Abstract
Rough Set Theory (RST) and Formal Concept Analysis (FCA) are two mathematical tools for data analysis which, in spite of considering different philosophies, are closely related. In this paper, we study the relation between the attribute reduction mechanisms in FCA and in RST. Different properties will be introduced which provide a new size reduction mechanism in FCA based on the philosophy of RST.
Partially supported by the State Research Agency (AEI) and the European Regional Development Fund (FEDER) project TIN2016-76653-P.
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Notes
- 1.
- 2.
Originally these operators were denoted as \('\) by Ganter and Wille and they were called derivation operators. In order to differentiate between the mapping on the set of objects and on the set of attributes, we have changed the notation.
- 3.
Note that the discernibility matrix is symmetric due to the discernibility relation is reflexive.
- 4.
In order to simplify the notation, we will write \((^{\uparrow _1},^{\downarrow ^1})\) and \((^{\uparrow _2},^{\downarrow ^2})\), instead of \((^{\uparrow _{D_1}},^{\downarrow ^{D_1}})\) and \((^{\uparrow _{D_2}},^{\downarrow ^{D_2}})\) to denote the concept-forming operators in the reduced contexts by \(D_1\) and \(D_2\), respectively.
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Benítez-Caballero, M.J., Medina, J., Ramírez-Poussa, E. (2017). Attribute Reduction in Rough Set Theory and Formal Concept Analysis. In: Polkowski, L., et al. Rough Sets. IJCRS 2017. Lecture Notes in Computer Science(), vol 10314. Springer, Cham. https://doi.org/10.1007/978-3-319-60840-2_37
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