{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T17:45:23Z","timestamp":1742924723672,"version":"3.40.3"},"publisher-location":"Singapore","reference-count":28,"publisher":"Springer Singapore","isbn-type":[{"type":"print","value":"9789811675010"},{"type":"electronic","value":"9789811675027"}],"license":[{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021]]},"DOI":"10.1007\/978-981-16-7502-7_38","type":"book-chapter","created":{"date-parts":[[2021,10,29]],"date-time":"2021-10-29T09:06:55Z","timestamp":1635498415000},"page":"402-417","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Approximation Relation for Rough Sets"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0848-5343","authenticated-orcid":false,"given":"Shaobo","family":"Deng","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7038-202X","authenticated-orcid":false,"given":"Huihui","family":"Lu","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9841-3393","authenticated-orcid":false,"given":"Sujie","family":"Guan","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5428-6276","authenticated-orcid":false,"given":"Min","family":"Li","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8213-1626","authenticated-orcid":false,"given":"Hui","family":"Wang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,10,30]]},"reference":[{"issue":"5","key":"38_CR1","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":"1","key":"38_CR2","doi-asserted-by":"publisher","first-page":"48","DOI":"10.1016\/S0377-2217(96)00382-7","volume":"99","author":"Z Pawlak","year":"1997","unstructured":"Pawlak, Z.: Rough set approach to knowledge-based decision support. Eur. J. Oper. Res. 99(1), 48\u201357 (1997)","journal-title":"Eur. J. Oper. Res."},{"key":"38_CR3","doi-asserted-by":"publisher","unstructured":"Yufeng, Y.: A novel data mining algorithm based on rough set. In: Software Engineering and Knowledge Engineering: Theory and Practice, pp. 1115\u20131121. Springer (2012). https:\/\/doi.org\/10.1007\/978-3-642-03718-4_136","DOI":"10.1007\/978-3-642-03718-4_136"},{"key":"38_CR4","series-title":"Communications in Computer and Information Science","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1007\/978-3-642-31709-5_34","volume-title":"Advances on Computational Intelligence","author":"SH Nguyen","year":"2012","unstructured":"Nguyen, S.H., Nguyen, H.S.: A rough set approach to knowledge discovery by relation approximation. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds.) IPMU 2012. CCIS, vol. 297, pp. 331\u2013340. Springer, Heidelberg (2012). https:\/\/doi.org\/10.1007\/978-3-642-31709-5_34"},{"key":"38_CR5","doi-asserted-by":"crossref","unstructured":"Wen, S.D., Bao, Q.H.: Attribute reduction in ordered decision tables via evidence theory. Inform. Sci. 364, 91\u2013110 (2016)","DOI":"10.1016\/j.ins.2016.05.011"},{"key":"38_CR6","unstructured":"Bingjiao, F., Tsang, E.C.C., Weihua, X., Jianhang, Y.: Double-quantitative rough fuzzy set based decisions: A logical operations method. Information Sciences (2016)"},{"key":"38_CR7","doi-asserted-by":"crossref","unstructured":"Qinghua, H., Yu, D., Zongxia, X., Jinfu, L.: Fuzzy probabilistic approximation spaces and their information measures. IEEE Trans. Fuzzy Syst. 14(2), 191\u2013201 (2006)","DOI":"10.1109\/TFUZZ.2005.864086"},{"key":"38_CR8","doi-asserted-by":"crossref","unstructured":"Duo, Q.M., Yan, Z., Yi, Y., Li, H.X., Xu, F.F.: Relative reducts in consistent and inconsistent decision tables of the pawlak rough set model. Inform. Sci. 179(24), 4140\u20134150 (2009)","DOI":"10.1016\/j.ins.2009.08.020"},{"key":"38_CR9","doi-asserted-by":"publisher","first-page":"614","DOI":"10.1016\/j.ins.2014.03.078","volume":"278","author":"XA Ma","year":"2014","unstructured":"Ma, X.A., Wang, G., Hong, Yu., Li, T.: Decision region distribution preservation reduction in decision-theoretic rough set model. Inform. Sci. 278, 614\u2013640 (2014)","journal-title":"Inform. Sci."