{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,28]],"date-time":"2025-03-28T04:16:41Z","timestamp":1743135401702,"version":"3.40.3"},"publisher-location":"Cham","reference-count":27,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319608365"},{"type":"electronic","value":"9783319608372"}],"license":[{"start":{"date-parts":[[2017,1,1]],"date-time":"2017-01-01T00:00:00Z","timestamp":1483228800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017]]},"DOI":"10.1007\/978-3-319-60837-2_13","type":"book-chapter","created":{"date-parts":[[2017,6,20]],"date-time":"2017-06-20T21:13:51Z","timestamp":1497993231000},"page":"154-164","source":"Crossref","is-referenced-by-count":0,"title":["Approximation Operators in Covering Based Rough Sets from Submodular Functions"],"prefix":"10.1007","author":[{"given":"Mauricio","family":"Restrepo","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,6,22]]},"reference":[{"key":"13_CR1","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1016\/j.ins.2015.03.060","volume":"314","author":"X Bian","year":"2015","unstructured":"Bian, X., Wang, P., Yu, Z., Bai, X., Chen, B.: Characterization of coverings for upper approximation operators being closure operators. Inf. Sci. 314, 41\u201354 (2015)","journal-title":"Inf. Sci."},{"key":"13_CR2","volume-title":"Lattices and Ordered Algebraic Structures","author":"TS Blyth","year":"2005","unstructured":"Blyth, T.S.: Lattices and Ordered Algebraic Structures. Springer Universitext, London (2005)"},{"key":"13_CR3","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1016\/j.ins.2015.12.007","volume":"336","author":"L Deer","year":"2016","unstructured":"Deer, L., Restrepo, M., Cornelis, C., G\u00f3mez, J.: Neighborhood operators for covering-based rough sets. Inf. Sci. 336, 21\u201344 (2016)","journal-title":"Inf. Sci."},{"key":"13_CR4","doi-asserted-by":"publisher","first-page":"513","DOI":"10.1016\/j.ijar.2011.12.005","volume":"53","author":"X Li","year":"2012","unstructured":"Li, X., Liu, S.: Matroidal approaches to rough sets via closure operators. Int. J. Approx. Reason. 53, 513\u2013527 (2012)","journal-title":"Int. J. Approx. Reason."},{"issue":"5","key":"13_CR5","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1007\/BF01001956","volume":"11","author":"Z Pawlak","year":"1982","unstructured":"Pawlak, Z.: Rough sets. Int. J. Comput. Inform. Sci. 11(5), 341\u2013356 (1982)","journal-title":"Int. J. Comput. Inform. Sci."},{"issue":"9\u201310","key":"13_CR6","first-page":"653","volume":"35","author":"JA Pomykala","year":"1987","unstructured":"Pomykala, J.A.: Approximation operations in approximation space. Bulletin de la Acad\u00e9mie Polonaise des Sciences 35(9\u201310), 653\u2013662 (1987)","journal-title":"Bulletin de la Acad\u00e9mie Polonaise des Sciences"},{"key":"13_CR7","doi-asserted-by":"publisher","first-page":"469","DOI":"10.1016\/j.ijar.2013.08.002","volume":"55","author":"M Restrepo","year":"2014","unstructured":"Restrepo, M., Cornelis, C., G\u00f3mez, J.: Duality, conjugacy and adjointness of approximation operators in covering-based rough sets. Int. J. Approx. Reason. 55, 469\u2013485 (2014)","journal-title":"Int. J. Approx. Reason."},{"key":"13_CR8","doi-asserted-by":"publisher","first-page":"44","DOI":"10.1016\/j.ins.2014.06.032","volume":"284","author":"M Restrepo","year":"2014","unstructured":"Restrepo, M., Cornelis, C., G\u00f3mez, J.: Partial order relation for approximation operators in covering-based rough sets. Inf. Sci. 284, 44\u201359 (2014)","journal-title":"Inf. Sci."},{"key":"13_CR9","unstructured":"Roa, L.: Una nueva construcci\u00f3n de los espacios topol\u00f3gicos finitos desde las funciones submodulares. Tesis de Maestr\u00eda en Matem\u00e1ticas. Universidad Nacional de Colombia, Bogot\u00e1 (2012)"},{"issue":"1","key":"13_CR10","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.tcs.2012.10.060","volume":"47","author":"J Tang","year":"2013","unstructured":"Tang, J., She, K., Min, F., Zhu, W.: A matroidal approach to rough set theory. Theoret. Comput. Sci. 47(1), 1\u201311 (2013)","journal-title":"Theoret. Comput. Sci."