{"id":"https://openalex.org/W2055641388","doi":"https://doi.org/10.1109/tfuzz.2013.2243456","title":"Defuzzification Functionals of Ordered Fuzzy Numbers","display_name":"Defuzzification Functionals of Ordered Fuzzy Numbers","publication_year":2013,"publication_date":"2013-01-28","ids":{"openalex":"https://openalex.org/W2055641388","doi":"https://doi.org/10.1109/tfuzz.2013.2243456","mag":"2055641388"},"language":"en","primary_location":{"id":"doi:10.1109/tfuzz.2013.2243456","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2013.2243456","pdf_url":null,"source":{"id":"https://openalex.org/S134177497","display_name":"IEEE Transactions on Fuzzy Systems","issn_l":"1063-6706","issn":["1063-6706","1941-0034"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Fuzzy Systems","raw_type":"journal-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/A5052425910","display_name":"Witold Kosi\u0144ski","orcid":null},"institutions":[{"id":"https://openalex.org/I149592570","display_name":"Kazimierz Wielki University in Bydgoszcz","ror":"https://ror.org/018zpxs61","country_code":"PL","type":"education","lineage":["https://openalex.org/I149592570"]},{"id":"https://openalex.org/I3017851245","display_name":"Polish-Japanese Academy of Information Technology","ror":"https://ror.org/01v542j61","country_code":"PL","type":"education","lineage":["https://openalex.org/I3017851245"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Witold Kosinski","raw_affiliation_strings":["Faculty of Mathematics, Physics and Technology, Kazimierz-Wielki, University, Bydgoszcz, Poland","Fac. of Comput. Sci., Polish-Japanese Inst. of Inf. Technol., Warsaw, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, Physics and Technology, Kazimierz-Wielki, University, Bydgoszcz, Poland","institution_ids":["https://openalex.org/I149592570"]},{"raw_affiliation_string":"Fac. of Comput. Sci., Polish-Japanese Inst. of Inf. Technol., Warsaw, Poland","institution_ids":["https://openalex.org/I3017851245"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064756823","display_name":"Piotr Prokopowicz","orcid":"https://orcid.org/0000-0002-7223-9008"},"institutions":[{"id":"https://openalex.org/I149592570","display_name":"Kazimierz Wielki University in Bydgoszcz","ror":"https://ror.org/018zpxs61","country_code":"PL","type":"education","lineage":["https://openalex.org/I149592570"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Piotr Prokopowicz","raw_affiliation_strings":["Faculty of Mathematics, Kazimierz-Wielki, University, Bydgoszcz, Poland","Fac. of Math., Kazimierz-Wielki Univ., Bydgoszcz, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, Kazimierz-Wielki, University, Bydgoszcz, Poland","institution_ids":["https://openalex.org/I149592570"]},{"raw_affiliation_string":"Fac. of Math., Kazimierz-Wielki Univ., Bydgoszcz, Poland","institution_ids":["https://openalex.org/I149592570"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076878635","display_name":"Agnieszka Rosa","orcid":"https://orcid.org/0000-0001-7779-9525"},"institutions":[{"id":"https://openalex.org/I149592570","display_name":"Kazimierz Wielki University in Bydgoszcz","ror":"https://ror.org/018zpxs61","country_code":"PL","type":"education","lineage":["https://openalex.org/I149592570"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Agnieszka Rosa","raw_affiliation_strings":["Faculty of Mathematics, Kazimierz-Wielki, University, Bydgoszcz, Poland","Fac. of Math., Kazimierz-Wielki Univ., Bydgoszcz, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, Kazimierz-Wielki, University, Bydgoszcz, Poland","institution_ids":["https://openalex.org/I149592570"]},{"raw_affiliation_string":"Fac. of Math., Kazimierz-Wielki Univ., Bydgoszcz, Poland","institution_ids":["https://openalex.org/I149592570"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.1611,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.9585526,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"21","issue":"6","first_page":"1163","last_page":"1169"},"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/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9990000128746033,"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":0.9983999729156494,"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/defuzzification","display_name":"Defuzzification","score":0.9092678427696228},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6933341026306152},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.6570277810096741},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.6291228532791138},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5547705888748169},{"id":"https://openalex.org/keywords/fuzzy-control-system","display_name":"Fuzzy control system","score":0.5509700179100037},{"id":"https://openalex.org/keywords/fuzzy-set-operations","display_name":"Fuzzy set operations","score":0.5455403923988342},{"id":"https://openalex.org/keywords/fuzzy-associative-matrix","display_name":"Fuzzy associative matrix","score":0.5427842140197754},{"id":"https://openalex.org/keywords/fuzzy-inference","display_name":"Fuzzy inference","score":0.5385689735412598},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.49933743476867676},{"id":"https://openalex.org/keywords/fuzzy-mathematics","display_name":"Fuzzy mathematics","score":0.4905325770378113},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.48822644352912903},{"id":"https://openalex.org/keywords/fuzzy-classification","display_name":"Fuzzy