{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,19]],"date-time":"2026-01-19T02:29:49Z","timestamp":1768789789280,"version":"3.49.0"},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Soft Comput"],"published-print":{"date-parts":[[2022,1]]},"DOI":"10.1007\/s00500-021-06601-8","type":"journal-article","created":{"date-parts":[[2022,1,5]],"date-time":"2022-01-05T15:02:51Z","timestamp":1641394971000},"page":"589-603","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Derivation and structural analysis of a three-input interval type-2 TS fuzzy PID controller"],"prefix":"10.1007","volume":"26","author":[{"given":"Ritu","family":"Raj","sequence":"first","affiliation":[]},{"given":"B. M.","family":"Mohan","sequence":"additional","affiliation":[]},{"given":"Dong-Eun","family":"Lee","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1743-1061","authenticated-orcid":false,"given":"Jung-Min","family":"Yang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,1,5]]},"reference":[{"key":"6601_CR1","doi-asserted-by":"publisher","first-page":"615","DOI":"10.1016\/j.ins.2014.04.015","volume":"279","author":"O Castillo","year":"2014","unstructured":"Castillo O, Melin P (2014) A review on interval type-2 fuzzy logic applications in intelligent control. Inf Sci 279:615\u2013631","journal-title":"Inf Sci"},{"issue":"3","key":"6601_CR2","doi-asserted-by":"publisher","first-page":"1274","DOI":"10.1016\/j.asoc.2007.02.021","volume":"8","author":"O Castillo","year":"2008","unstructured":"Castillo O, Aguilar L, Cazarez N, Cardenas S (2008) Systematic design of a stable type-2 fuzzy logic controller. Appl Soft Comput 8(3):1274\u20131279","journal-title":"Appl Soft Comput"},{"key":"6601_CR3","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1016\/j.ins.2016.03.026","volume":"354","author":"O Castillo","year":"2016","unstructured":"Castillo O, Amador-Angulo L, Castro JR, Garcia-Valdez M (2016) A comparative study of type-1 fuzzy logic systems, interval type-2 fuzzy logic systems and generalized type-2 fuzzy logic systems in control problems. Inf Sci 354:257\u2013274","journal-title":"Inf Sci"},{"issue":"4","key":"6601_CR4","doi-asserted-by":"publisher","first-page":"802","DOI":"10.1109\/TFUZZ.2010.2049022","volume":"18","author":"X Du","year":"2010","unstructured":"Du X, Ying H (2010) Derivation and analysis of the analytical structures of the interval type-2 fuzzy PI and PD controllers. IEEE Trans Fuzzy Syst 18(4):802\u2013814","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"6601_CR5","doi-asserted-by":"publisher","first-page":"704","DOI":"10.1016\/j.asoc.2014.08.040","volume":"24","author":"AM El-Nagar","year":"2014","unstructured":"El-Nagar AM, El-Bardini M (2014) Derivation and stability analysis of the analytical structures of the interval type-2 fuzzy PID controller. Appl Soft Comput 24:704\u2013716","journal-title":"Appl Soft Comput"},{"issue":"3","key":"6601_CR6","doi-asserted-by":"publisher","first-page":"2346","DOI":"10.1016\/j.apm.2015.09.005","volume":"40","author":"AM El-Nagar","year":"2016","unstructured":"El-Nagar AM, El-Bardini M (2016) Hardware-in-the-loop simulation of interval type-2 fuzzy PD controller for uncertain nonlinear system using low-cost microcontroller. Appl Math Model 40(3):2346\u20132355","journal-title":"Appl Math Model"},{"key":"6601_CR7","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1016\/j.eswa.2016.12.029","volume":"73","author":"A Kumar","year":"2017","unstructured":"Kumar A, Kumar V (2017) Evolving an interval type-2 fuzzy PID controller for the redundant robotic manipulator. Expert Syst Appl 73:161\u2013177","journal-title":"Expert Syst