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2017 | OriginalPaper | Chapter

6. Compound Information Systems

Author : Piotr Hońko

Published in: Granular-Relational Data Mining

Publisher: Springer International Publishing

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Abstract

This chapter provides a general framework for analyzing and processing relational data in a granular computing environment. It introduces compound information systems for relational data. It also extends an attribute-value language for defining relational patterns.

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previous chapter Rough-Granular Computing
next chapter From Granular-Data Mining Framework to Its Relational Version
Footnotes
1
The approach introduced in this chapter can also be applied with no changes to a framework that uses a covering of the universe to form granules.
 
2
In this approach the equality relation in the construction of conditions is used. The approach can easily be extended to a case where the conditions are also constructed by applying equality relations and a membership relation.
 
3
The notation \(SEM_{IS}((a,v))\) is simplified by writing \(SEM_{IS}(a,v)\).
 
4
Symbolic values are abbreviated to their first letters. Granules in the table are presented in a simplified form, e.g. the granule \(\left( 30,\{3,4\}\right) \) from column age corresponds to the granule \(\left( (age,30),\{3,4\}\right) \).
 
5
\(SEM_i\) is the semantics of \(L_i\).
 
6
The index (i.e. the relation identifier) is omitted if this does not lead to a confusion.
 
7
It is assumed by default that a condition can be constructed based on two key attributes if they are of the same type.
 
8
The intersection of \(A_i\) and \(A_j\) is empty because all attributes names are distinct from one another, e.g. \(customer.id\ne purchase.id\).
 
9
1. The subset of \(A_i\) that consists of all key attributes is denoted by \((A_i)_{key}\). 2. As previously, it is assumed that key attributes are of the same type.
 
10
\(\pi _{A}(\bullet )\) is understood as a projection over the attributes from A.
 
11
The rule conclusion is a trivial formula and means that an object which satisfies the formula belongs to the relation.
 
12
Proofs of the propositions formulated in this chapter can be found in [41].
 
Metadata
Title
Compound Information Systems
Author
Piotr Hońko
Copyright Year
2017
Book
Granular-Relational Data Mining

Print ISBN: 978-3-319-52750-5

Electronic ISBN: 978-3-319-52751-2

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-52751-2_6

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