{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T08:43:58Z","timestamp":1775724238146,"version":"3.50.1"},"reference-count":49,"publisher":"Springer Science and Business Media LLC","issue":"23","license":[{"start":{"date-parts":[[2023,10,31]],"date-time":"2023-10-31T00:00:00Z","timestamp":1698710400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,10,31]],"date-time":"2023-10-31T00:00:00Z","timestamp":1698710400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11971420"],"award-info":[{"award-number":["11971420"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Appl Intell"],"published-print":{"date-parts":[[2023,12]]},"DOI":"10.1007\/s10489-023-05078-2","type":"journal-article","created":{"date-parts":[[2023,10,31]],"date-time":"2023-10-31T02:02:22Z","timestamp":1698717742000},"page":"29486-29513","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Measures of uncertainty for partially labeled categorical data based on an indiscernibility relation: an application in semi-supervised attribute reduction"],"prefix":"10.1007","volume":"53","author":[{"given":"Jiali","family":"He","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5424-6389","authenticated-orcid":false,"given":"Gangqiang","family":"Zhang","sequence":"additional","affiliation":[]},{"given":"Dan","family":"Huang","sequence":"additional","affiliation":[]},{"given":"Pei","family":"Wang","sequence":"additional","affiliation":[]},{"given":"Guangji","family":"Yu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,10,31]]},"reference":[{"issue":"6","key":"5078_CR1","doi-asserted-by":"crossref","first-page":"921","DOI":"10.1016\/S0167-8655(02)00204-0","volume":"24","author":"C Andrzej","year":"2003","unstructured":"Andrzej C (2003) Automatic identication of sound source position employing neural networks and rough sets. Pattern Recognit Lett 24(6):921\u2013933","journal-title":"Pattern Recognit Lett"},{"key":"5078_CR2","doi-asserted-by":"crossref","first-page":"1131","DOI":"10.1109\/TKDE.2013.86","volume":"26","author":"K Benabdeslem","year":"2014","unstructured":"Benabdeslem K, Hindawi M (2014) Efficient semi-supervised feature selection: constraint, relevance and redundancy. IEEE Trans Knowl Data Eng 26:1131\u20131143","journal-title":"IEEE Trans Knowl Data Eng"},{"key":"5078_CR3","doi-asserted-by":"crossref","unstructured":"Bao WX, Hang JY, Zhang ML (2021) Partial label dimensionality reduction via confidence-based dependence maximization. In: Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery & Data Mining, pp. 46\u201354","DOI":"10.1145\/3447548.3467313"},{"key":"5078_CR4","doi-asserted-by":"crossref","unstructured":"Bao WX, Hang JY, Zhang ML (2022) Submodular feature selection for partial label learning. In: Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pp. 26\u201334","DOI":"10.1145\/3534678.3539292"},{"key":"5078_CR5","first-page":"761","volume-title":"International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems","author":"A Campagner","year":"2022","unstructured":"Campagner A, Ciucci D (2022) Rough-set based genetic algorithms for weakly supervised feature selection. International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems. Springer, Cham, pp 761\u2013773"},{"key":"5078_CR6","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1016\/j.ijar.2021.06.005","volume":"136","author":"A Campagner","year":"2021","unstructured":"Campagner A, Ciucci D, Huellermeier E (2021) Rough set-based feature selection for weakly labeled data. Int J Approx Reason 136:150\u2013167","journal-title":"Int J Approx Reason"},{"key":"5078_CR7","doi-asserted-by":"crossref","unstructured":"Blum A, Mitchell T (1998) Combining labeled and unlabeled data with cortraining\/\/Proceedings of