{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T17:57:48Z","timestamp":1754157468056,"version":"3.41.2"},"reference-count":11,"publisher":"Emerald","issue":"3\/4","license":[{"start":{"date-parts":[[2009,4,10]],"date-time":"2009-04-10T00:00:00Z","timestamp":1239321600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.emerald.com\/insight\/site-policies"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2009,4,10]]},"abstract":"<jats:sec><jats:title content-type=\"abstract-heading\">Purpose<\/jats:title><jats:p>The purpose of this paper is to answer the question that what the best shape of fuzzy sets is in fuzzy systems for function approximation which is essential in many applications of fuzzy systems.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Design\/methodology\/approach<\/jats:title><jats:p>The uniform approximation rates indicate the approximating capabilities of fuzzy systems for function approximation. By Fourier analysis, the uniform approximation rates are estimated for the fuzzy systems with various shapes of if\u2010part fuzzy sets in the case of single\u2010input and single\u2010output. Based on the approximation rates, the relationships between the approximating capabilities and the shapes of fuzzy sets are developed and compared.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Findings<\/jats:title><jats:p>The since functions as the input membership functions in fuzzy systems are proved to have the almost best approximation property in a particular class of membership functions.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Research limitations\/implications<\/jats:title><jats:p>From the viewpoint of function approximation, the input membership functions are not necessarily positive in fuzzy systems.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Practical implications<\/jats:title><jats:p>For engineers, the sinc\u2010shaped membership function is a good choice to improve their fuzzy systems in real applications.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Originality\/value<\/jats:title><jats:p>The uniform approximation rates of fuzzy systems for function approximation are estimated. Mathematically, the relationships between the approximating capabilities and the shapes of fuzzy sets are analyzed for fuzzy systems.<\/jats:p><\/jats:sec>","DOI":"10.1108\/03684920910944128","type":"journal-article","created":{"date-parts":[[2009,5,30]],"date-time":"2009-05-30T07:06:18Z","timestamp":1243667178000},"page":"426-434","source":"Crossref","is-referenced-by-count":1,"title":["The relationship between the uniform approximation rates and the shapes of fuzzy sets in fuzzy systems"],"prefix":"10.1108","volume":"38","author":[{"given":"Qiang","family":"Luo","sequence":"first","affiliation":[]},{"given":"Dongyun","family":"Yi","sequence":"additional","affiliation":[]},{"given":"Wenqiang","family":"Yang","sequence":"additional","affiliation":[]}],"member":"140","reference":[{"key":"key2022012919511535700_b11","doi-asserted-by":"crossref","unstructured":"Butzer, P.L. and Nessel, R.J. (1971), Fourier Analysis and Approximation, Vol. 1, Brikh\u00e4user Press, Weinheim.","DOI":"10.1007\/978-3-0348-7448-9_1"},{"key":"key2022012919511535700_b2","unstructured":"Chen, H. (2005), \u201cFault tolerant control for switched reluctance motor drive based on fuzzy logic\u201d, Advances in Systems Science and Applications, Vol. 5 No. 2, pp. 219\u201024."},{"key":"key2022012919511535700_b3","unstructured":"Cheng, M. and Li, Z. (2004), \u201cTraffic forecasting model based on Takagi\u2010Sugeno fuzzy logical system\u201d, Advances in Systems Science and Applications, Vol. 4 No. 3, pp. 356\u201061."},{"key":"key2022012919511535700_b10","doi-asserted-by":"crossref","unstructured":"Hassine, R., Karray, F., Alimi, A.M. and Selmi, M. 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