Abstract
This chapter develops compound approximation spaces and their constrained versions defined for relational data. These spaces are constructed based on information systems and the tolerance rough set model extended to a relational case. The chapter also shows that in constrained compound approximations spaces it is possible to approximate not only a combination of concepts, each of which is defined in one database table, but also the relationships that occur among the concepts.
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Notes
- 1.
Proofs of the propositions formulated in this chapter can be found in [43].
- 2.
The uncertainty and rough inclusion functions are defined as in Chap. 5. The distance measure is defined as follows \(d(x,y)=|a(x)-a(y)|\).
- 3.
Here, a purchase is identified by one row in the purchase table.
- 4.
The condition is required for the last two equalities.
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Hońko, P. (2017). Compound Approximation Spaces. In: Granular-Relational Data Mining. Studies in Computational Intelligence, vol 702. Springer, Cham. https://doi.org/10.1007/978-3-319-52751-2_9
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DOI: https://doi.org/10.1007/978-3-319-52751-2_9
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-52750-5
Online ISBN: 978-3-319-52751-2
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