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We then exploit Weierstrass\u2019s approximation theorem to show that this new type of fuzzy system can approximate any real continuous function on a closed interval to arbitrary accuracy and provide the corresponding approximation accuracy with respect to infinite norms. We also provide two numerical examples to illustrate the effectiveness of this new type of fuzzy system. Both theoretical and numerical results show that this new type of fuzzy system achieves the quite approximation effect with a few fuzzy rules.<\/jats:p>","DOI":"10.3233\/jifs-223542","type":"journal-article","created":{"date-parts":[[2023,3,24]],"date-time":"2023-03-24T16:27:45Z","timestamp":1679675265000},"page":"9545-9563","source":"Crossref","is-referenced-by-count":1,"title":["A new type of fuzzy systems in terms of vague partitions"],"prefix":"10.1177","volume":"44","author":[{"given":"Hanhan","family":"Shen","sequence":"first","affiliation":[{"name":"School of Mathematics, Southwest Jiaotong University, Chengdu, PR China"}]},{"given":"Xiaodong","family":"Pan","sequence":"additional","affiliation":[{"name":"School of Mathematics, Southwest Jiaotong University, Chengdu, PR China"}]},{"given":"Xiaoyu","family":"Peng","sequence":"additional","affiliation":[{"name":"School of Mathematics, Southwest Jiaotong University, Chengdu, PR China"}]},{"given":"Yexing","family":"Dan","sequence":"additional","affiliation":[{"name":"School of Mathematics, Southwest Jiaotong University, Chengdu, PR China"}]},{"given":"Junsheng","family":"Qiao","sequence":"additional","affiliation":[{"name":"College of Mathematics and Statistics, Northwest Normal University, Lanzhou, PR China"}]}],"member":"179","reference":[{"issue":"1","key":"10.3233\/JIFS-223542_ref1","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","article-title":"Fuzzy set","volume":"8","author":"Zadeh","year":"1965","journal-title":"Information and Control"},{"issue":"2","key":"10.3233\/JIFS-223542_ref2","doi-asserted-by":"crossref","first-page":"270","DOI":"10.1109\/3477.915352","article-title":"Sufficient conditions on fuzzy logic controllers asuniversal approximators","volume":"31","author":"Weitian","year":"2001","journal-title":"IEEE Transactions on Systems, Man, andCybernetics, Part B (Cybernetics)"},{"issue":"3","key":"10.3233\/JIFS-223542_ref3","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1016\/0005-1098(94)90130-9","article-title":"Sufficient conditions on general fuzzy systems as functionapproximators","volume":"30","author":"Ying","year":"1994","journal-title":"Automatica"},{"issue":"1","key":"10.3233\/JIFS-223542_ref5","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1109\/3477.740162","article-title":"Simplifying fuzzy rule-based models usingorthogonal transformation methods","volume":"29","author":"Yen","year":"1999","journal-title":"IEEE Transactions onSystems, Man, and Cybernetics, Part B (Cybernetics)"},{"issue":"2","key":"10.3233\/JIFS-223542_ref6","doi-asserted-by":"crossref","first-page":"344","DOI":"10.1109\/3477.485887","article-title":"Simplification of fuzzy-neural systems using similarity analysis","volume":"26","author":"Chao","year":"1996","journal-title":"IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics)"},{"issue":"3","key":"10.3233\/JIFS-223542_ref7","doi-asserted-by":"crossref","first-page":"376","DOI":"10.1109\/3477.678632","article-title":"Similarity measures infuzzy rule base simplification","volume":"28","author":"Setnes","year":"1998","journal-title":"IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics)"},{"issue":"5","key":"10.3233\/JIFS-223542_ref8","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1109\/TFUZZ.2005.856566","article-title":"A novel fuzzy system with dynamic rule base","volume":"13","author":"Chen","year":"2005","journal-title":"IEEE Transactions on Fuzzy Systems"},{"key":"10.3233\/JIFS-223542_ref9","unstructured":"Wang L.X. , A course in fuzzy systems & control, Prentice- Hall, Inc. 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