{"id":"https://openalex.org/W3189196468","doi":"https://doi.org/10.1109/tfuzz.2021.3097810","title":"Interval Type-2 Fuzzy Differential Equations and Stability","display_name":"Interval Type-2 Fuzzy Differential Equations and Stability","publication_year":2021,"publication_date":"2021-08-10","ids":{"openalex":"https://openalex.org/W3189196468","doi":"https://doi.org/10.1109/tfuzz.2021.3097810","mag":"3189196468"},"language":"en","primary_location":{"id":"doi:10.1109/tfuzz.2021.3097810","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2021.3097810","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/A5023932385","display_name":"Marzieh Najariyan","orcid":"https://orcid.org/0000-0001-8043-7808"},"institutions":[{"id":"https://openalex.org/I180726961","display_name":"Shenzhen University","ror":"https://ror.org/01vy4gh70","country_code":"CN","type":"education","lineage":["https://openalex.org/I180726961"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Marzieh Najariyan","raw_affiliation_strings":["College of Mechatronics and Control Engineering, Shenzhen Univerity, Shenzhen, China"],"raw_orcid":"https://orcid.org/0000-0001-8043-7808","affiliations":[{"raw_affiliation_string":"College of Mechatronics and Control Engineering, Shenzhen Univerity, Shenzhen, China","institution_ids":["https://openalex.org/I180726961"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100722029","display_name":"Li Qiu","orcid":"https://orcid.org/0000-0001-7049-4518"},"institutions":[{"id":"https://openalex.org/I180726961","display_name":"Shenzhen University","ror":"https://ror.org/01vy4gh70","country_code":"CN","type":"education","lineage":["https://openalex.org/I180726961"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li Qiu","raw_affiliation_strings":["College of Mechatronics and Control Engineering, Shenzhen Univerity, Shenzhen, China"],"raw_orcid":"https://orcid.org/0000-0001-7049-4518","affiliations":[{"raw_affiliation_string":"College of Mechatronics and Control Engineering, Shenzhen Univerity, Shenzhen, China","institution_ids":["https://openalex.org/I180726961"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I180726961"],"apc_list":null,"apc_paid":null,"fwci":3.6008,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.9423918,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"30","issue":"8","first_page":"2915","last_page":"2929"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9979000091552734,"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":0.9779000282287598,"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/mathematics","display_name":"Mathematics","score":0.7381390333175659},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.6421087980270386},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.5995078086853027},{"id":"https://openalex.org/keywords/fuzzy-subalgebra","display_name":"Fuzzy subalgebra","score":0.531245231628418},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.4992640018463135},{"id":"https://openalex.org/keywords/fuzzy-set-operations","display_name":"Fuzzy set operations","score":0.4954005479812622},{"id":"https://openalex.org/keywords/defuzzification","display_name":"Defuzzification","score":0.48457229137420654},{"id":"https://openalex.org/keywords/type-2-fuzzy-sets-and-systems","display_name":"Type-2 fuzzy sets and systems","score":0.44305792450904846},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41282257437705994},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.321617066860199},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16882282495498657},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1292279064655304}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7381390333175659},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.6421087980270386},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.5995078086853027},{"id":"https://openalex.org/C115740575","wikidata":"https://www.wikidata.org/wiki/Q5511136","display_name":"Fuzzy subalgebra","level":5,"score":0.531245231628418},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.4992640018463135},{"id":"https://openalex.org/C148671577","wikidata":"https://www.wikidata.org/wiki/Q5511133","display_name":"Fuzzy set