},{"key":"38_CR10","doi-asserted-by":"publisher","unstructured":"Zbigniew, B.: Algebraic structures of rough sets. In: Rough Sets, Fuzzy Sets and Knowledge Discovery, pp. 242\u2013247. Springer (1994). https:\/\/doi.org\/10.1007\/978-1-4471-3238-7_29","DOI":"10.1007\/978-1-4471-3238-7_29"},{"key":"38_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"208","DOI":"10.1007\/978-3-540-27778-1_12","volume-title":"Transactions on Rough Sets II","author":"G Cattaneo","year":"2004","unstructured":"Cattaneo, G., Ciucci, D.: Algebraic structures for rough sets. In: Peters, J.F., Skowron, A., Dubois, D., Grzyma\u0142a-Busse, J.W., Inuiguchi, M., Polkowski, L. (eds.) Transactions on Rough Sets II. LNCS, vol. 3135, pp. 208\u2013252. Springer, Heidelberg (2004). https:\/\/doi.org\/10.1007\/978-3-540-27778-1_12"},{"issue":"1","key":"38_CR12","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1016\/j.ins.2004.06.006","volume":"173","author":"G Qi","year":"2005","unstructured":"Qi, G., Liu, W.: Rough operations on boolean algebras. Inform. Sci. 173(1), 49\u201363 (2005)","journal-title":"Inform. Sci."},{"key":"38_CR13","doi-asserted-by":"publisher","unstructured":"Liu, G.-L.: Rough sets over the boolean algebras. In: International Workshop on Rough Sets, Fuzzy Sets, Data Mining, and Granular- Soft Computing. LNCS (LNAI), vol. 3641, pp. 124\u2013131. Springer, Heidelberg (2005). https:\/\/doi.org\/10.1007\/11548669_13","DOI":"10.1007\/11548669_13"},{"issue":"21","key":"38_CR14","doi-asserted-by":"publisher","first-page":"4105","DOI":"10.1016\/j.ins.2008.06.021","volume":"178","author":"G Liu","year":"2008","unstructured":"Liu, G., Zhu, W.: The algebraic structures of generalized rough set theory. Inform. Sci. 178(21), 4105\u20134113 (2008)","journal-title":"Inform. Sci."},{"key":"38_CR15","doi-asserted-by":"crossref","unstructured":"Mohua, B., Chakraborty, M.K.: Rough sets through algebraic logic. Fundam. Inform. 28(3), 211\u2013221 (1996)","DOI":"10.3233\/FI-1996-283401"},{"key":"38_CR16","unstructured":"Yiyu, Y., Yanhong, S.: Rough set models in multigranulation spaces. Elsevier Science Inc. (2016)"},{"key":"38_CR17","unstructured":"Xibei, Y., Xiaoning, S., Huili, D., Jingyu, Y.: Multi-granulation rough set: from crisp to fuzzy case. Ann. Fuzzy Math. Inform. 1(1), 55\u201370 (2011)"},{"key":"38_CR18","doi-asserted-by":"crossref","unstructured":"Minlun, Y.: Multigranulations rough set method of attribute reduction in information systems based on evidence theory. J. Appl. Math. 2014(4), 1\u20139 (2014)","DOI":"10.1155\/2014\/857186"},{"key":"38_CR19","doi-asserted-by":"crossref","unstructured":"Anhui, T., Weizhi, W., Jinjin, L., Guoping, L.: Evidence-theory-based numerical characterization of multigranulation rough sets in incomplete information systems. Fuzzy Sets Syst. 294(C), 18\u201335 (2015)","DOI":"10.1016\/j.fss.2015.08.016"},{"key":"38_CR20","doi-asserted-by":"publisher","first-page":"270","DOI":"10.1016\/j.ijar.2016.12.006","volume":"82","author":"Y She","year":"2017","unstructured":"She, Y., He, X., Shi, H., Qian, Y.: A multiple-valued logic approach for multigranulation rough set model. Int. J. Approximate Reason. 82, 270\u2013284 (2017)","journal-title":"Int. J. Approximate Reason."},{"key":"38_CR21","doi-asserted-by":"publisher","first-page":"106","DOI":"10.1016\/j.ijar.2019.11.002","volume":"116","author":"Y Yao","year":"2020","unstructured":"Yao, Y.: Three-way granular computing, rough sets, and formal concept analysis. Int. J. Approximate Reason. 116, 106\u2013125 (2020)","journal-title":"Int. J. Approximate Reason."