the 11th annual Conference on Computational Learning Theory. New York: ACM, 92\u2013100","DOI":"10.1145\/279943.279962"},{"key":"5078_CR8","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1016\/S0020-0255(98)00019-X","volume":"109","author":"T Beaubouef","year":"1998","unstructured":"Beaubouef T, Petry FE, Arora G (1998) Information-theoretic measures of uncertainty for rough sets and rough relational databases. Inf Sci 109:185\u2013195","journal-title":"Inf Sci"},{"issue":"1","key":"5078_CR9","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1023\/A:1015568521453","volume":"19","author":"YQ Chen","year":"2002","unstructured":"Chen YQ, Gao W, Zhu TS (2002) Learning prosodic patterns for mandarin speech synthesis. J Intell Inf Syst 19(1):95\u2013109","journal-title":"J Intell Inf Syst"},{"key":"5078_CR10","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/j.ijar.2021.09.016","volume":"140","author":"Z Chen","year":"2022","unstructured":"Chen Z, Liu KY, Yang XB, Fujita H (2022) Random sampling accelerator for attribute reduction. Int J Approx Reason 140:75\u201391","journal-title":"Int J Approx Reason"},{"key":"5078_CR11","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1016\/j.ins.2020.05.010","volume":"535","author":"Y Chen","year":"2020","unstructured":"Chen Y, Liu KY, Song JJ, Fujita H, Yang XB, Qian YH (2020) Attribute group for attribute reduction. Inf Sci 535:64\u201380","journal-title":"Inf Sci"},{"key":"5078_CR12","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1016\/j.compeleceng.2013.11.024","volume":"40","author":"C Girish","year":"2014","unstructured":"Girish C, Ferat S (2014) A survey on feature selection methods. Comput Electr Eng 40:16\u201328","journal-title":"Comput Electr Eng"},{"key":"5078_CR13","doi-asserted-by":"crossref","first-page":"2460","DOI":"10.1109\/TCYB.2016.2636339","volume":"47","author":"JH Dai","year":"2017","unstructured":"Dai JH, Hu QH, Zhang JH, Hu H, Zheng NG (2017) Attribute selection for partially labeled categorical data by rough set approach. IEEE Trans Cybernet 47:2460\u20132471","journal-title":"IEEE Trans Cybernet"},{"issue":"4","key":"5078_CR14","doi-asserted-by":"crossref","first-page":"1445","DOI":"10.1007\/s13042-022-01708-2","volume":"14","author":"JH Dai","year":"2023","unstructured":"Dai JH, Wang WS, Zhang CC, Qu SJ (2023) Semi-supervised attribute reduction via attribute indiscernibility. Int J Mach Learn Cybernet 14(4):1445\u20131464","journal-title":"Int J Mach Learn Cybernet"},{"issue":"11","key":"5078_CR15","doi-asserted-by":"crossref","first-page":"12316","DOI":"10.1007\/s10489-021-03076-w","volume":"52","author":"V Feofanov","year":"2022","unstructured":"Feofanov V, Devijver E, Amini MR (2022) Wrapper feature selection with partially labeled data. Appl Intell 52(11):12316\u201312329","journal-title":"Appl Intell"},{"key":"5078_CR16","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1016\/j.ejor.2006.08.029","volume":"182","author":"TF Fan","year":"2007","unstructured":"Fan TF, Liu DR, Tzeng GH (2007) Rough set-based logics for multicriteria decision analysis. European J Operat Res 182:340\u2013355","journal-title":"European J Operat Res"},{"key":"5078_CR17","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1016\/j.ins.2016.04.040","volume":"361\u2013362","author":"G Forestier","year":"2016","unstructured":"Forestier G, Wemmert C (2016) Semi-supervised learning using multiple clustering with limited labeled data. Inf Sci 361\u2013362:48\u201365","journal-title":"Inf Sci"},{"key":"5078_CR18","unstructured":"He XF, Deng C, Partha N (2005) Laplacian score for feature selection\/\/Proceedings of the 18th International Conference on Neural Information Processing Systems (NIPS\u201905). Cambridge, USA: MIT Press, 507\u2013514"},{"key":"5078_CR19","doi-asserted-by":"crossref","unstructured":"Handl J, Knowles J (2006) Semi-supervised feature selection via multi-objective optimization\/\/The 2006 International Joint Conference on Neural Networks","DOI":"10.1109\/IJCNN.2006.247330"},{"issue":"1\u20132","key":"5078_CR20","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/j.ijar.2004.11.008","volume":"40","author":"S Hirano","year":"2005","unstructured":"Hirano S, Tsumoto S (2005) Rough representation of a region of interest in medical images. Int J Approx Reason 40(1\u20132):23\u201334","journal-title":"Int J Approx Reason"},{"key":"5078_CR21","doi-asserted-by":"crossref","first-page":"252","DOI":"10.1109\/TNNLS.2014.2314123","volume":"26","author":"YH Han","year":"2015","unstructured":"Han YH, Yang Y, Yan Y, Ma ZG, Zhou XF (2015) Semisupervised feature selection via spline regression for video semantic recognition. IEEE Trans Neural Netw Learn Syst 26:252\u2013264","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"key":"5078_CR22","first-page":"1439","volume":"3","author":"J Weston","year":"2003","unstructured":"Weston J, Andre E, Bernhard S (2003) Use of the zero-norm with linear models and kernel methods. J Mach Learn Res 3:1439\u20131461","journal-title":"J Mach Learn Res"},{"key":"5078_CR23","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1016\/j.ijar.2019.12.013","volume":"119","author":"ZH Jiang","year":"2020","unstructured":"Jiang ZH, Liu KY, Yang XB, Yu HL, Fujita H, Qian YH (2020) Accelerator for supervised neighborhood based attribute reduction. Int J Approx Reason 119:122\u2013150","journal-title":"Int J Approx Reason"},{"key":"5078_CR24","doi-asserted-by":"crossref","first-page":"6338","DOI":"10.1016\/j.eswa.2010.02.087","volume":"37","author":"F Jiang","year":"2010","unstructured":"Jiang F, Sui YF, Cao CG (2010) An information entropy-based approach to outlier detection in rough sets. Exp Syst Appl 37:6338\u20136344","journal-title":"Exp Syst Appl"},{"key":"5078_CR25","volume":"89","author":"P Jain","year":"2020","unstructured":"Jain P, Tiwari AK, Som T (2020) A fitting model based intuitionistic fuzzy rough feature selection. Eng Appl Art Intell 89:103421","journal-title":"Eng Appl Art Intell"},{"issue":"1\u20132","key":"5078_CR26","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1016\/S0004-3702(97)00043-X","volume":"97","author":"R Kohavi","year":"1997","unstructured":"Kohavi R, John GH (1997) Wrappers for feature subset selection. Art Intell 97(1\u20132):273\u2013324","journal-title":"Art Intell"},{"key":"5078_CR27","doi-asserted-by":"crossref","first-page":"1818","DOI":"10.1007\/s12559-021-09887-w","volume":"14","author":"GL Liu","year":"2022","unstructured":"Liu GL (2022) Attribute reduction algorithms determined by invariants for decision tables. Cognit Comput 14:1818\u20131825","journal-title":"Cognit Comput"},{"key":"5078_CR28","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1080\/03081070600687668","volume":"35","author":"JY Liang","year":"2006","unstructured":"Liang JY, Shi ZZ, Li DY (2006) Information entropy, rough entropy and knowledge granulation in incomplete information systems. Int J Gen Syst 35:641\u2013654","journal-title":"Int J Gen Syst"},{"key":"5078_CR29","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1016\/j.knosys.2018.11.034","volume":"165","author":"KY Liu","year":"2019","unstructured":"Liu KY, Yang XB, Yu HL, Mi JS (2019) Rough set based semi-supervised feature selection via ensemble selector. Knowl-Based Syst 165:282\u2013296","journal-title":"Knowl-Based Syst"},{"key":"5078_CR30","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1016\/S0020-0255(98)10065-8","volume":"113","author":"M