operations","level":4,"score":0.4954005479812622},{"id":"https://openalex.org/C170260401","wikidata":"https://www.wikidata.org/wiki/Q5251735","display_name":"Defuzzification","level":5,"score":0.48457229137420654},{"id":"https://openalex.org/C17350324","wikidata":"https://www.wikidata.org/wiki/Q7860605","display_name":"Type-2 fuzzy sets and systems","level":5,"score":0.44305792450904846},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41282257437705994},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.321617066860199},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16882282495498657},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1292279064655304}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tfuzz.2021.3097810","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tfuzz.2021.3097810","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":[],"awards":[{"id":"https://openalex.org/G5292448070","display_name":null,"funder_award_id":"U1813225","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7953400257","display_name":null,"funder_award_id":"61873170","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W90750737","https://openalex.org/W607489306","https://openalex.org/W1535657934","https://openalex.org/W1574822903","https://openalex.org/W1642042653","https://openalex.org/W1992777250","https://openalex.org/W2009871771","https://openalex.org/W2021212601","https://openalex.org/W2048212998","https://openalex.org/W2055443629","https://openalex.org/W2074683918","https://openalex.org/W2095292012","https://openalex.org/W2169665448","https://openalex.org/W2465932600","https://openalex.org/W2474649570","https://openalex.org/W2529621486","https://openalex.org/W2580890888","https://openalex.org/W2585824213","https://openalex.org/W2773189249","https://openalex.org/W2793584758","https://openalex.org/W2801570955","https://openalex.org/W2803260244","https://openalex.org/W2946167914","https://openalex.org/W2972213371","https://openalex.org/W3008061058","https://openalex.org/W3034858087","https://openalex.org/W3090479667","https://openalex.org/W3095141645","https://openalex.org/W3122881245","https://openalex.org/W3153599949","https://openalex.org/W3186580698","https://openalex.org/W6636908030","https://openalex.org/W6683025888"],"related_works":["https://openalex.org/W2184441312","https://openalex.org/W4361984403","https://openalex.org/W1975005191","https://openalex.org/W1485268022","https://openalex.org/W2674573885","https://openalex.org/W2331106272","https://openalex.org/W3176863924","https://openalex.org/W2253053392","https://openalex.org/W1542808721","https://openalex.org/W2060361571"],"abstract_inverted_index":{"This":[0],"article":[1],"is":[2,48,98],"devoted":[3],"to":[4,17,50,172],"present":[5],"a":[6],"framework":[7],"for":[8,161],"studying":[9],"type-2":[10,19,25,40,44,59,73,82,117],"fuzzy":[11,20,26,41,60,74,83,119,147,149,153],"calculus.":[12],"Some":[13],"new":[14,37,143],"concepts":[15,103,144],"pertaining":[16],"interval":[18,24,72,81,137,165],"functions":[21],"(IT2FF)":[22],"and":[23,77,107,122,133,155],"differential":[27],"equations":[28],"(IT2FDE)":[29],"with":[30],"their":[31],"stability":[32],"analysis":[33,163],"are":[34,86,111,139,170],"introduced.":[35,112],"A":[36],"definition":[38],"of":[39,54,58,65,71,80,90,96,104,109,116,125,136,164],"derivative":[42,46],"called":[43],"granular":[45,91,118],"(T2gr-derivative)":[47],"defined":[49],"overcome":[51],"the":[52,55,63,69,78,94,102,114,123,131,159,162,174],"disadvantages":[53],"previous":[56],"definitions":[57,64],"derivatives.":[61],"Furthermore,":[62],"elementary":[66],"arithmetic":[67],"on":[68,93],"set":[70,79,95],"numbers":[75,85],"(IT2FNs)":[76],"complex":[84],"presented.":[87,140],"The":[88],"notion":[89],"metric":[92],"IT2FNs":[97],"also":[99],"defined.":[100],"Besides,":[101],"continuity,":[105],"integral,":[106],"limit":[108],"IT2FFs":[110],"Using":[113],"concept":[115],"Laplace":[120],"transform":[121],"approximations":[124],"T2gr-derivative":[126],"proposed":[127],"in":[128],"this":[129],"article,":[130],"exact":[132],"approximate":[134],"solutions":[135],"T2FDE":[138,166],"Then,":[141],"some":[142],"such":[145],"as":[146],"node,":[148],"saddle":[150],"spiral":[151],"point,":[152],"star,":[154],"so":[156],"forth":[157],"lay":[158],"groundwork":[160],"stability.":[167],"Several":[168],"examples":[169],"given":[171],"illustrate":[173],"presented":[175],"notions.":[176]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}