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The proposed methodology presents an online evolving clustering algorithm composed of participatory learning based on the maximum likelihood norm. To avoid the curse of dimensionality in relation to the number of evolving rules, the algorithm uses an online adaptive norm strategy in the creation of fuzzy rules. The performance of the proposed methodology is concerned to benchmark problems: experiments considering the convergence analysis, by proposal of three Lemmas and one Theorem, of the fuzzy instrumental variable applied to the parametric estimation of nonlinear systems in a noise environment; nonlinear systems identification are performed and compared to evaluate the performance of the approach proposed with other models of evolving systems widely cited in the literature and statistical analysis of experimental results from black box modeling of a helicopter with two degrees of freedom are used for the purpose of show the performance and efficiency the proposed approach.<\/jats:p>","DOI":"10.3233\/jifs-16569","type":"journal-article","created":{"date-parts":[[2017,5,26]],"date-time":"2017-05-26T14:42:54Z","timestamp":1495809774000},"page":"4159-4172","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Evolving Neuro\u2013Fuzzy network modeling\u00a0approach based on recursive fuzzy\u00a0instrumental variable"],"prefix":"10.1177","volume":"32","author":[{"given":"Orlando Donato","family":"Rocha Filho","sequence":"first","affiliation":[{"name":"Federal Institute of Education, Science and Technology, S\u00e3o Luis, MA, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ginalber Luiz Serra","family":"de Oliveira","sequence":"additional","affiliation":[{"name":"Federal Institute of Education, Science and Technology, S\u00e3o Luis, MA, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2017,5,23]]},"reference":[{"key":"e_1_3_1_2_2","first-page":"101","article-title":"Neural Network Controller for Two-Degree-Freedom Helicopter Control System","author":"Abdul Rahman R.Z.","year":"2012","unstructured":"Abdul RahmanR.Z. and ShoumyN.J., Neural Network Controller for Two-Degree-Freedom Helicopter Control System, 2012 12th International Conference on Control, Automation and Systems (ICCAS), 2012, pp. 101\u2013106.","journal-title":"2012 12th International Conference on Control, Automation and Systems (ICCAS)"},{"key":"e_1_3_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijar.2014.02.003"},{"key":"e_1_3_1_4_2","first-page":"29","article-title":"Evolving fuzzy systems from data streams in real-time","author":"Angelov P.","year":"2006","unstructured":"AngelovP. and ZhouX., Evolving fuzzy systems from data streams in real-time, IEEE (2006), 29\u201335.","journal-title":"IEEE"},{"key":"e_1_3_1_5_2","volume-title":"IEEE Press Series on Computational Intelligence","author":"Angelov P.","year":"2013","unstructured":"AngelovP., Autonomous Learning Systems, From Data Streams to Knowledge in Real-time, IEEE Press Series on Computational Intelligence, Willey, ISBN 9781119951520, 2013."},{"key":"e_1_3_1_6_2","volume-title":"IEEE Press Series on Computational Intelligence","author":"Angelov P.","year":"2010","unstructured":"AngelovP., FilevD. and KasabovN., Evolving Intelligent Systems: Methology and applications, IEEE Press Series on Computational Intelligence, Willey-Blackwell, ISBN 9780470287194, 2010."},{"key":"e_1_3_1_7_2","first-page":"161","article-title":"An Efficient Neuro-Fuzzy Approach for Classification of Iris Dataset","author":"Arya V.","year":"2014","unstructured":"AryaV. and RathyR.K., An Efficient Neuro-Fuzzy Approach for Classification of Iris Dataset, International Conference on Reliability, Optimization and Information Technology, 2014, pp. 161\u2013165. doi: 10.1109\/ICROIT.2014.6798304","journal-title":"International Conference on Reliability, Optimization and Information Technology"},{"key":"e_1_3_1_8_2","doi-asserted-by":"crossref","unstructured":"BabuskaR. 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