{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T08:43:03Z","timestamp":1761986583031,"version":"build-2065373602"},"reference-count":42,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,8,20]],"date-time":"2025-08-20T00:00:00Z","timestamp":1755648000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Special Projects in National Key Research and Development Program of China","award":["2018YFB1802200","2022SDKYA029","2019B010118001","NSFC: 11561029"],"award-info":[{"award-number":["2018YFB1802200","2022SDKYA029","2019B010118001","NSFC: 11561029"]}]},{"name":"GPNU Foundation","award":["2018YFB1802200","2022SDKYA029","2019B010118001","NSFC: 11561029"],"award-info":[{"award-number":["2018YFB1802200","2022SDKYA029","2019B010118001","NSFC: 11561029"]}]},{"name":"Key Areas of Guangdong Province","award":["2018YFB1802200","2022SDKYA029","2019B010118001","NSFC: 11561029"],"award-info":[{"award-number":["2018YFB1802200","2022SDKYA029","2019B010118001","NSFC: 11561029"]}]},{"name":"National Natural Science Foundation of China","award":["2018YFB1802200","2022SDKYA029","2019B010118001","NSFC: 11561029"],"award-info":[{"award-number":["2018YFB1802200","2022SDKYA029","2019B010118001","NSFC: 11561029"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Discrete time-varying matrix problems are prevalent in scientific and engineering fields, and their efficient solution remains a key research objective. Existing direct discrete recurrent neural network models exhibit limitations in noise resistance and are prone to accuracy degradation in complex noise environments. To overcome these deficiencies, this paper proposes a fuzzy integral direct discrete recurrent neural network (FITDRNN) model. The FITDRNN model incorporates an integral term to counteract noise interference and employs a fuzzy logic system for dynamic adjustment of the integral parameter magnitude, thereby further enhancing its noise resistance. Theoretical analysis, combined with numerical experiments and robotic arm trajectory tracking experiments, verifies the convergence and noise resistance of the proposed FITDRNN model.<\/jats:p>","DOI":"10.3390\/sym17081359","type":"journal-article","created":{"date-parts":[[2025,8,20]],"date-time":"2025-08-20T07:50:46Z","timestamp":1755676246000},"page":"1359","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Direct Discrete Recurrent Neural Network with Integral Noise Tolerance and Fuzzy Integral Parameters for Discrete Time-Varying Matrix Problem Solving"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0478-719X","authenticated-orcid":false,"given":"Chenfu","family":"Yi","sequence":"first","affiliation":[{"name":"School of Cyber Security, Guangdong Polytechnic Normal University, Guangzhou 510630, China"},{"name":"School of Information Engineering, Jiangxi University of Science and Technology, Ganzhou 341000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jie","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Cyber Security, Guangdong Polytechnic Normal University, Guangzhou 510630, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ling","family":"Li","sequence":"additional","affiliation":[{"name":"School of Cyber Security, Guangdong Polytechnic Normal University, Guangzhou 510630, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.matcom.2024.05.006","article-title":"New Activation Functions and Zhangians In Zeroing Neural Network and Applications to Time-Varying Matrix Pseudoinversion","volume":"225","author":"Gao","year":"2024","journal-title":"Math. 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