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Geometric lattice has been widely used in diverse fields, especially search algorithm design, which plays an important role in covering reductions. In this paper, we construct three geometric lattice structures of covering\u2010based rough sets through matroids and study the relationship among them. First, a geometric lattice structure of covering\u2010based rough sets is established through the transversal matroid induced by a covering. Then its characteristics, such as atoms, modular elements, and modular pairs, are studied. We also construct a one\u2010to\u2010one correspondence between this type of geometric lattices and transversal matroids in the context of covering\u2010based rough sets. Second, we present three sufficient and necessary conditions for two types of covering upper approximation operators to be closure operators of matroids. We also represent two types of matroids through closure axioms and then obtain two geometric lattice structures of covering\u2010based rough sets. Third, we study the relationship among these three geometric lattice structures. Some core concepts such as reducible elements in covering\u2010based rough sets are investigated with geometric lattices. In a word, this work points out an interesting view, namely, geometric lattice, to study covering\u2010based rough sets.<\/jats:p>","DOI":"10.1155\/2012\/236307","type":"journal-article","created":{"date-parts":[[2012,12,18]],"date-time":"2012-12-18T21:01:01Z","timestamp":1355864461000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Geometric Lattice Structure of Covering\u2010Based Rough Sets through Matroids"],"prefix":"10.1155","volume":"2012","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":"311","published-online":{"date-parts":[[2012,12,18]]},"reference":[{"key":"e_1_2_8_1_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01001956"},{"key":"e_1_2_8_2_2","doi-asserted-by":"publisher","DOI":"10.3233\/FI-1996-272311"},{"key":"e_1_2_8_3_2","doi-asserted-by":"publisher","DOI":"10.1109\/69.842271"},{"key":"e_1_2_8_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2008.06.021"},{"key":"e_1_2_8_5_2","doi-asserted-by":"crossref","unstructured":"YaoY. 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