{"id":"https://openalex.org/W3008851511","doi":"https://doi.org/10.1080/01969722.2020.1723872","title":"On Degree of Fuzziness and Fuzzy Decision Making","display_name":"On Degree of Fuzziness and Fuzzy Decision Making","publication_year":2020,"publication_date":"2020-02-18","ids":{"openalex":"https://openalex.org/W3008851511","doi":"https://doi.org/10.1080/01969722.2020.1723872","mag":"3008851511"},"language":"en","primary_location":{"id":"doi:10.1080/01969722.2020.1723872","is_oa":false,"landing_page_url":"https://doi.org/10.1080/01969722.2020.1723872","pdf_url":null,"source":{"id":"https://openalex.org/S117436046","display_name":"Cybernetics & Systems","issn_l":"0196-9722","issn":["0196-9722","1087-6553"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cybernetics and 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/A5078430868","display_name":"Sujit Kumar De","orcid":"https://orcid.org/0000-0003-4889-8043"},"institutions":[{"id":"https://openalex.org/I251397004","display_name":"Midnapore Medical College and Hospital","ror":"https://ror.org/03p37kd86","country_code":"IN","type":"education","lineage":["https://openalex.org/I251397004"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Sujit Kumar De","raw_affiliation_strings":["Department of Mathematics, Midnapore College (Autonomous), Paschim Medinipur, West Bengal, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Midnapore College (Autonomous), Paschim Medinipur, West Bengal, India","institution_ids":["https://openalex.org/I251397004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5078430868"],"corresponding_institution_ids":["https://openalex.org/I251397004"],"apc_list":null,"apc_paid":null,"fwci":3.4104,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.92651689,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"51","issue":"5","first_page":"600","last_page":"614"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9990000128746033,"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"}},"topics":[{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9990000128746033,"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/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9836000204086304,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9811999797821045,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.769411027431488},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.6347023248672485},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.621943473815918},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.5706194639205933},{"id":"https://openalex.org/keywords/ellipse","display_name":"Ellipse","score":0.5509480834007263},{"id":"https://openalex.org/keywords/polygon","display_name":"Polygon (computer graphics)","score":0.5409356951713562},{"id":"https://openalex.org/keywords/novelty","display_name":"Novelty","score":0.5373863577842712},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.5146273374557495},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.49637705087661743},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4923907518386841},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.4559635818004608},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.4420749545097351},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.4112318754196167},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37845978140830994},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3293841481208801},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.24257725477218628},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.20296984910964966},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.12347763776779175},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1147392988204956},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08639869093894958}],"concepts":[{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.769411027431488},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.6347023248672485},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.621943473815918},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.5706194639205933},{"id":"https://openalex.org/C74261601","wikidata":"https://www.wikidata.org/wiki/Q40112","display_name":"Ellipse","level":2,"score":0.5509480834007263},{"id":"https://openalex.org/C190694206","wikidata":"https://www.wikidata.org/wiki/Q3276654","display_name":"Polygon (computer graphics)","level":3,"score":0.5409356951713562},{"id":"https://openalex.org/C2778738651","wikidata":"https://www.wikidata.org/wiki/Q16546687","display_name":"Novelty","level":2,"score":0.5373863577842712},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.5146273374557495},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.49637705087661743},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4923907518386841},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.4559635818004608},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.4420749545097351},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.4112318754196167},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37845978140830994},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3293841481208801},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.24257725477218628},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.20296984910964966},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.12347763776779175},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1147392988204956},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08639869093894958},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C27206212","wikidata":"https://www.wikidata.org/wiki/Q34178","display_name":"Theology","level":1,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/01969722.2020.1723872","is_oa":false,"landing_page_url":"https://doi.org/10.1080/01969722.2020.1723872","pdf_url":null,"source":{"id":"https://openalex.org/S117436046","display_name":"Cybernetics & Systems","issn_l":"0196-9722","issn":["0196-9722","1087-6553"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cybernetics and Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.8299999833106995,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":49,"referenced_works":["https://openalex.org/W74452416","https://openalex.org/W99247360","https://openalex.org/W184408651","https://openalex.org/W246298385","https://openalex.org/W1508236978","https://openalex.org/W1989832241","https://openalex.org/W1990501514","https://openalex.org/W1992176519","https://openalex.org/W2001173661","https://openalex.org/W2006127887","https://openalex.org/W2019901578","https://openalex.org/W2026113410","https://openalex.org/W2026832772","https://openalex.org/W2027654459","https://openalex.org/W2027655085","https://openalex.org/W2036341849","https://openalex.org/W2041280856","https://openalex.org/W2051798785","https://openalex.org/W2066559088","https://openalex.org/W2068823774","https://openalex.org/W2069069851","https://openalex.org/W2070108551","https://openalex.org/W2072503251","https://openalex.org/W2079325629","https://openalex.org/W2090049960","https://openalex.org/W2116605411","https://openalex.org/W2137645553","https://openalex.org/W2157041604","https://openalex.org/W2165094119","https://openalex.org/W2171715801","https://openalex.org/W2188674146","https://openalex.org/W2362494595","https://openalex.org/W2397815181","https://openalex.org/W2530162603","https://openalex.org/W2557609975","https://openalex.org/W2600514641","https://openalex.org/W2736017423","https://openalex.org/W2792337586","https://openalex.org/W2792926333","https://openalex.org/W2912565176","https://openalex.org/W2952022111","https://openalex.org/W2970987959","https://openalex.org/W3127575558","https://openalex.org/W4211007335","https://openalex.org/W4245152641","https://openalex.org/W4249749961","https://openalex.org/W4252374882","https://openalex.org/W4255264342","https://openalex.org/W4292158025"],"related_works":["https://openalex.org/W4200515764","https://openalex.org/W2160831542","https://openalex.org/W2345991957","https://openalex.org/W37664198","https://openalex.org/W2098767154","https://openalex.org/W2037438837","https://openalex.org/W2952642102","https://openalex.org/W3187601603","https://openalex.org/W2173034867","https://openalex.org/W2148467997"],"abstract_inverted_index":{"In":[0],"this":[1],"article,":[2],"we":[3,20,31,36],"develop":[4],"the":[5,8,38,50,53,57,70,74,77,83,87,109,112],"definition":[6],"of":[7,10,18,24,40,46,52,56,76,79,86,111],"degree":[9,78],"fuzziness":[11,80],"for":[12],"a":[13,22],"polygonal":[14],"fuzzy":[15,54,59,88],"set.":[16],"First":[17],"all":[19],"take":[21],"polygon":[23],"sides":[25],"2n":[26],"+":[27],"1":[28],"and":[29,61,81,93],"then":[30],"calculate":[32],"its":[33,62,94],"area.":[34],"Also":[35],"consider":[37],"area":[39],"an":[41],"half":[42],"ellipse":[43],"whose":[44],"length":[45,51],"major":[47],"axis":[48,65],"are":[49,105],"interval":[55],"given":[58],"set":[60],"semi":[63],"minor":[64],"is":[66],"1.":[67],"We":[68],"construct":[69],"relative":[71],"error":[72],"as":[73],"measure":[75],"present":[82],"index":[84],"value":[85],"parameter":[89],"after":[90],"K":[91],"years":[92],"role":[95],"in":[96],"modern":[97],"decision":[98],"making":[99],"problems.":[100],"Finally":[101],"real":[102],"life":[103],"applications":[104],"discussed":[106],"to":[107],"justify":[108],"novelty":[110],"new":[113],"method.":[114]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":4}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}
