{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,1]],"date-time":"2025-06-01T04:10:01Z","timestamp":1748751001968,"version":"3.41.0"},"publisher-location":"Cham","reference-count":32,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319257822"},{"type":"electronic","value":"9783319257839"}],"license":[{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015]]},"DOI":"10.1007\/978-3-319-25783-9_11","type":"book-chapter","created":{"date-parts":[[2015,11,7]],"date-time":"2015-11-07T01:25:39Z","timestamp":1446859539000},"page":"112-123","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Topological Properties for Approximation Operators in Covering Based Rough Sets"],"prefix":"10.1007","author":[{"given":"Mauricio","family":"Restrepo","sequence":"first","affiliation":[]},{"given":"Jonatan","family":"G\u00f3mez","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,11,8]]},"reference":[{"key":"11_CR1","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1007\/s13042-012-0107-7","volume":"4","author":"EA Abo","year":"2013","unstructured":"Abo, E.A.: Rough sets and topological spaces based on similarity. Int. J. Mach. Learn. Cybern. 4, 451\u2013458 (2013)","journal-title":"Int. J. Mach. Learn. Cybern."},{"key":"11_CR2","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":"11_CR3","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":"11_CR4","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1016\/S0020-0255(97)10046-9","volume":"107","author":"Z Bonikowski","year":"1998","unstructured":"Bonikowski, Z., Brynarski, E.: Extensions and Intensions in rough set theory. Inform. Sci. 107, 149\u2013167 (1998)","journal-title":"Inform. Sci."},{"issue":"1","key":"11_CR5","first-page":"141","volume":"263","author":"Y Hai","year":"2014","unstructured":"Hai, Y., Wan-rong, Z.: On the topological properties of generalized rough sets. Inform. Sci. 263(1), 141\u2013152 (2014)","journal-title":"Inform. Sci."},{"key":"11_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"400","DOI":"10.1007\/978-3-540-71200-8_22","volume-title":"Transactions on Rough Sets VI","author":"J J\u00e4rvinen","year":"2007","unstructured":"J\u00e4rvinen, J.: Lattice theory for rough sets. In: Peters, J.F., Skowron, A., D\u00fcntsch, I., Grzyma\u0142a-Busse, J.W., Or\u0142owska, E., Polkowski, L. (eds.) Transactions on Rough Sets VI. Lncs, vol. 4374, pp. 400\u2013498. Springer, Heidelberg (2007)"},{"issue":"5","key":"11_CR7","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."},{"key":"11_CR8","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1016\/j.ijar.2010.07.010","volume":"52","author":"Z Pei","year":"2011","unstructured":"Pei, Z., Pei, D., Zheng, L.: Topology vs generalized rough sets. Int. J. Approximate Reasoning 52, 231\u2013239 (2011)","journal-title":"Int. J. Approximate Reasoning"},{"issue":"9\u201310","key":"11_CR9","first-page":"653","volume":"35","author":"JA Pomykala","year":"1987","unstructured":"Pomykala, J.A.: Approximation operations in approximation space. Bull. Acad. Pol. Sci. 35(9\u201310), 653\u2013662 (1987)","journal-title":"Bull. Acad. Pol. Sci."},{"key":"11_CR10","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1109\/TSMCB.2007.908866","volume":"38","author":"Q Wu","year":"2008","unstructured":"Wu, Q., Wang, T., Huan, Y., Li, J.: Topology theory on rough sets. IEEE Trans. Syst. Man Cybern. 38, 68\u201377 (2008)","journal-title":"IEEE Trans. Syst. Man Cybern."},{"key":"11_CR11","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. Approximate Reasoning 55, 469\u2013485 (2014)","journal-title":"Int. J. Approximate Reasoning"},{"key":"11_CR12","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":"11_CR13","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":"11_CR14","doi-asserted-by":"publisher","first-page":"66","DOI":"10.1016\/j.ins.2012.03.023","volume":"207","author":"L Wang","year":"2012","unstructured":"Wang, L., Yang, X., Yang, J., Wu, C.: Relationships among generalized rough sets in six coverings and pure reflexive neighborhood system. Inf. Sci. 207, 66\u201378 (2012)","journal-title":"Inf. Sci."