{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,11]],"date-time":"2025-09-11T19:02:15Z","timestamp":1757617335452,"version":"3.44.0"},"reference-count":45,"publisher":"Springer Science and Business Media LLC","issue":"7-8","license":[{"start":{"date-parts":[[2025,1,9]],"date-time":"2025-01-09T00:00:00Z","timestamp":1736380800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,1,9]],"date-time":"2025-01-09T00:00:00Z","timestamp":1736380800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int. J. Mach. Learn. & Cyber."],"published-print":{"date-parts":[[2025,8]]},"DOI":"10.1007\/s13042-024-02522-8","type":"journal-article","created":{"date-parts":[[2025,1,9]],"date-time":"2025-01-09T08:51:01Z","timestamp":1736412661000},"page":"4525-4544","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Rough set interpretation to RBF neural network"],"prefix":"10.1007","volume":"16","author":[{"given":"Dayong","family":"Deng","sequence":"first","affiliation":[]},{"given":"Jie","family":"Wang","sequence":"additional","affiliation":[]},{"given":"Zhixuan","family":"Deng","sequence":"additional","affiliation":[]},{"given":"Keyu","family":"Liu","sequence":"additional","affiliation":[]},{"given":"Pengfei","family":"Zhang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,1,9]]},"reference":[{"issue":"3","key":"2522_CR1","first-page":"321","volume":"2","author":"DS Broomhead","year":"1988","unstructured":"Broomhead DS, Lowe D (1988) Multivariable functional interpolation and adaptive networks. Complex Syst 2(3):321\u2013355","journal-title":"Complex Syst"},{"doi-asserted-by":"crossref","unstructured":"Fong RC, Vedaldi A (2017) Interpretable explanations of black boxes by meaningful perturbation. In: Proceedings of the IEEE International Conference on Computer Vision, pp. 3429\u20133437","key":"2522_CR2","DOI":"10.1109\/ICCV.2017.371"},{"issue":"7","key":"2522_CR3","first-page":"1","volume":"10","author":"B Sebastian","year":"2015","unstructured":"Sebastian B, Alexander B, Gr\u00e9goire M, Frederick K, Klaus RM, Wojciech S (2015) On pixel-wise explanations for non-linear classifier decisions by layer-wise relevance propagation. PLOS ONE 10(7):1\u201346","journal-title":"PLOS ONE"},{"issue":"7","key":"2522_CR4","first-page":"38","volume":"14","author":"G Hinton","year":"2015","unstructured":"Hinton G, Vinyals O, Dean J (2015) Distilling the knowledge in a neural network. Comput Sci 14(7):38\u201339","journal-title":"Comput Sci"},{"unstructured":"Inseop C, SeongUk P, Jangho K, Nojun K (2020) Feature-map-level online adversarial knowledge distillation. In: Proceedings of the 37th International Conference on Machine Learning, Virtual Event, pp. 2006\u20132015","key":"2522_CR5"},{"unstructured":"Bahdanau D, Cho K, Bengio Y (2014) Neural machine translation by jointly learning to align and translate. Computer Science. arXiv preprint arXiv:1409.0473","key":"2522_CR6"},{"unstructured":"Simonyan K, Vedaldi A, Zisserman A (2014) Deep inside convolutional networks: visualising image classification models and saliency maps. In: Workshop at International Conference on Learning Representations","key":"2522_CR7"},{"key":"2522_CR8","doi-asserted-by":"publisher","first-page":"96","DOI":"10.1016\/j.neuroimage.2013.10.067","volume":"87","author":"S Haufe","year":"2014","unstructured":"Haufe S, Meinecke F, G\u00f6rgen K, D\u00e4hne S, Haynes J-D, Blankertz B, Bie\u00dfmann F (2014) On the interpretation of weight vectors of linear models in multivariate neuroimaging. Neuroimage 87:96\u2013110","journal-title":"Neuroimage"},{"doi-asserted-by":"crossref","unstructured":"Ribeiro MT, Singh S, Guestrin C (2016) \"why should i trust you?\": explaining the predictions of any classifier. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1135\u20131144","key":"2522_CR9","DOI":"10.1145\/2939672.2939778"},{"doi-asserted-by":"crossref","unstructured":"Lou Y, Caruana R, Gehrke J (2012) Intelligible models for classification and regression. In: Proceedings of the 18th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 150\u2013158","key":"2522_CR10","DOI":"10.1145\/2339530.2339556"},{"unstructured":"Frosst N, Hinton G (2017) Distilling a neural network into a soft decision tree. In: CEUR Workshop Proceedings","key":"2522_CR11"},{"doi-asserted-by":"crossref","unstructured":"Zhang QS, Yang Y, Ma HT, Nian\u00a0Wu Y (2019) Interpreting cnns via decision trees. In: Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, pp. 6261\u20136270","key":"2522_CR12","DOI":"10.1109\/CVPR.2019.00642"},{"doi-asserted-by":"crossref","unstructured":"Wu M, Parbhoo S, Hughes MC, Kindle R, Celi LA, Zazzi M, Roth V, Doshi-Velez F (2020) Regional tree regularization for interpretability in deep neural networks. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 34, pp. 6413\u20136421","key":"2522_CR13","DOI":"10.1609\/aaai.v34i04.6112"},{"key":"2522_CR14","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2023.110685","volume":"275","author":"G Shashank","year":"2023","unstructured":"Shashank G, Bouadjenek MR, Robles-Kelly A (2023) Percy: a post-hoc explanation-based score for logic rule dissemination consistency assessment in sentiment classification. Knowl-Based Syst 275:110685","journal-title":"Knowl-Based Syst"},{"unstructured":"Bondarenko A, Zmanovska T, Borisov A (2010) Decompositional rules extraction methods from neural networks. In: Proceedings of the 16th International Conference on Soft Computing MENDEL\u201910, Brno, Czech Republic, pp. 256\u2013262","key":"2522_CR15"},{"key":"2522_CR16","doi-asserted-by":"publisher","DOI":"10.1016\/j.ymssp.2021.108155","volume":"163","author":"W Zhou","year":"2022","unstructured":"Zhou W, Feng Z, Xu Y, Wang X, Lv H (2022) Empirical Fourier decomposition: an accurate signal decomposition method for nonlinear and non-stationary time series analysis. Mech Syst Signal Process 163:108155","journal-title":"Mech Syst Signal Process"},{"issue":"1","key":"2522_CR17","first-page":"3","volume":"16","author":"ZH Zhou","year":"2003","unstructured":"Zhou ZH, Jiang Y, Chen SF (2003) Extracting symbolic rules from trained neural network ensembles. Ai Commun 16(1):3\u201315","journal-title":"Ai Commun"},{"key":"2522_CR18","doi-asserted-by":"publisher","first-page":"2583","DOI":"10.1007\/s00521-021-05846-6","volume":"34","author":"S Wang","year":"2022","unstructured":"Wang S, Mu M (2022) Exploring online intelligent teaching method with machine learning and svm algorithm. Neural Comput Appl 34:2583\u20132596","journal-title":"Neural Comput Appl"},{"key":"2522_CR19","doi-asserted-by":"publisher","first-page":"351","DOI":"10.1016\/j.renene.2021.10.070","volume":"183","author":"G L\u00f3pez","year":"2022","unstructured":"L\u00f3pez G, Arboleya P (2022) Short-term wind speed forecasting over complex terrain using linear regression models and multivariable lstm and narx networks in the andes mountains, ecuador. Renew Energy 183:351\u2013368","journal-title":"Renew Energy"},{"key":"2522_CR20","first-page":"3","volume":"22","author":"T Adam","year":"2022","unstructured":"Adam T, Mayr A, Kneib T (2022) Gradient boosting in Markov-switching generalized additive models for location, scale, and shape. Econom Stat 22:3\u201316","journal-title":"Econom Stat"},{"issue":"6","key":"2522_CR21","first-page":"1161","volume":"45","author":"GY Wang","year":"2022","unstructured":"Wang GY, Fu S, Yang J (2022) A review of research on multi-granularity cognition based intelligent computing. Chin J Comput 45(6):1161\u20131175","journal-title":"Chin J Comput"},{"issue":"7","key":"2522_CR22","doi-asserted-by":"publisher","first-page":"6855","DOI":"10.1007\/s10462-022-10346-7","volume":"56","author":"TM Al-shami","year":"2023","unstructured":"Al-shami TM, Alshammari I (2023) Rough sets models inspired by supra-topology structures. Artif Intell Rev 56(7):6855\u20136883","journal-title":"Artif Intell Rev"},{"key":"2522_CR23","first-page":"251","volume-title":"Advances in the Dempster-Shafer theory of evidence","author":"Z Pawlak","year":"1994","unstructured":"Pawlak Z, Skowron A (1994) Rough membership functions. Advances in the Dempster-Shafer theory of evidence. Wiley, New York, pp 251\u2013271"},{"issue":"6","key":"2522_CR24","first-page":"681","volume":"36","author":"DQ Miao","year":"1999","unstructured":"Miao DQ, Hu GR (1999) A heuristic algorithm for reduction of knowledge. J Comput Res Dev 36(6):681\u2013684","journal-title":"J Comput Res Dev"},{"issue":"6","key":"2522_CR25","doi-asserted-by":"publisher","first-page":"7169","DOI":"10.1007\/s10489-022-03763-2","volume":"53","author":"M Prasad","year":"2023","unstructured":"Prasad M, Tripathi S, Dahal KP (2023) A probability estimation-based feature reduction and Bayesian rough set approach for intrusion detection in mobile ad-hoc network. Appl Intell 