Skip to main content

Table 2 An example generalized decision table \(\mathcal{D}=\left(U,A\cup \left\{d\right\}\right)\) for case–control study of autism, where \(A\) is a set of three genes \(\left\{{g}_{1},{g}_{2},{g}_{3}\right\}\) and a risk factor \(\left\{rf\right\}\), and \(U\) is a set of objects that belong to equivalence classes \({[q}_{1}], \dots , [{q}_{8}]\). The values in \(U\) are discrete gene expression levels “low”, “medium” or “high” and a presence of undefined risk factor “yes” or “no”. For simplicity we omit the brackets in the notation in the table. For the equivalence classes \({q}_{4}\) and \({q}_{5}\) both diagnoses are written since some of the indiscernible objects belong to the boundary region

From: R.ROSETTA: an interpretable machine learning framework

Equivalence class

\({g}_{1}\)

\({g}_{2}\)

\({g}_{3}\)

\(rf\)

\(diagnosis\)

\({q}_{1}\)

Low

Low

Medium

Yes

Autism

\({q}_{2}\)

Medium

Medium

Medium

Yes

Autism

\({q}_{3}\)

Medium

Low

Medium

Yes

Autism

\({q}_{4}\)

Medium

Low

High

No

Autism or control

\({q}_{5}\)

Low

Low

High

No

Autism or control

\({q}_{6}\)

Low

High

Medium

No

Control

\({q}_{7}\)

Medium

High

Medium

Yes

Control

\({q}_{8}\)

Medium

High

High

No

Control