{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,26]],"date-time":"2026-07-26T01:30:37Z","timestamp":1785029437652,"version":"3.55.0"},"publisher-location":"Cham","reference-count":31,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783031656644","type":"print"},{"value":"9783031656651","type":"electronic"}],"license":[{"start":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T00:00:00Z","timestamp":1704067200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T00:00:00Z","timestamp":1704067200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024]]},"DOI":"10.1007\/978-3-031-65665-1_1","type":"book-chapter","created":{"date-parts":[[2024,7,24]],"date-time":"2024-07-24T07:04:54Z","timestamp":1721804694000},"page":"3-17","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Mapper-Based Rough Sets"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1007-353X","authenticated-orcid":false,"given":"Mauricio","family":"Restrepo","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6852-4041","authenticated-orcid":false,"given":"Chris","family":"Cornelis","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,7,25]]},"reference":[{"key":"1_CR1","doi-asserted-by":"crossref","unstructured":"Aljanobi, F.A., Lee, J.: Topological data analysis for classification of heart disease data. In: 2021 IEEE International Conference on Big Data and Smart Computing (BigComp), pp. 210\u2013213 (2021)","DOI":"10.1109\/BigComp51126.2021.00047"},{"key":"1_CR2","doi-asserted-by":"publisher","first-page":"667963","DOI":"10.3389\/frai.2021.667963","volume":"4","author":"F Chazal","year":"2021","unstructured":"Chazal, F., Michel, B.: An introduction to topological data analysis: fundamental and practical aspects for data scientists. Front. Artif. Intell. 4, 667963 (2021)","journal-title":"Front. Artif. Intell."},{"key":"1_CR3","doi-asserted-by":"publisher","first-page":"72","DOI":"10.1016\/j.ins.2013.03.045","volume":"240","author":"J Dai","year":"2013","unstructured":"Dai, J., Tian, H.: Entropy measures and granularity measures for set-valued information systems. Inf. Sci. 240, 72\u201382 (2013)","journal-title":"Inf. Sci."},{"key":"1_CR4","doi-asserted-by":"publisher","first-page":"62","DOI":"10.1016\/j.ijar.2016.06.013","volume":"78","author":"L D\u2019eer","year":"2016","unstructured":"D\u2019eer, L., Cornelis, C., Yao, Y.: A semantically sound approach to Pawlak rough sets and covering-based rough sets. Int. J. Approximate Reasoning 78, 62\u201372 (2016)","journal-title":"Int. J. Approximate Reasoning"},{"key":"1_CR5","doi-asserted-by":"crossref","unstructured":"Dey, T.K., Memoli, F., Wang, Y.: Multiscale mapper: a framework for topological summarization of data and maps. arXiv:1504.03763 (2016)","DOI":"10.1137\/1.9781611974331.ch71"},{"key":"1_CR6","doi-asserted-by":"publisher","first-page":"511","DOI":"10.1007\/s00454-002-2885-2","volume":"28","author":"H Edelsbrunner","year":"2002","unstructured":"Edelsbrunner, H., Letscher, D., Zomorodian, A.: Topological persistence and simplification. Discret. Comput. Geom. 28, 511\u2013533 (2002)","journal-title":"Discret. Comput. Geom."},{"key":"1_CR7","series-title":"Springer Proceedings in Complexity","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1007\/978-3-319-55471-6_5","volume-title":"3rd International Winter School and Conference on Network Science","author":"M Gidea","year":"2017","unstructured":"Gidea, M.: Topological data analysis of critical transitions in financial networks. In: Shmueli, E., Barzel, B., Puzis, R. (eds.) NetSci-X 2017. SPC, pp. 47\u201359. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-55471-6_5"},{"key":"1_CR8","doi-asserted-by":"publisher","first-page":"113222","DOI":"10.1016\/j.eswa.2020.113222","volume":"147","author":"A Goel","year":"2020","unstructured":"Goel, A., Pasricha, P., Mehra, A.: Topological data analysis in investment decisions. Expert Syst. Appl. 147, 113222 (2020)","journal-title":"Expert Syst. Appl."},{"key":"1_CR9","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0377-2217(00)00167-3","volume":"129","author":"S Greco","year":"2001","unstructured":"Greco, S., Matarazzo, B., S\u0142owinski, R.: Rough sets theory for multicriteria decision analysis. Eur. J. Oper. Res. 129, 1\u201347 (2001)","journal-title":"Eur. J. Oper. Res."},{"key":"1_CR10","doi-asserted-by":"crossref","unstructured":"Gunnar, G.: Topology and data. Bulletin (New Series) AMS. 46(2), 255\u2013308 (2009)","DOI":"10.1090\/S0273-0979-09-01249-X"},{"issue":"7","key":"1_CR11","first-page":"1410","volume":"14","author":"D Hwang","year":"2021","unstructured":"Hwang, D., et al.: Topological data analysis of coronary plaques demonstrates the natural history of coronary artherosclerosis. Cardiovas. Imaging 14(7), 1410\u20131421 (2021)","journal-title":"Cardiovas. Imaging"},{"key":"1_CR12","unstructured":"Kelly, M., Longjohn, R., Nottingham, K.: The UCI Machine learning repository. https:\/\/archive.ics.uci.edu"},{"key":"1_CR13","doi-asserted-by":"crossref","unstructured":"Li, L., et al.: Identification of type 2 diabetes subgroups through topological analysis of patient similarity7(311), 311ra174\u2013311ra174 (2015)","DOI":"10.1126\/scitranslmed.aaa9364"},{"key":"1_CR14","doi-asserted-by":"publisher","first-page":"1236","DOI":"10.1038\/srep01236","volume":"3","author":"P Lum","year":"2013","unstructured":"Lum, P., et al.: Extracting insights from the shape of complex data using topology. Sci. Rep. 3, 1236 (2013)","journal-title":"Sci. Rep."