Kryszkiewicz","year":"1999","unstructured":"Kryszkiewicz M (1999) Rules in incomplete information systems. Inf Sci 113:271\u2013292","journal-title":"Inf Sci"},{"key":"5078_CR31","doi-asserted-by":"crossref","first-page":"1103","DOI":"10.1016\/j.ijar.2011.05.006","volume":"52","author":"D Miao","year":"2011","unstructured":"Miao D, Gao C, Zhang N (2011) Diverse reduct subspaces based co-training for partially labeled data. Int J Approx Reason 52:1103\u20131117","journal-title":"Int J Approx Reason"},{"key":"5078_CR32","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1002\/scj.20757","volume":"38","author":"Y Nakatani","year":"2007","unstructured":"Nakatani Y, Zhu K, Uehara K (2007) Semi-supervised learning using feature selection based on maximum density subgraphs. Syst Comput Japan 38:32\u201343","journal-title":"Syst Comput Japan"},{"key":"5078_CR33","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1007\/BF01001956","volume":"11","author":"Z Pawlak","year":"1982","unstructured":"Pawlak Z (1982) Rough sets. Int J Comput Inf Sci 11:341\u2013356","journal-title":"Int J Comput Inf Sci"},{"key":"5078_CR34","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1142\/S0218488508005121","volume":"16","author":"YH Qian","year":"2008","unstructured":"Qian YH, Liang JY (2008) Combination entropy and combination granulation in rough set theory. Int J Uncert Fuzz Knowl-Based Syst 16:179\u2013193","journal-title":"Int J Uncert Fuzz Knowl-Based Syst"},{"key":"5078_CR35","doi-asserted-by":"crossref","unstructured":"Ren JY, Qiu ZY, Fan W (2008) Forward semi-supervised feature selectio. in: Proceedings of the 12th Pacific-Asia conference on Advances in Knowledge Discovery and Data Mining (PAKDD\u201908). Springer-Verlag, Berlin, pp. 970\u2013976","DOI":"10.1007\/978-3-540-68125-0_101"},{"key":"5078_CR36","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","volume":"27","author":"C Shannon","year":"1948","unstructured":"Shannon C (1948) A mathematical theory of communication. Bell Syst Tech J 27:379\u2013423","journal-title":"Bell Syst Tech J"},{"issue":"6","key":"5078_CR37","doi-asserted-by":"crossref","first-page":"1683","DOI":"10.1109\/TFUZZ.2021.3064686","volume":"30","author":"BB Sang","year":"2021","unstructured":"Sang BB, Chen HM, Yang L, Li TR, Xu WH (2021) Incremental feature selection using a conditional entropy based on fuzzy dominance neighborhood rough sets. IEEE Trans Fuzz Syst 30(6):1683\u20131697","journal-title":"IEEE Trans Fuzz Syst"},{"key":"5078_CR38","unstructured":"UCI Machine Learning Repository. http:\/\/archive.ics.uci.edu\/ml\/datasets.html"},{"key":"5078_CR39","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1080\/03081079908935239","volume":"28","author":"MJ Wierman","year":"1999","unstructured":"Wierman MJ (1999) Measuring uncertainty in rough set theory. Int J Gen Syst 28:283\u2013297","journal-title":"Int J Gen Syst"},{"key":"5078_CR40","doi-asserted-by":"crossref","first-page":"4493","DOI":"10.1016\/j.ins.2007.04.010","volume":"177","author":"XZ Wang","year":"2007","unstructured":"Wang XZ, Tsang ECC, Zhao SY, Chen DG, Yeung DS (2007) Learning fuzzy rules from fuzzy samples based on rough set technique. Inf Sci 177:4493\u20134514","journal-title":"Inf Sci"},{"key":"5078_CR41","doi-asserted-by":"crossref","first-page":"818","DOI":"10.1109\/TFUZZ.2019.2949765","volume":"28","author":"CZ Wang","year":"2020","unstructured":"Wang CZ, Wang Y, Shao MW, Qian YH, Chen DG (2020) Fuzzy rough attribute reduction for categorical data. IEEE Trans Fuzz Syst 28:818\u2013830","journal-title":"IEEE Trans Fuzz Syst"},{"key":"5078_CR42","first-page":"66","volume":"17","author":"L Wan","year":"2021","unstructured":"Wan L, Xia SJ, Zhu Y, Lyu ZH (2021) An