Appl"},{"issue":"7","key":"6601_CR8","doi-asserted-by":"publisher","first-page":"1293","DOI":"10.1007\/s00500-013-1144-1","volume":"18","author":"T Kumbasar","year":"2014","unstructured":"Kumbasar T (2014) A simple design method for interval type-2 fuzzy PID controllers. Soft Comput 18(7):1293\u20131304","journal-title":"Soft Comput"},{"issue":"3","key":"6601_CR9","doi-asserted-by":"publisher","first-page":"675","DOI":"10.1109\/TFUZZ.2015.2471805","volume":"24","author":"T Kumbasar","year":"2016","unstructured":"Kumbasar T (2016) Robust stability analysis and systematic design of single-input interval type-2 fuzzy logic controllers. IEEE Trans Fuzzy Syst 24(3):675\u2013694","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"10","key":"6601_CR10","doi-asserted-by":"publisher","first-page":"2665","DOI":"10.1007\/s00500-015-1966-0","volume":"21","author":"T Kumbasar","year":"2017","unstructured":"Kumbasar T, Eksin I, Guzelkaya M, Yesil E (2017) An inverse controller design method for interval type-2 fuzzy models. Soft Comput 21(10):2665\u20132686","journal-title":"Soft Comput"},{"issue":"6","key":"6601_CR11","doi-asserted-by":"crossref","first-page":"1344","DOI":"10.1109\/JAS.2019.1911723","volume":"6","author":"R Li","year":"2019","unstructured":"Li R, Huang Y, Wang J (2019) Long-term traffic volume prediction based on K-means Gaussian interval type-2 fuzzy sets. IEEE\/CAA J Autom Sinica 6(6):1344\u20131351","journal-title":"IEEE\/CAA J Autom Sinica"},{"key":"6601_CR12","unstructured":"Magnetic levitation: control experiments feedback instruments limited, (2011) UK"},{"issue":"11","key":"6601_CR13","doi-asserted-by":"publisher","first-page":"3887","DOI":"10.1007\/s00500-018-3503-4","volume":"23","author":"P Melin","year":"2019","unstructured":"Melin P, Ontiveros-Robles E, Gonzalez CI, Castro JR, Castillo O (2019) An approach for parameterized shadowed type-2 fuzzy membership functions applied in control applications. Soft Comput 23(11):3887\u20133901","journal-title":"Soft Comput"},{"issue":"4","key":"6601_CR14","doi-asserted-by":"publisher","first-page":"2362","DOI":"10.1109\/TFUZZ.2017.2774190","volume":"26","author":"JM Mendel","year":"2018","unstructured":"Mendel JM (2018) Explaining the performance potential of rule-based fuzzy systems as a greater sculpting of the state space. IEEE Trans Fuzzy Syst 26(4):2362\u20132373","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"6601_CR15","doi-asserted-by":"publisher","DOI":"10.1002\/9781118886540","volume-title":"Introduction to type-2 fuzzy logic control: theory and applications","author":"J Mendel","year":"2014","unstructured":"Mendel J, Hagras H, Tan WW, Melek WW, Ying H (2014) Introduction to type-2 fuzzy logic control: theory and applications. Wiley, New York, NY"},{"issue":"3","key":"6601_CR16","doi-asserted-by":"publisher","first-page":"416","DOI":"10.1109\/TFUZZ.2011.2174061","volume":"20","author":"M Nei","year":"2012","unstructured":"Nei M, Tan WW (2012) Analytical structure and characteristics of symmetric Karnik-Mendel type-reduced interval type-2 fuzzy PI and PD controllers. IEEE Trans Fuzzy Syst 20(3):416\u2013430","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"6601_CR17","doi-asserted-by":"publisher","first-page":"186","DOI":"10.1016\/j.engappai.2018.06.013","volume":"74","author":"E Ontiveros","year":"2018","unstructured":"Ontiveros E, Melin P, Castillo O (2018) High order $$\\alpha $$-planes integration: a new approach to computational cost reduction of general type-2 fuzzy systems. Eng Appl Artif Intel 74:186\u2013197","journal-title":"Eng Appl Artif Intel"},{"key":"6601_CR18","doi-asserted-by":"crossref","unstructured":"Raj R, Mohan BM, Yang JM (2020) A simplified