Approximation via a double-matroid structure.

*(English)*Zbl 1418.68206Summary: Approximation is an important issue in rough set theory. In this study, we consider approximation by the matroidal approach. First, we study three lattices induced by an information system. Two of the three lattices are selected as the macrostructure and microstructure for approximation, respectively. Second, based on the two lattices, we define double-matroid lattices, where the upper and lower approximations with respect to an information system are depicted. Since the two lattices are geometric, we actually present approximation by the matroidal approach. Finally, we study the connection between our double-matroid lattices and granular partition lattices. Specifically, the comparison of these two structures is presented in both micro-level and macro-level.

##### MSC:

68T37 | Reasoning under uncertainty in the context of artificial intelligence |

05B35 | Combinatorial aspects of matroids and geometric lattices |

06C10 | Semimodular lattices, geometric lattices |

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\textit{X. Li} et al., Soft Comput. 23, No. 17, 7557--7568 (2019; Zbl 1418.68206)

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##### References:

[1] | Bisi, C.; Chiaselotti, G.; Ciucci, D.; Gentile, T.; Infusino, FG, Micro and macro models of granular computing induced by the indiscernibility relation, Inf Sci, 388-389, 247-273, (2017) |

[2] | Cattaneo, G.; Ciucci, D.; Peters, JF (ed.); etal., Lattices with interior and closure operators and abstract approximation spaces, No. 5656, 67-116, (2009), Heidelberg · Zbl 1248.06005 |

[3] | Chen, XY; Li, QG, Construction of rough approximations in fuzzy setting, Fuzzy Sets Syst, 159, 2641-2653, (2007) · Zbl 1127.68105 |

[4] | Chiaselotti, G.; Ciucci, D.; Gentile, T.; Infusino, FG, The granular partition lattice of an information table, Inf Sci, 373, 57-78, (2016) · Zbl 1388.03045 |

[5] | Dubois, D.; Prade, H., Rough fuzzy sets and fuzzy rough sets, Int J Gen Syst, 17, 191-209, (1990) · Zbl 0715.04006 |

[6] | Lee, T., An information-theoretic analysisof relational databases- part 1: data dependencies and metric, IEEE Trans Softw Eng SE-13, 10, 1049-1061, (1987) |

[7] | Li, XN; Liu, SY, Matroidal approaches to rough sets via closure operators, Int J Approx Reason, 53, 513-527, (2012) · Zbl 1246.68233 |

[8] | Li, XN; Yi, HJ; Liu, SY, Rough sets and matroids from a lattice-theoretic viewpoint, Inf Sci, 342, 37-52, (2016) · Zbl 1403.06018 |

[9] | Li, XN; Yi, HJ; She, YH; Sun, BZ, Generalized three-way models based on subset-evaluation, Int J Approx Reason, 83, 142-159, (2017) · Zbl 1404.68168 |

[10] | Li, XN; Sun, BZ; She, YH, Generalized matroids based on three-way decision models, Int J Approx Reason, 90, 192-207, (2017) · Zbl 1419.68170 |

[11] | Mao, H., Characterization and reduction of concept lattices through matroid theory, Inf Sci, 281, 338-354, (2014) · Zbl 1355.68248 |

[12] | Marek VW, Skowron A (2014) Rough sets and matroids. In: Peters JF, Skowron A (eds) Transactions on rough sets XVII, LNCS, vol 8375, pp 74-81 · Zbl 1404.68169 |

[13] | Oxley JG (1992) Matroid theory. Oxford University Press, New York · Zbl 0784.05002 |

[14] | Pawlak, Z., Rough sets, Int J Comput Inf Sci, 11, 341-356, (1982) · Zbl 0501.68053 |

[15] | Pawlak Z (1991) Rough sets: theoretical aspects of reasoning about data, system theory, knowledge engineering and problem solving, vol 9. Kluwer Academic Publishers, Dordrecht |

[16] | Skowron, A., Tolerance approximation spaces, Fundam Inform, 27, 245-253, (1996) · Zbl 0868.68103 |

[17] | Wang GY, Skowron A, Yao YY, Ślȩzak D, Polkowski L (eds) (2017) Thriving rough sets: 10th anniversary- Honoring professor Z. Pawlak’s life and legacy and 35 years of rough sets. Springer, Cham · Zbl 1374.68011 |

[18] | Wang, SP; Zhu, QX; Zhu, W.; Min, F., Matroidal structure of rough sets and its characterization to attribute reduction, Knowl-Based Syst, 36, 155-161, (2012) |

[19] | Wang, SP; Zhu, QX; Zhu, W.; Min, F., Rough set characterization for 2-circuit matroid, Fundam Inform, 129, 377-393, (2014) · Zbl 1285.68186 |

[20] | Welsh D (1976) Matroid theory. Academic press, London · Zbl 0343.05002 |

[21] | Yao YY (2004) A partition model of granular computing. In: Peters JF et al (eds) Transactions on rough sets I, LNCS, vol 3100, pp 232-253 |

[22] | Yao, YY; Yao, BX, Covering based rough set approximations, Inf Sci, 200, 91-107, (2012) · Zbl 1248.68496 |

[23] | Zhu, W.; Wang, SP, Rough matroids based on relations, Inf Sci, 232, 241-252, (2013) · Zbl 1293.05036 |

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