53(6):7169\u20137185","journal-title":"Appl Intell"},{"issue":"3","key":"2522_CR26","doi-asserted-by":"publisher","first-page":"3514","DOI":"10.1109\/TNNLS.2022.3193929","volume":"35","author":"P Zhang","year":"2024","unstructured":"Zhang P, Li T, Yuan Z, Luo C, Liu K, Yang X (2024) Heterogeneous feature selection based on neighborhood combination entropy. IEEE Trans Neural Netw Learn Syst 35(3):3514\u20133527","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"issue":"6","key":"2522_CR27","doi-asserted-by":"publisher","first-page":"1955","DOI":"10.1007\/s12559-021-09863-4","volume":"14","author":"J Yang","year":"2022","unstructured":"Yang J, Zhang X, Qin K (2022) Constructing robust fuzzy rough set models based on three-way decisions. Cogn Comput 14(6):1955\u20131977","journal-title":"Cogn Comput"},{"key":"2522_CR28","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1016\/j.ins.2022.10.054","volume":"615","author":"Z Deng","year":"2022","unstructured":"Deng Z, Li T, Deng D, Liu K, Zhang P, Zhang S, Luo Z (2022) Feature selection for label distribution learning using dual-similarity based neighborhood fuzzy entropy. Inf Sci 615:385\u2013404","journal-title":"Inf Sci"},{"issue":"8","key":"2522_CR29","doi-asserted-by":"publisher","first-page":"2871","DOI":"10.1109\/TFUZZ.2023.3248060","volume":"31","author":"XY Ce","year":"2023","unstructured":"Ce XY, Chen DG, Mi JS (2023) Learning instance-level label correlation distribution for multilabel classification with fuzzy rough sets. IEEE Trans Fuzzy Syst 31(8):2871\u20132884","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"8","key":"2522_CR30","doi-asserted-by":"publisher","first-page":"4436","DOI":"10.1109\/TFUZZ.2024.3399617","volume":"32","author":"ZX Deng","year":"2024","unstructured":"Deng ZX, Li TR, Deng DY, Liu KY, Luo ZP, Zhang PF (2024) Feature selection for handling label ambiguity using weighted label-fuzzy relevancy and redundancy. IEEE Trans Fuzzy Syst 32(8):4436\u20134447","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"1","key":"2522_CR31","first-page":"1899","volume":"46","author":"ZW Li","year":"2024","unstructured":"Li ZW, Wei SX, Liu SP (2024) Outlier detection using conditional information entropy and rough set theory. J Intell Fuzzy Syst 46(1):1899\u20131918","journal-title":"J Intell Fuzzy Syst"},{"issue":"2","key":"2522_CR32","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1631\/jzus.C1100176","volume":"13","author":"XZ Xu","year":"2012","unstructured":"Xu XZ, Ding SF, Shi ZZ, Zhu H (2012) Optimizing radial basis function neural network based on rough sets and affinity propagation clustering algorithm. J Zhejiang Univ (SCIENCE C) 13(2):131\u2013138","journal-title":"J Zhejiang Univ (SCIENCE C)"},{"issue":"1","key":"2522_CR33","doi-asserted-by":"publisher","first-page":"1529","DOI":"10.1109\/72.182710","volume":"4","author":"JSR Jang","year":"1993","unstructured":"Jang JSR, Sun CT (1993) Functional equivalence between radial basis function networks and fuzzy inference systems. IEEE Trans Neural Netw 4(1):1529\u20131531","journal-title":"IEEE Trans Neural Netw"},{"doi-asserted-by":"crossref","unstructured":"Rubio-Solis A, Panoutsos G (2014) Fuzzy uncertainty assessment in RBF neural networks using neutrosophic sets for multiclass classification. In: 2014 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), pp. 1591\u20131598. IEEE","key":"2522_CR34","DOI":"10.1109\/FUZZ-IEEE.2014.6891715"},{"issue":"11","key":"2522_CR35","first-page":"2848","volume":"38","author":"ZH Deng","year":"2016","unstructured":"Deng ZH, Chen JY, Liu JF, Wang ST (2016) Radial basic minimax probability classification tree for epilepsy electroencephalogram signal recognition. J Electron Infor Technol 38(11):2848\u20132855","journal-title":"J Electron Infor Technol"},{"key":"2522_CR36","doi-asserted-by":"publisher","first-page":"123087","DOI":"10.1109\/ACCESS.2020.3007337","volume":"8","author":"M Amirian","year":"2020","unstructured":"Amirian M, Schwenker F (2020) Radial basis function networks for convolutional neural networks to learn similarity distance metric and improve interpretability. IEEE Access 8:123087\u2013123097","journal-title":"IEEE Access"},{"key":"2522_CR37","first-page":"246","volume":"4","author":"S Chen","year":"1991","unstructured":"Chen S (1991) Orthogonal least squares learning algorithm for radial basis function networks. IEEE Trans