},{"key":"38_CR22","doi-asserted-by":"publisher","first-page":"427","DOI":"10.1016\/j.ins.2020.08.049","volume":"547","author":"HNA Hameda","year":"2021","unstructured":"Hameda, H.N.A., Sobhy, A.: Distributed approach for computing rough set approximations of big incomplete information systems - sciencedirect. Inform. Sci. 547, 427\u2013449 (2021)","journal-title":"Inform. Sci."},{"key":"38_CR23","doi-asserted-by":"crossref","unstructured":"Yang, X., Chen, H., Li, T., Wan, J., Sang, B.: Neighborhood rough sets with distance metric learning for feature selection. Knowl.-Based Syst. 224, 107076 (2021)","DOI":"10.1016\/j.knosys.2021.107076"},{"key":"38_CR24","doi-asserted-by":"crossref","unstructured":"Zied, C., Semeh, B.S., Sami, N.: A rough set based algorithm for updating the modes in categorical clustering. Int. J. Mach. Learn. Cybern. 12, 2069\u20132090 (2021)","DOI":"10.1007\/s13042-021-01293-w"},{"key":"38_CR25","unstructured":"Jacek, P., Pomykala, J.M.: The stone algebra of rough sets. Bull. Polish Acad. Sci. Math. 36(7\u20138), 495\u2013508 (1988)"},{"key":"38_CR26","doi-asserted-by":"publisher","first-page":"227","DOI":"10.1016\/j.ins.2020.03.064","volume":"527","author":"H Wang","year":"2020","unstructured":"Wang, H., Wang, W., Xiao, S., Cui, Z., Minyang, X., Zhou, X.: Improving artificial bee colony algorithm using a new neighborhood selection mechanism. Inform. Sci. 527, 227\u2013240 (2020)","journal-title":"Inform. Sci."},{"issue":"3","key":"38_CR27","doi-asserted-by":"publisher","first-page":"1139","DOI":"10.1007\/s40747-020-00171-2","volume":"7","author":"H Wang","year":"2020","unstructured":"Wang, H., et al.: Artificial bee colony algorithm based on knowledge fusion. Complex Intell. Syst. 7(3), 1139\u20131152 (2020). https:\/\/doi.org\/10.1007\/s40747-020-00171-2","journal-title":"Complex Intell. Syst."},{"key":"38_CR28","unstructured":"Whitesitt, J.E.: Boolean Algebra and its applications. Courier Dover Publications (1995)"}],"container-title":["Communications in Computer and Information Science","Data Mining and Big Data"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-981-16-7502-7_38","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,10,29]],"date-time":"2021-10-29T09:13:01Z","timestamp":1635498781000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-981-16-7502-7_38"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021]]},"ISBN":["9789811675010","9789811675027"],"references-count":28,"URL":"https:\/\/doi.org\/10.1007\/978-981-16-7502-7_38","relation":{},"ISSN":["1865-0929","1865-0937"],"issn-type":[{"type":"print","value":"1865-0929"},{"type":"electronic","value":"1865-0937"}],"subject":[],"published":{"date-parts":[[2021]]},"assertion":[{"value":"30 October 2021","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"DMBD","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Data Mining and Big Data","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Guangzhou","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"China","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2021","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"20 October 2021","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"22 October 2021","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"6","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"dmbd2021","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/nsclab.org\/dmbd2021\/index.html","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Double-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"EasyChair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"258","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"57","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"28","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"22% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"2.5","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"8","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}