structure of the simplest interval type-2 fuzzy two-term controller. In: proceedings advances in control and optimization of dynamical systems (ACODS 2020). Chennai, India, pp. 661\u2013666","DOI":"10.1016\/j.ifacol.2020.06.110"},{"issue":"2","key":"6601_CR19","doi-asserted-by":"publisher","first-page":"196","DOI":"10.1080\/16168658.2018.1517974","volume":"10","author":"R Raj","year":"2018","unstructured":"Raj R, Mohan BM (2018) Stability analysis of general Takagi-Sugeno fuzzy two-term controllers. Fuzzy Inf Eng 10(2):196\u2013212","journal-title":"Fuzzy Inf Eng"},{"issue":"15","key":"6601_CR20","doi-asserted-by":"publisher","first-page":"5147","DOI":"10.1007\/s00500-017-2674-8","volume":"22","author":"R Raj","year":"2018","unstructured":"Raj R, Mohan BM (2018) Modeling and analysis of the simplest fuzzy PID controller of Takagi-Sugeno type with modified rule base. Soft Comput 22(15):5147\u20135161","journal-title":"Soft Comput"},{"issue":"1","key":"6601_CR21","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1504\/IJPSE.2019.096674","volume":"5","author":"R Raj","year":"2019","unstructured":"Raj R, Mohan BM (2019) Analytical structures and stability analysis of the simplest Takagi-Sugeno fuzzy two-term controllers. Int J Process Syst Eng 5(1):67\u201392","journal-title":"Int J Process Syst Eng"},{"key":"6601_CR22","doi-asserted-by":"publisher","first-page":"103273","DOI":"10.1016\/j.engappai.2019.103273","volume":"87","author":"R Raj","year":"2020","unstructured":"Raj R, Mohan BM (2020) General structure of interval type-2 fuzzy PI\/PD controller of Takagi-Sugeno type. Eng Appl Artif Intel 87:103273","journal-title":"Eng Appl Artif Intel"},{"issue":"5","key":"6601_CR23","doi-asserted-by":"publisher","first-page":"832","DOI":"10.1109\/TFUZZ.2012.2186818","volume":"10","author":"D Wu","year":"2012","unstructured":"Wu D (2012) On the fundamental differences between interval type-2 and type-1 fuzzy logic controllers. IEEE Trans Fuzzy Syst 10(5):832\u2013848","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"1","key":"6601_CR24","doi-asserted-by":"publisher","first-page":"80","DOI":"10.1109\/TFUZZ.2012.2201728","volume":"21","author":"D Wu","year":"2013","unstructured":"Wu D (2013) Approaches for reducing the computational cost of interval type-2 fuzzy logic controllers: overview and comparison. IEEE Trans Fuzzy Syst 21(1):80\u201399","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"8","key":"6601_CR25","doi-asserted-by":"publisher","first-page":"829","DOI":"10.1016\/j.engappai.2005.12.011","volume":"19","author":"D Wu","year":"2006","unstructured":"Wu D, Tan WW (2006) Genetic learning and performance evaluation of interval type-2 fuzzy logic controllers. Eng Appl Artif Intel 19(8):829\u2013841","journal-title":"Eng Appl Artif Intel"},{"issue":"4","key":"6601_CR26","first-page":"503","volume":"45","author":"D Wu","year":"2007","unstructured":"Wu D, Tan WW (2007) A simplified type-2 fuzzy controller for real-time control. ISA Trans 45(4):503\u2013516","journal-title":"ISA Trans"},{"key":"6601_CR27","doi-asserted-by":"crossref","unstructured":"Ying H (1993) The simplest fuzzy controllers using different inference methods are different nonlinear proportional-integral controllers with variable gains. Automatica 29(6):1579","DOI":"10.1016\/0005-1098(93)90025-O"},{"issue":"2","key":"6601_CR28","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1016\/S0005-1098(97)00173-8","volume":"34","author":"H Ying","year":"1998","unstructured":"Ying H (1998a) The Takagi-Sugeno fuzzy controllers using the simplified linear control rules are nonlinear variable gain controllers. Automatica 