072250366},{"id":"https://openalex.org/keywords/nearest-neighbor-interpolation","display_name":"Nearest-neighbor interpolation","score":0.10900670289993286},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10235640406608582},{"id":"https://openalex.org/keywords/frame","display_name":"Frame (networking)","score":0.06379857659339905}],"concepts":[{"id":"https://openalex.org/C186429297","wikidata":"https://www.wikidata.org/wiki/Q44451","display_name":"Hermite interpolation","level":3,"score":0.9199613332748413},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6874884366989136},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.595565140247345},{"id":"https://openalex.org/C124966035","wikidata":"https://www.wikidata.org/wiki/Q33104507","display_name":"Quintic function","level":3,"score":0.5884734392166138},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.579933226108551},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.5736345648765564},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5568535923957825},{"id":"https://openalex.org/C64485984","wikidata":"https://www.wikidata.org/wiki/Q4044484","display_name":"Monotone cubic interpolation","level":5,"score":0.5366591215133667},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5215475559234619},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5127964615821838},{"id":"https://openalex.org/C84607441","wikidata":"https://www.wikidata.org/wiki/Q1537263","display_name":"Cubic Hermite spline","level":5,"score":0.5068352818489075},{"id":"https://openalex.org/C186763157","wikidata":"https://www.wikidata.org/wiki/Q5741918","display_name":"Hermite spline","level":5,"score":0.4457835257053375},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.44534415006637573},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.4125860929489136},{"id":"https://openalex.org/C88080468","wikidata":"https://www.wikidata.org/wiki/Q637347","display_name":"Polynomial interpolation","level":4,"score":0.36788880825042725},{"id":"https://openalex.org/C31447003","wikidata":"https://www.wikidata.org/wiki/Q545002","display_name":"Spline interpolation","level":3,"score":0.3446650505065918},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.32498621940612793},{"id":"https://openalex.org/C171836373","wikidata":"https://www.wikidata.org/wiki/Q2266329","display_name":"Linear interpolation","level":3,"score":0.3063219487667084},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29646167159080505},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.22470638155937195},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19574150443077087},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.11456865072250366},{"id":"https://openalex.org/C207214200","wikidata":"https://www.wikidata.org/wiki/Q4202129","display_name":"Nearest-neighbor interpolation","level":4,"score":0.10900670289993286},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10235640406608582},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.06379857659339905},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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},{"id":"https://openalex.org/C107457265","wikidata":"https://www.wikidata.org/wiki/Q7546460","display_name":"Smoothing spline","level":4,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1155/2016/8127215","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2016/8127215","pdf_url":"http://downloads.hindawi.com/journals/afs/2016/8127215.pdf","source":{"id":"https://openalex.org/S117816480","display_name":"Advances in Fuzzy Systems","issn_l":"1687-7101","issn":["1687-7101","1687-711X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Fuzzy Systems","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:c6d2277181ad40ea95161418e883f0cf","is_oa":true,"landing_page_url":"https://doaj.org/article/c6d2277181ad40ea95161418e883f0cf","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Advances in Fuzzy Systems, Vol 2016 (2016)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2016/8127215","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2016/8127215","pdf_url":"http://downloads.hindawi.com/journals/afs/2016/8127215.pdf","source":{"id":"https://openalex.org/S117816480","display_name":"Advances in Fuzzy Systems","issn_l":"1687-7101","issn":["1687-7101","1687-711X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Fuzzy Systems","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2561332882.pdf","grobid_xml":"https://content.openalex.org/works/W2561332882.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W85547847","https://openalex.org/W167868945","https://openalex.org/W1611524765","https://openalex.org/W1778801682","https://openalex.org/W1984218554","https://openalex.org/W1987252213","https://openalex.org/W2019878538","https://openalex.org/W2062524572","https://openalex.org/W2082009146","https://openalex.org/W2088216818","https://openalex.org/W2089624753","https://openalex.org/W2093925907","https://openalex.org/W2255745993","https://openalex.org/W2294756238","https://openalex.org/W2316418224"],"related_works":["https://openalex.org/W3025960644","https://openalex.org/W1611524765","https://openalex.org/W2008015671","https://openalex.org/W1993375521","https://openalex.org/W3023816430","https://openalex.org/W2031303010","https://openalex.org/W4200162759","https://openalex.org/W2091727476","https://openalex.org/W2133632514","https://openalex.org/W4313680078"],"abstract_inverted_index":{"A":[0],"numerical":[1,50],"method":[2,51,70],"along":[3],"with":[4],"explicit":[5],"construction":[6],"to":[7,67,77],"interpolation":[8],"of":[9],"fuzzy":[10],"data":[11],"through":[12],"the":[13,29,39,56,62,69],"extension":[14],"principle":[15],"results":[16],"by":[17],"widely":[18],"used":[19],"fuzzy-valued":[20],"piecewise":[21],"Hermite":[22],"polynomial":[23],"in":[24,52,71],"general":[25],"case":[26],"based":[27],"on":[28,38],"cardinal":[30],"basis":[31],"functions,":[32],"which":[33],"satisfy":[34],"a":[35,49],"vanishing":[36],"property":[37],"successive":[40],"intervals,":[41],"has":[42],"been":[43],"introduced":[44],"here.":[45],"We":[46],"have":[47],"provided":[48],"full":[53],"detail":[54],"using":[55],"linear":[57],"space":[58],"notions":[59],"for":[60],"calculating":[61],"presented":[63],"method.":[64],"In":[65],"order":[66],"illustrate":[68],"computational":[72],"examples,":[73],"we":[74],"take":[75],"recourse":[76],"three":[78],"prime":[79],"cases:":[80],"linear,":[81],"cubic,":[82],"and":[83],"quintic.":[84]},"counts_by_year":[],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}
