{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T08:23:38Z","timestamp":1760171018925,"version":"3.37.3"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2017,7,14]],"date-time":"2017-07-14T00:00:00Z","timestamp":1499990400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61170128"],"award-info":[{"award-number":["61170128"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61379049","61379089"],"award-info":[{"award-number":["61379049","61379089"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Science and Technology Key Project of Fujian Province","award":["2012H0043"],"award-info":[{"award-number":["2012H0043"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int. J. Mach. Learn. & Cyber."],"published-print":{"date-parts":[[2019,1]]},"DOI":"10.1007\/s13042-017-0701-9","type":"journal-article","created":{"date-parts":[[2017,7,14]],"date-time":"2017-07-14T09:32:27Z","timestamp":1500024747000},"page":"75-85","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Characteristic matrices of compound operations of coverings and their relationships with rough sets"],"prefix":"10.1007","volume":"10","author":[{"given":"Aiping","family":"Huang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"William","family":"Zhu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,7,14]]},"reference":[{"key":"701_CR1","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-3534-4","volume-title":"Rough sets: theoretical aspects of reasoning about data","author":"Z Pawlak","year":"1991","unstructured":"Pawlak Z (1991) Rough sets: theoretical aspects of reasoning about data. Kluwer Academic Publishers, Boston"},{"key":"701_CR2","doi-asserted-by":"publisher","first-page":"62","DOI":"10.1016\/j.ins.2012.02.032","volume":"198","author":"J Dai","year":"2012","unstructured":"Dai J, Xu Q (2012) Approximations and uncertainty measures in incomplete information systems. Inf Sci 198:62\u201380","journal-title":"Inf Sci"},{"issue":"9\u201310","key":"701_CR3","doi-asserted-by":"publisher","first-page":"597","DOI":"10.1016\/j.artint.2010.04.018","volume":"174","author":"Y Qian","year":"2010","unstructured":"Qian Y, Liang J, Pedrycz W, Dang C (2010) Positive approximation: an accelerator for attribute reduction in rough set theory. Artif Intell 174(9\u201310):597\u2013618","journal-title":"Artif Intell"},{"key":"701_CR4","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1016\/j.ins.2011.08.001","volume":"184","author":"A Skowron","year":"2012","unstructured":"Skowron A, Stepaniuk J, Swiniarski R (2012) Modeling rough granular computing based on approximation spaces. Inf Sci 184:20\u201343","journal-title":"Inf Sci"},{"key":"701_CR5","doi-asserted-by":"publisher","first-page":"483","DOI":"10.1016\/j.ins.2012.07.030","volume":"220","author":"S Wang","year":"2013","unstructured":"Wang S, Zhu Q, Zhu W, Min F (2013) Quantitative analysis for covering-based rough sets through the upper approximation number. Inf Sci 220:483\u2013491","journal-title":"Inf Sci"},{"key":"701_CR6","doi-asserted-by":"publisher","first-page":"256","DOI":"10.1007\/978-1-4471-3238-7_31","volume-title":"Rough sets, fuzzy sets and knowledge discovery","author":"TY Lin","year":"1994","unstructured":"Lin TY, Liu Q (1994) Rough approximate operators: axiomatic rough set theory. In: Ziarko W (ed) Rough sets, fuzzy sets and knowledge discovery. Springer, Berlin, pp 256\u2013260"},{"issue":"3","key":"701_CR7","doi-asserted-by":"publisher","first-page":"857","DOI":"10.1016\/j.ijar.2008.02.001","volume":"48","author":"G Liu","year":"2008","unstructured":"Liu G (2008) Axiomatic systems for rough sets and fuzzy rough sets. Int J Approx Reason 48(3):857\u2013867","journal-title":"Int J Approx Reason"},{"issue":"2","key":"701_CR8","doi-asserted-by":"publisher","first-page":"274","DOI":"10.1016\/j.ins.2009.08.031","volume":"180","author":"Y Zhang","year":"2010","unstructured":"Zhang Y, Li J, Wu W (2010) On axiomatic characterizations of three pairs of covering based approximation operators. Inf Sci 180(2):274\u2013287","journal-title":"Inf Sci"},{"issue":"8","key":"701_CR9","doi-asserted-by":"publisher","first-page":"1131","DOI":"10.1109\/TKDE.2007.1044","volume":"19","author":"W Zhu","year":"2007","unstructured":"Zhu W, Wang F (2007) On three types of covering rough sets. IEEE Trans Knowl Data Eng 19(8):1131\u20131144","journal-title":"IEEE Trans Knowl Data Eng"},{"issue":"3","key":"701_CR10","doi-asserted-by":"publisher","first-page":"640","DOI":"10.3724\/SP.J.1001.2008.00640","volume":"19","author":"Q Hu","year":"2008","unstructured":"Hu Q, Yu D, Xie Z (2008) Numerical attribute reduction