34(2):157\u2013167","journal-title":"Automatica"},{"issue":"2","key":"6601_CR29","doi-asserted-by":"publisher","first-page":"226","DOI":"10.1109\/91.669021","volume":"6","author":"H Ying","year":"1998","unstructured":"Ying H (1998b) Constructing nonlinear variable gain controllers via the Takagi-Sugeno fuzzy control. IEEE Trans Fuzzy Syst 6(2):226\u2013234","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"6601_CR30","doi-asserted-by":"publisher","first-page":"517","DOI":"10.1016\/j.asoc.2018.12.039","volume":"76","author":"CMT Yip","year":"2019","unstructured":"Yip CMT, Tan WW, Nie M (2019) On the difference in control performance of interval type-2 fuzzy PI control system with different FOU shapes. Appl Soft Comput 76:517\u2013532","journal-title":"Appl Soft Comput"},{"issue":"1","key":"6601_CR31","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1109\/TSMC.1973.5408575","volume":"3","author":"LA Zadeh","year":"1973","unstructured":"Zadeh LA (1973) Outline of a new approach to the analysis of complex systems and decision processes. IEEE Trans Syst Man Cybern SMC 3(1):28\u201344","journal-title":"IEEE Trans Syst Man Cybern SMC"},{"issue":"1","key":"6601_CR32","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1109\/JAS.2019.1911810","volume":"7","author":"X Zhao","year":"2020","unstructured":"Zhao X, Mo H, Yan K, Li L (2020) Type-2 fuzzy control for driving state and behavioral decisions of unmanned vehicle. IEEE\/CAA J Autom Sinica 7(1):178\u2013186","journal-title":"IEEE\/CAA J Autom Sinica"},{"issue":"3","key":"6601_CR33","doi-asserted-by":"publisher","first-page":"447","DOI":"10.1109\/TFUZZ.2012.2226891","volume":"21","author":"H Zhou","year":"2013","unstructured":"Zhou H, Ying H (2013) A method for deriving the analytical structure of a broad class of typical interval type-2 Mamdani fuzzy controllers. IEEE Trans Fuzzy Syst 21(3):447\u2013458","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"9","key":"6601_CR34","doi-asserted-by":"publisher","first-page":"2492","DOI":"10.1109\/TCYB.2016.2570239","volume":"21","author":"H Zhou","year":"2017","unstructured":"Zhou H, Ying H (2017) Deriving and analyzing analytical structures of a class of typical interval type-2 TS fuzzy controllers. IEEE Trans Cybern 21(9):2492\u20132503","journal-title":"IEEE Trans Cybern"},{"issue":"9","key":"6601_CR35","doi-asserted-by":"publisher","first-page":"1881","DOI":"10.1109\/TFUZZ.2019.2892354","volume":"27","author":"H Zhou","year":"2019","unstructured":"Zhou H, Ying H, Zhang C (2019) Effects of increasing the footprints of uncertainty on analytical structure of the classes of interval type-2 Mamdani and TS fuzzy controllers. IEEE Trans Fuzzy Syst 27(9):1881\u20131890","journal-title":"IEEE Trans Fuzzy Syst"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-021-06601-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00500-021-06601-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-021-06601-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,15]],"date-time":"2024-09-15T19:02:35Z","timestamp":1726426955000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00500-021-06601-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1]]},"references-count":35,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2022,1]]}},"alternative-id":["6601"],"URL":"https:\/\/doi.org\/10.1007\/s00500-021-06601-8","relation":{},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"value":"1432-7643","type":"print"},{"value":"1433-7479","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,1]]},"assertion":[{"value":"19 November 2021","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 January 2022","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}