Neural Netw 4:246\u2013257","journal-title":"IEEE Trans Neural Netw"},{"issue":"3","key":"2522_CR38","first-page":"267","volume":"2","author":"SL Chiu","year":"1994","unstructured":"Chiu SL (1994) Fuzzy model identification based on cluster estimation. J Intell Fuzzy Syst 2(3):267\u2013278","journal-title":"J Intell Fuzzy Syst"},{"issue":"8","key":"2522_CR39","doi-asserted-by":"publisher","first-page":"1905","DOI":"10.1029\/JB076i008p01905","volume":"76","author":"RL Hardy","year":"1971","unstructured":"Hardy RL (1971) Multiquadric equations of topography and other irregular surfaces. J Geophys Res 76(8):1905\u20131915","journal-title":"J Geophys Res"},{"issue":"3","key":"2522_CR40","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1016\/0165-1684(93)90001-Q","volume":"32","author":"RG Baraniuk","year":"1993","unstructured":"Baraniuk RG, Jones DL (1993) Signal-dependent time-frequency analysis using a radially gaussian kernel. Signal Process 32(3):263\u2013284","journal-title":"Signal Process"},{"doi-asserted-by":"crossref","unstructured":"Duchon J (1977) Splines minimizing rotation-invariant semi-norms in Sobolev spaces. In: Constructive theory of functions of several variables: Proceedings of a Conference Held at Oberwolfach April 25\u2013May 1, 1976, pp. 85\u2013100. Springer","key":"2522_CR41","DOI":"10.1007\/BFb0086566"},{"issue":"4","key":"2522_CR42","first-page":"5617","volume":"44","author":"J Qian","year":"2023","unstructured":"Qian J, Han X, Yu Y, Liu CH (2023) Multi-granularity decision-theoretic rough sets based on the fuzzy t-equivalence relation with new strategies. J Intell Fuzzy Syst 44(4):5617\u20135631","journal-title":"J Intell Fuzzy Syst"},{"issue":"1","key":"2522_CR43","doi-asserted-by":"publisher","first-page":"622","DOI":"10.1007\/s40815-021-01167-x","volume":"24","author":"XH Liu","year":"2022","unstructured":"Liu XH, Dai JH (2022) A fuzzy decision-theoretic rough set approach for type-2 fuzzy conditional information systems and its application in decision-making. Int J Fuzzy Syst 24(1):622\u2013634","journal-title":"Int J Fuzzy Syst"},{"issue":"8","key":"2522_CR44","first-page":"69","volume":"59","author":"K Pearson","year":"1895","unstructured":"Pearson K (1895) Contributions to the mathematical theory of evolution iii regression, heredity, and panmixia. Proc R Soc Lond 59(8):69\u201371","journal-title":"Proc R Soc Lond"},{"doi-asserted-by":"crossref","unstructured":"Lijie J, Wenjing L, Junfei Q (2020) Design of RBF neural network based on improved canopy-k-means algorithm. HPCCT and BDAI 2020: 2020 4th High Performance Computing and Cluster Technologies Conference and 2020 3rd International Conference on Big Data and Artificial Intelligence","key":"2522_CR45","DOI":"10.1145\/3409501.3409526"}],"container-title":["International Journal of Machine Learning and Cybernetics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13042-024-02522-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s13042-024-02522-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13042-024-02522-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,6]],"date-time":"2025-09-06T03:12:17Z","timestamp":1757128337000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s13042-024-02522-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,1,9]]},"references-count":45,"journal-issue":{"issue":"7-8","published-print":{"date-parts":[[2025,8]]}},"alternative-id":["2522"],"URL":"https:\/\/doi.org\/10.1007\/s13042-024-02522-8","relation":{},"ISSN":["1868-8071","1868-808X"],"issn-type":[{"type":"print","value":"1868-8071"},{"type":"electronic","value":"1868-808X"}],"subject":[],"published":{"date-parts":[[2025,1,9]]},"assertion":[{"value":"19 April 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 December 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 January 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Author Dayong Deng declares that he has no Conflict of interest. Author Jie Wang declares that he has no Conflict of interest. Author Zhixuan Deng declares that he has no Conflict of interest. Author Keyu Liu declares that he has no Conflict of interest. Author Pengfei Zhang declares that he has no Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"This article does not contain any studies with human participants or animals performed by any of the authors.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}}]}}