based on neighborhood granulation and rough approximation. J Softw 19(3):640\u2013649 (in Chinese)","journal-title":"J Softw"},{"issue":"16","key":"701_CR11","doi-asserted-by":"publisher","first-page":"2774","DOI":"10.1016\/j.ins.2009.04.002","volume":"179","author":"Z Meng","year":"2009","unstructured":"Meng Z, Shi Z (2009) A fast approach to attribute reduction in incomplete decision systems with tolerance relation-based rough sets. Inf Sci 179(16):2774\u20132793","journal-title":"Inf Sci"},{"key":"701_CR12","doi-asserted-by":"publisher","first-page":"48","DOI":"10.1016\/j.ins.2012.04.031","volume":"211","author":"F Min","year":"2012","unstructured":"Min F, Zhu W (2012) Attribute reduction of data with error ranges and test costs. Inf Sci 211:48\u201367","journal-title":"Inf Sci"},{"issue":"1","key":"701_CR13","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1016\/j.camwa.2006.12.104","volume":"56","author":"ECC Tsang","year":"2008","unstructured":"Tsang ECC, Chen D, Yeung DS (2008) Approximations and reducts with covering generalized rough sets. Comput Math Appl 56(1):279\u2013289","journal-title":"Comput Math Appl"},{"issue":"24","key":"701_CR14","doi-asserted-by":"publisher","first-page":"5457","DOI":"10.1016\/j.ins.2011.07.038","volume":"181","author":"Y Du","year":"2011","unstructured":"Du Y, Hu Q, Zhu P, Ma P (2011) Rule learning for classification based on neighborhood covering reduction. Inf Sci 181(24):5457\u20135467","journal-title":"Inf Sci"},{"key":"701_CR15","doi-asserted-by":"crossref","unstructured":"Inuiguchi M, Tanino T (2002) Generalized rough sets and rule extraction. In: Rough sets and current trends in computing, vol 2475 of LNCS, pp 105\u2013112","DOI":"10.1007\/3-540-45813-1_13"},{"key":"701_CR16","doi-asserted-by":"crossref","unstructured":"Lee S, Propes N, Zhang G, Zhao Y, Vachtsevanos GJ (2002) Rough set feature selection and diagnostic rule generation for industrial applications. In: Rough sets and current trends in computing, vol 2475 of LNCS, pp 568\u2013571","DOI":"10.1007\/3-540-45813-1_75"},{"key":"701_CR17","unstructured":"Wang G, Liu F (2000) The inconsistency in rough set based rule generation. In: Rough sets and current trends in computing, vol 2005 of LNCS, pp 370\u2013377"},{"key":"701_CR18","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1016\/j.ins.2013.11.014","volume":"263","author":"A Huang","year":"2013","unstructured":"Huang A, Zhao H, Zhu W (2013) Nullity-based matroid of rough sets and its application to attribute reduction. Inf Sci 263:153\u2013165","journal-title":"Inf Sci"},{"key":"701_CR19","unstructured":"Huang A, Zhu W (2012) Geometric lattice structure of covering-based rough sets through matroids. J Appl Math. Article ID 236307:1\u201325"},{"key":"701_CR20","unstructured":"Huang A, Zhu W (2014) Geometric lattice structure of covering and its application to attribute reduction through matroids. J Appl Math. Article ID 183621:8"},{"key":"701_CR21","doi-asserted-by":"publisher","unstructured":"Huang A, Zhu W. Connectedness of graphs and its application to matroids through covering-based rough sets. Soft Comput. doi:\n                    10.1007\/s00500-015-1859-2","DOI":"10.1007\/s00500-015-1859-2"},{"issue":"2","key":"701_CR22","first-page":"141","volume":"2","author":"S Wang","year":"2011","unstructured":"Wang S, Zhu W (2011) Matroidal structure of covering-based rough sets through the upper approximation number. Int J Granul Comput Rough Sets Intell Syst 2(2):141\u2013148","journal-title":"Int J Granul Comput Rough Sets Intell Syst"},{"key":"701_CR23","doi-asserted-by":"crossref","unstructured":"Eld\u00e9n L (2007) Matrix methods in data mining and pattern recognition. The Society for Industrial and Applied Mathematics","DOI":"10.1137\/1.9780898718867"},{"key":"701_CR24","doi-asserted-by":"publisher","first-page":"186","DOI":"10.1016\/j.ins.2013.10.018","volume":"263","author":"S Wang","year":"2013","unstructured":"Wang S, Zhu W, Min QZF (2013) Characteristic matrix of covering and its application to boolean matrix decomposition. Inf Sci 263:186\u2013197","journal-title":"Inf Sci"},{"key":"701_CR25","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1016\/j.ins.2013.08.016","volume":"257","author":"J Zhang","year":"2014","unstructured":"Zhang J, Li T, Chen H (2014) Composite rough sets for dynamic data mining. Inf Sci 257:81\u2013100","journal-title":"Inf Sci"},{"key":"701_CR26","doi-asserted-by":"crossref","unstructured":"lang G, Li Q, Cai M, Yang T (2015) Characteristic matrixes-based knowledge reduction in dynamic covering decision information systems. Knowl