},{"key":"11_CR15","doi-asserted-by":"publisher","first-page":"2443","DOI":"10.1016\/j.fss.2007.03.018","volume":"158","author":"W Xu","year":"2007","unstructured":"Xu, W., Zhang, W.: Measuring roughness of generalized rough sets induced by a covering. Fuzzy Sets Syst. 158, 2443\u20132455 (2007)","journal-title":"Fuzzy Sets Syst."},{"issue":"1","key":"11_CR16","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":"11_CR17","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1016\/j.ins.2012.04.005","volume":"204","author":"G Xun","year":"2012","unstructured":"Xun, G., Xiaole, B., Yun, Z.: Topological characterization of coverings for special covering based upper approximation operators. Inf. Sci. 204, 70\u201381 (2012)","journal-title":"Inf. Sci."},{"key":"11_CR18","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. Approximate Reasoning 51, 335\u2013345 (2010)","journal-title":"Int. J. Approximate Reasoning"},{"key":"11_CR19","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":"11_CR20","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":"11_CR21","first-page":"761","volume":"16","author":"W Zakowski","year":"1983","unstructured":"Zakowski, W.: Approximations in the space $$(u,\\pi )$$. Demonstratio Math. 16, 761\u2013769 (1983)","journal-title":"Demonstratio Math."},{"issue":"2","key":"11_CR22","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.: On axiomatic characterizations of three pairs of covering based approximation operators. Inf. Sci. 180(2), 274\u2013287 (2010)","journal-title":"Inf. Sci."},{"issue":"8","key":"11_CR23","first-page":"1131","volume":"19","author":"L Zhaowen","year":"2012","unstructured":"Zhaowen, L.: Topological structure of generalized rough sets. IEEE Trans. Knowl. Data Eng. 19(8), 1131\u20131144 (2012)","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"11_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":"11_CR25","doi-asserted-by":"crossref","unstructured":"Zhu, W.: Properties of the second type of covering-based rough sets. In: Proceedings of the IEEE\/WIC\/ACM International Conference on Web Intelligence and Intelligent Agent Technology, pp. 494\u2013497 (2006)","DOI":"10.1109\/WI-IATW.2006.107"},{"key":"11_CR26","doi-asserted-by":"crossref","unstructured":"Zhu, W.: Basic concepts in covering-based rough sets. In: Proceedings of Third International Conference on Natural Computation, pp. 283\u2013286 (2007)","DOI":"10.1109\/ICNC.2007.281"},{"key":"11_CR27","doi-asserted-by":"crossref","unstructured":"Zhu, W.: Properties of the third type of covering-based rough sets. In: Proceedings of International Conference on Machine Learning and Cybernetics, pp. 3746\u20132751 (2007)","DOI":"10.1109\/ICMLC.2007.4370799"},{"key":"11_CR28","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":"11_CR29","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1016\/S0020-0255(03)00056-2","volume":"152","author":"W Zhu","year":"2003","unstructured":"Zhu, W., Wang, F.: Reduction and axiomatization of covering generalized rough sets. Inf. Sci. 152, 217\u2013230 (2003)","journal-title":"Inf. Sci."},{"key":"11_CR30","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"},{"issue":"8","key":"11_CR31","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.: On three types of covering based rough sets. IEEE Trans. Knowl. Data Eng. 19(8), 1131\u20131144 (2007)","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"11_CR32","doi-asserted-by":"publisher","first-page":"1499","DOI":"10.1016\/j.ins.2006.06.009","volume":"177","author":"W Zhu","year":"2007","unstructured":"Zhu, W.: Topological approach to covering rough sets. Inf. Sci. 177, 1499\u20131508 (2007)","journal-title":"Inf. Sci."}],"container-title":["Lecture Notes in Computer Science","Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-25783-9_11","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,31]],"date-time":"2025-05-31T10:22:05Z","timestamp":1748686925000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-319-25783-9_11"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"ISBN":["9783319257822","9783319257839"],"references-count":32,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-25783-9_11","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2015]]},"assertion":[{"value":"8 November 2015","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}