improved semi-supervised feature selection algorithm based on information entropy. Stat Decis Making 17:66\u201370","journal-title":"Stat Decis Making"},{"key":"5078_CR43","doi-asserted-by":"crossref","first-page":"3619","DOI":"10.1007\/s13042-019-00948-z","volume":"10","author":"YB Wang","year":"2019","unstructured":"Wang YB, Chen XJ, Dong K (2019) Attribute reduction via local conditional entropy. Int J Mach Learn Cybernet 10:3619\u20133634","journal-title":"Int J Mach Learn Cybernet"},{"issue":"9","key":"5078_CR44","doi-asserted-by":"crossref","first-page":"3395","DOI":"10.1109\/TFUZZ.2021.3114734","volume":"30","author":"Z Yuan","year":"2021","unstructured":"Yuan Z, Chen HM, Zhang PF, Wan JH, Li TR (2021) A novel unsupervised approach to heterogeneous feature selection based on fuzzy mutual information. IEEE Trans Fuzz Syst 30(9):3395\u20133409","journal-title":"IEEE Trans Fuzz Syst"},{"key":"5078_CR45","volume":"237","author":"X Yang","year":"2022","unstructured":"Yang X, Chen Y, Fujita H, Liu D, Li TR (2022) Mixed data-driven sequential three-way decision via subjective-objective dynamic fusion. Knowl-Based Syst 237:107728","journal-title":"Knowl-Based Syst"},{"key":"5078_CR46","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1016\/j.patcog.2015.09.008","volume":"51","author":"MY Zhao","year":"2016","unstructured":"Zhao MY, Jiao LC, Ma WP (2016) Classification and saliency detection by semi-supervised low-rank representation. Pattern Recognit 51:281\u2013294","journal-title":"Pattern Recognit"},{"key":"5078_CR47","first-page":"2727","volume":"37","author":"W Zhang","year":"2016","unstructured":"Zhang W, Miao DQ, Gao C, Li F (2016) Semi-supervised attribute reduction based on rough-subspace ensemble learning. J Chinese Comput Syst 37:2727\u20132732","journal-title":"J Chinese Comput Syst"},{"key":"5078_CR48","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1016\/j.inffus.2018.11.019","volume":"50","author":"R Zhang","year":"2019","unstructured":"Zhang R, Nie F, Li X (2019) Feature selection with multi-view data: A survey. Inf Fusion 50:158\u2013167","journal-title":"Inf Fusion"},{"key":"5078_CR49","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1007\/s11704-016-5489-3","volume":"12","author":"X Hu","year":"2018","unstructured":"Hu X, Zhou P, Li P, Wang J, Wu X (2018) A survey on online feature selection with streaming features. Front Comput Sci 12:479\u2013493","journal-title":"Front Comput Sci"}],"container-title":["Applied Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10489-023-05078-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10489-023-05078-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10489-023-05078-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,29]],"date-time":"2023-11-29T14:33:43Z","timestamp":1701268423000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10489-023-05078-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,10,31]]},"references-count":49,"journal-issue":{"issue":"23","published-print":{"date-parts":[[2023,12]]}},"alternative-id":["5078"],"URL":"https:\/\/doi.org\/10.1007\/s10489-023-05078-2","relation":{},"ISSN":["0924-669X","1573-7497"],"issn-type":[{"value":"0924-669X","type":"print"},{"value":"1573-7497","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,10,31]]},"assertion":[{"value":"30 September 2023","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 October 2023","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing Interests"}},{"value":"The data used or analyzed during the current study are available from the corresponding author after the paper is accepted for publication.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical and informed consent for data used"}}]}}