Based Syst 85:1\u201326","DOI":"10.1016\/j.knosys.2015.03.021"},{"key":"701_CR27","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1016\/j.knosys.2016.01.042","volume":"99","author":"C Luo","year":"2016","unstructured":"Luo C, Li T, Yi Z, Fujita H (2016) Matrix approach to decision-theoretic rough sets for evolving data. Knowl Based Syst 99:123\u2013134","journal-title":"Knowl Based Syst"},{"issue":"6","key":"701_CR28","doi-asserted-by":"publisher","first-page":"1651","DOI":"10.1016\/j.ins.2007.11.010","volume":"178","author":"G Liu","year":"2008","unstructured":"Liu G (2008) Generalized rough sets over fuzzy lattices. Inf Sci 178(6):1651\u20131662","journal-title":"Inf Sci"},{"issue":"7","key":"701_CR29","doi-asserted-by":"publisher","first-page":"772","DOI":"10.1016\/j.aml.2010.03.007","volume":"23","author":"G Liu","year":"2010","unstructured":"Liu G (2010) Closures and topological closures in quasi-discrete closure. Appl Math Lett 23(7):772\u2013776","journal-title":"Appl Math Lett"},{"issue":"11","key":"701_CR30","doi-asserted-by":"publisher","first-page":"2221","DOI":"10.1016\/j.ins.2010.01.033","volume":"180","author":"G Liu","year":"2010","unstructured":"Liu G, Sai Y (2010) Invertible approximation operators of generalized rough sets and fuzzy rough sets. Inf Sci 180(11):2221\u20132229","journal-title":"Inf Sci"},{"issue":"8","key":"701_CR31","doi-asserted-by":"publisher","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, Zhang Z (2011) Diverse reduct subspaces based co-training for partially labeled data. Int J Approx Reason 52(8):1103\u20131117","journal-title":"Int J Approx Reason"},{"key":"701_CR32","doi-asserted-by":"crossref","unstructured":"Skowron A, Rauszer C (1992) The discernibility matrices and functions in information systems. In: Intelligent Decision Support","DOI":"10.1007\/978-94-015-7975-9_21"},{"issue":"7","key":"701_CR33","doi-asserted-by":"publisher","first-page":"867","DOI":"10.1016\/j.ins.2008.11.020","volume":"179","author":"Y Yao","year":"2009","unstructured":"Yao Y, Zhao Y (2009) Discernibility matrix simplification for constructing attribute reducts. Inf Sci 179(7):867\u2013882","journal-title":"Inf Sci"},{"issue":"23","key":"701_CR34","doi-asserted-by":"publisher","first-page":"5169","DOI":"10.1016\/j.ins.2011.07.025","volume":"181","author":"D Chen","year":"2011","unstructured":"Chen D, Hu Q, Yang Y (2011) Parameterized attribute reduction with gaussian kernel based fuzzy rough sets. Inf Sci 181(23):5169\u20135179","journal-title":"Inf Sci"},{"issue":"11","key":"701_CR35","doi-asserted-by":"publisher","first-page":"1649","DOI":"10.1109\/TKDE.2010.260","volume":"23","author":"Q Hu","year":"2011","unstructured":"Hu Q, Yu D, Pedrycz W, Chen D (2011) Kernelized fuzzy rough sets and their applications. IEEE Trans Knowl Data Eng 23(11):1649\u20131667","journal-title":"IEEE Trans Knowl Data Eng"},{"issue":"9\u201310","key":"701_CR36","first-page":"653","volume":"35","author":"JA Pomykala","year":"1987","unstructured":"Pomykala JA (1987) Approximation operations in approximation space. Bull Polish Acad Sci 35(9\u201310):653\u2013662","journal-title":"Bull Polish Acad Sci"},{"issue":"3","key":"701_CR37","doi-asserted-by":"publisher","first-page":"210","DOI":"10.1016\/j.ins.2008.09.015","volume":"179","author":"W Zhu","year":"2009","unstructured":"Zhu W (2009) Relationship between generalized rough sets based on binary relation and covering. Inf Sci 179(3):210\u2013225","journal-title":"Inf Sci"}],"container-title":["International Journal of Machine Learning and Cybernetics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s13042-017-0701-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s13042-017-0701-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s13042-017-0701-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,1,20]],"date-time":"2019-01-20T02:37:28Z","timestamp":1547951848000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s13042-017-0701-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,7,14]]},"references-count":37,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,1]]}},"alternative-id":["701"],"URL":"https:\/\/doi.org\/10.1007\/s13042-017-0701-9","relation":{},"ISSN":["1868-8071","1868-808X"],"issn-type":[{"type":"print","value":"1868-8071"},{"type":"electronic","value":"1868-808X"}],"subject":[],"published":{"date-parts":[[2017,7,14]]},"assertion":[{"value":"24 May 2015","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 June 2017","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 July 2017","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}