},{"key":"13_CR11","doi-asserted-by":"crossref","unstructured":"Tsang, E., Chen, D., Lee, J., Yeung, D.S.: On the upper approximations of covering generalized rough sets. In: Proceedings of the 3rd International Conference on Machine Learning and Cybernetics, pp. 4200\u20134203 (2004)","DOI":"10.1109\/ICMLC.2004.1384576"},{"key":"13_CR12","unstructured":"Varela, R.: FD- Relaciones. Tesis de Maestr\u00eda en Matem\u00e1ticas. Universidad Nacional de Colombia, Bogot\u00e1 (2011)"},{"key":"13_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"146","DOI":"10.1007\/978-3-642-24425-4_21","volume-title":"Rough Sets and Knowledge Technology","author":"S Wang","year":"2011","unstructured":"Wang, S., Zhu, W., Min, F.: Transversal and function matroidal structures of covering-based rough sets. In: Yao, J.T., Ramanna, S., Wang, G., Suraj, Z. (eds.) RSKT 2011. LNCS, vol. 6954, pp. 146\u2013155. Springer, Heidelberg (2011). doi:\n10.1007\/978-3-642-24425-4_21"},{"key":"13_CR14","doi-asserted-by":"crossref","unstructured":"Wu, M., Wu, X., Shen, T.: A new type of covering approximation operators. In: IEEE International Conference on Electronic Computer Technology, pp. 334\u2013338 (2009)","DOI":"10.1109\/ICECT.2009.42"},{"issue":"1","key":"13_CR15","first-page":"130","volume":"33","author":"Z Xu","year":"2005","unstructured":"Xu, Z., Wang, Q.: On the properties of covering rough sets model. J. Henan Normal Univ. (Nat. Sci.) 33(1), 130\u2013132 (2005)","journal-title":"J. Henan Normal Univ. (Nat. Sci.)"},{"key":"13_CR16","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1016\/j.ijar.2009.11.001","volume":"51","author":"T Yang","year":"2010","unstructured":"Yang, T., Li, Q.: Reduction about approximation spaces of covering generalized rough sets. Int. J. Approx. Reason. 51, 335\u2013345 (2010)","journal-title":"Int. J. Approx. Reason."},{"key":"13_CR17","unstructured":"Liu, Y., Zhu, W.: Relation matroid and its relationship with generalized rough set based on relations. CoRR abs 1209.5456 (2012)"},{"key":"13_CR18","first-page":"2151","volume":"8","author":"Y Liu","year":"2012","unstructured":"Liu, Y., Zhu, W., Zhang, Y.: Relationship between partition matroids and rough sets through $$k$$-rank matroids. J. Inf. Comput. Sci. 8, 2151\u20132163 (2012)","journal-title":"J. Inf. Comput. Sci."},{"issue":"1","key":"13_CR19","first-page":"139","volume":"12","author":"Y Li","year":"2012","unstructured":"Li, Y., Wang, Z.: The relationships between degree rough sets and matroids. Anals Fuzzy Math. Inform. 12(1), 139\u2013153 (2012)","journal-title":"Anals Fuzzy Math. Inform."},{"key":"13_CR20","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1016\/S0020-0255(98)00012-7","volume":"109","author":"YY Yao","year":"1998","unstructured":"Yao, Y.Y.: Constructive and algebraic methods of the theory of rough sets. Inf. Sci. 109, 21\u201347 (1998)","journal-title":"Inf. Sci."},{"key":"13_CR21","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1016\/j.ins.2012.02.065","volume":"200","author":"YY Yao","year":"2012","unstructured":"Yao, Y.Y., Yao, B.: Covering based rough sets approximations. Inf. Sci. 200, 91\u2013107 (2012)","journal-title":"Inf. Sci."},{"key":"13_CR22","first-page":"761","volume":"16","author":"W Zakowski","year":"1983","unstructured":"Zakowski, W.: Approximations in the space $$(u,\\pi )$$. Demonstr. Math. 16, 761\u2013769 (1983)","journal-title":"Demonstr. Math."},{"key":"13_CR23","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.ijar.2015.09.003","volume":"68","author":"Z Zhao","year":"2016","unstructured":"Zhao, Z.: On some types of covering rough sets from topological points of view. Int. J. Approx. Reason. 68, 1\u201314 (2016)","journal-title":"Int. J. Approx. Reason."},{"key":"13_CR24","doi-asserted-by":"crossref","unstructured":"Zhu, W.: Properties of the first type of covering-based rough sets. In: Proceedings of Sixth IEEE International Conference on Data Mining - Workshops, pp. 407\u2013411 (2006)","DOI":"10.1109\/ICDMW.2006.136"},{"key":"13_CR25","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.: Relationship between generalized rough sets based on binary relation and covering. Inf. Sci. 179, 210\u2013225 (2009)","journal-title":"Inf. Sci."},{"key":"13_CR26","doi-asserted-by":"crossref","unstructured":"Zhu, W., Wang, F.: A new type of covering rough set. In: Proceedings of Third International IEEE Conference on Intelligence Systems, pp. 444\u2013449 (2006)","DOI":"10.1109\/IS.2006.348460"},{"key":"13_CR27","doi-asserted-by":"publisher","first-page":"3699","DOI":"10.1007\/s00500-015-2024-7","volume":"21","author":"XZ Zhu","year":"2017","unstructured":"Zhu, X.Z., Zhu, W., Fan, X.N.: Rough sets methods in features selection via submodular function. Soft Comput. 21, 3699\u20133711 (2017)","journal-title":"Soft Comput."}],"container-title":["Lecture Notes in Computer Science","Rough Sets"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-60837-2_13","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2018,11,30]],"date-time":"2018-11-30T00:42:43Z","timestamp":1543538563000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-60837-2_13"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017]]},"ISBN":["9783319608365","9783319608372"],"references-count":27,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-60837-2_13","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2017]]}}}