Abstract
Due to real databases usually contain redundant information, reducing them preserving the main information is one of the most important branches of study within the theory of Formal Concept Analysis (FCA). Taking advantage of the close relationship between Rough Set Theory (RST) and FCA, in this work, we address the problem of attribute reduction in FCA using the reduction mechanism given in RST. We analyze the properties obtained from this kind of reduction and show an illustrative example.
Partially supported by the State Research Agency (AEI) and the European Regional Development Fund (FEDER) project TIN2016-76653-P.
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- 1.
Originally, Ganter and Wille denoted these operators as \('\) and they were called derivation operators. We have modified this notation to distinguish between the mapping defined on objects and on attributes.
- 2.
Observe that the discernibility matrix is symmetric matrix since the discernibility relation is reflexive.
- 3.
For the sake of simplicity, 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, . (2018). Reducing Concept Lattices from Rough Set Theory. In: Kacprzyk, J., Szmidt, E., Zadrożny, S., Atanassov, K., Krawczak, M. (eds) Advances in Fuzzy Logic and Technology 2017. EUSFLAT IWIFSGN 2017 2017. Advances in Intelligent Systems and Computing, vol 641. Springer, Cham. https://doi.org/10.1007/978-3-319-66830-7_17
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DOI: https://doi.org/10.1007/978-3-319-66830-7_17
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