classification","score":0.4548403322696686},{"id":"https://openalex.org/keywords/fuzzy-subalgebra","display_name":"Fuzzy subalgebra","score":0.4281773567199707},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4251924157142639},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3447023332118988},{"id":"https://openalex.org/keywords/adaptive-neuro-fuzzy-inference-system","display_name":"Adaptive neuro fuzzy inference system","score":0.28548672795295715},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2676909565925598},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2573142945766449},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.05787700414657593}],"concepts":[{"id":"https://openalex.org/C170260401","wikidata":"https://www.wikidata.org/wiki/Q5251735","display_name":"Defuzzification","level":5,"score":0.9092678427696228},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6933341026306152},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.6570277810096741},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.6291228532791138},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5547705888748169},{"id":"https://openalex.org/C195975749","wikidata":"https://www.wikidata.org/wiki/Q1475705","display_name":"Fuzzy control system","level":3,"score":0.5509700179100037},{"id":"https://openalex.org/C148671577","wikidata":"https://www.wikidata.org/wiki/Q5511133","display_name":"Fuzzy set operations","level":4,"score":0.5455403923988342},{"id":"https://openalex.org/C144170203","wikidata":"https://www.wikidata.org/wiki/Q5511099","display_name":"Fuzzy associative matrix","level":5,"score":0.5427842140197754},{"id":"https://openalex.org/C2986395286","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy inference","level":5,"score":0.5385689735412598},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.49933743476867676},{"id":"https://openalex.org/C166586474","wikidata":"https://www.wikidata.org/wiki/Q5511129","display_name":"Fuzzy mathematics","level":5,"score":0.4905325770378113},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.48822644352912903},{"id":"https://openalex.org/C127385683","wikidata":"https://www.wikidata.org/wiki/Q1475696","display_name":"Fuzzy classification","level":4,"score":0.4548403322696686},{"id":"https://openalex.org/C115740575","wikidata":"https://www.wikidata.org/wiki/Q5511136","display_name":"Fuzzy subalgebra","level":5,"score":0.4281773567199707},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4251924157142639},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3447023332118988},{"id":"https://openalex.org/C186108316","wikidata":"https://www.wikidata.org/wiki/Q352530","display_name":"Adaptive neuro fuzzy inference system","level":4,"score":0.28548672795295715},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2676909565925598},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2573142945766449},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.05787700414657593}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tfuzz.2013.2243456","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2013.2243456","pdf_url":null,"source":{"id":"https://openalex.org/S134177497","display_name":"IEEE Transactions on Fuzzy Systems","issn_l":"1063-6706","issn":["1063-6706","1941-0034"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Fuzzy Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.5199999809265137,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W8726444","https://openalex.org/W1490729186","https://openalex.org/W1562049240","https://openalex.org/W1568420925","https://openalex.org/W1975212232","https://openalex.org/W1994178762","https://openalex.org/W2006879295","https://openalex.org/W2034358412","https://openalex.org/W2051734340","https://openalex.org/W2057132322","https://openalex.org/W2058983288","https://openalex.org/W2069069851","https://openalex.org/W2076764311","https://openalex.org/W2089135909","https://openalex.org/W2089439621","https://openalex.org/W2089624753","https://openalex.org/W2099285375","https://openalex.org/W2113720027","https://openalex.org/W2136708504","https://openalex.org/W2150087267","https://openalex.org/W2156246735","https://openalex.org/W2494614593","https://openalex.org/W4205772790","https://openalex.org/W4300068885","https://openalex.org/W4300653233"],"related_works":["https://openalex.org/W2037428035","https://openalex.org/W4242545108","https://openalex.org/W2088978098","https://openalex.org/W2048452567","https://openalex.org/W193191735","https://openalex.org/W2586653035","https://openalex.org/W2466052371","https://openalex.org/W1561699096","https://openalex.org/W2116600453","https://openalex.org/W1992951133"],"abstract_inverted_index":{"Defuzzification":[0],"functionals,":[1],"which":[2],"play":[3],"the":[4,39,48],"main":[5],"role":[6],"when":[7],"dealing":[8],"with":[9,58],"fuzzy":[10,13,22,53],"controllers":[11],"and":[12],"inference":[14],"systems,":[15],"for":[16,20,29,46],"convex":[17,52],"as":[18],"well":[19],"ordered":[21],"numbers,":[23],"are":[24,31,55],"discussed.":[25],"Three":[26],"characteristic":[27],"conditions":[28],"them":[30],"formulated.":[32],"It":[33],"is":[34],"shown":[35],"that":[36],"most":[37],"of":[38,51],"known":[40],"defuzzification":[41],"functionals":[42],"satisfy":[43],"them.":[44,61],"Motivations":[45],"introducing":[47],"extended":[49],"class":[50],"numbers":[54],"presented,":[56],"together":[57],"operations":[59],"on":[60]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":12},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}