},{"key":"1_CR15","doi-asserted-by":"publisher","first-page":"113868","DOI":"10.1016\/j.eswa.2020.113868","volume":"162","author":"S Majumdar","year":"2020","unstructured":"Majumdar, S., Laha, A.K.: Clustering and classification of time series using topological data analysis with applications to finance. Expert Syst. Appl. 162, 113868 (2020)","journal-title":"Expert Syst. Appl."},{"key":"1_CR16","first-page":"1","volume":"70","author":"G Migda\u0142ek","year":"2022","unstructured":"Migda\u0142ek, G., Zelawski, M.: Measuring population-level plant gene flow with topological data analysis. Eco. Inform. 70, 1\u201311 (2022)","journal-title":"Eco. Inform."},{"issue":"17","key":"1_CR17","doi-asserted-by":"publisher","first-page":"7265","DOI":"10.1073\/pnas.1102826108","volume":"108","author":"M Nicolau","year":"2011","unstructured":"Nicolau, M., Levine, A.J., Carlsson, G.: Topology based data analysis identifies a subgroup of breast cancers with a unique mutational profile and excellent survival. Proc. Nat. Acad. Sci. U.S.A. 108(17), 7265\u20137270 (2011)","journal-title":"Proc. Nat. Acad. Sci. U.S.A."},{"key":"1_CR18","doi-asserted-by":"crossref","unstructured":"Offroy, M., Duponchel, L.: Topological data analysis: a promising big data exploration tool in biology, analytical chemistry and physical chemistry. Analytica Chimica Acta 910, 1\u201311 (2016). ISSN 0003-2670","DOI":"10.1016\/j.aca.2015.12.037"},{"issue":"3","key":"1_CR19","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1016\/0306-4379(81)90023-5","volume":"6","author":"Z Pawlak","year":"1981","unstructured":"Pawlak, Z.: Information systems theoretical foundations. Inf. Syst. 6(3), 205\u2013218 (1981)","journal-title":"Inf. Syst."},{"issue":"5","key":"1_CR20","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":"1_CR21","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":"1_CR22","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":"1_CR23","doi-asserted-by":"publisher","first-page":"105228","DOI":"10.1016\/j.cnsns.2020.105228","volume":"85","author":"K Sasaki","year":"2020","unstructured":"Sasaki, K., Bruder, D., Hernandez-Vargas, E.A.: Topological data analysis to model the shape of immune responses during co-infections. Commun. Nonlinear Sci. Numer. Simul. 85, 105228 (2020)","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"1_CR24","first-page":"091","volume":"2","author":"G Singh","year":"2007","unstructured":"Singh, G., M\u00e9moli, F., Carlsson, G.: Topological methods for the analysis of high dimensional data sets and 3D object recognition. Eurographics Symp. Point-Based Graph. 2, 091\u2013100 (2007)","journal-title":"Eurographics Symp. Point-Based Graph."},{"key":"1_CR25","doi-asserted-by":"publisher","first-page":"107202","DOI":"10.1016\/j.compchemeng.2020.107202","volume":"146","author":"A Smith","year":"2021","unstructured":"Smith, A., Dlotko, P., Zavala, V.: Topological data analysis: concepts, computation, and applications in chemical engineering. Comput. Chem. Eng. 146, 107202 (2021)","journal-title":"Comput. Chem. Eng."},{"issue":"42","key":"1_CR26","doi-asserted-by":"publisher","first-page":"1315","DOI":"10.21105\/joss.01315","volume":"4","author":"HJ Van Veen","year":"2019","unstructured":"Van Veen, H.J., Saul, N., Eargle, D., Manghmam, S.W.: Kepler mapper: a flexible python implementation of the mapper algorithm. J. Open Source Softw. 4(42), 1315 (2019)","journal-title":"J. Open Source Softw."},{"key":"1_CR27","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":"1_CR28","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."},{"key":"1_CR29","doi-asserted-by":"publisher","first-page":"11909","DOI":"10.1007\/s00500-020-05098-x","volume":"24","author":"W Zhaohao","year":"2020","unstructured":"Zhaohao, W., Xiaoping, Z., Jianping, D.: The uncertainty measures for covering rough set models. Soft Comput. 24, 11909\u201311929 (2020)","journal-title":"Soft Comput."},{"key":"1_CR30","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":"1_CR31","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"}],"container-title":["Lecture Notes in Computer Science","Rough Sets"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-65665-1_1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,24]],"date-time":"2024-07-24T07:05:12Z","timestamp":1721804712000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-65665-1_1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024]]},"ISBN":["9783031656644","9783031656651"],"references-count":31,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-65665-1_1","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024]]},"assertion":[{"value":"25 July 2024","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"IJCRS","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Joint Conference on Rough Sets","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Halifax, NS","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Canada","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2024","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"17 May 2024","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"20 May 2024","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"ijcrs2024","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/ijcrs24.cs.smu.ca","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}