partially ordered by inclusion on : . is a concept lattice.

In the context given figure 1(a), but, following the previous definition, the formal concept built by closure is . The lattice has one top concept which extent groups all the objects of the context and, by duality, one *bottom* concept which intent groups all the attributes of the context. 

Objects in the extension of a concept are inherited from the bottom to the top of the lattice. In a dual way, attributes are inherited from top to bottom. Figure 1(b) is the concept lattice of the context (a). The concept is named in the lattice.

| M   | F   | D1   | D2   | D3   | D4   | D5   | AE1   | AE2   |
|-----|-----|------|------|------|------|------|-------|-------|
| P1  | X   | X    | X    | X    |      |      |       |       |
| P2  | X   | X    | X    | X    |      |      |       |       |
| P3  | X   | X    | X    | X    |      |      |       |       |
| P4  | X   | X    | X    |      |      |      |       |       |
| P5  | X   | X    | X    | X    |      |      |       |       |
| P6  | X   | X    | X    | X    |      |      |       |       |
| P7  | X   | X    | X    | X    |      |      |       |       |
| P8  | X   | X    | X    | X    |      |      |       |       |

![0_image_0.png](0_image_0.png)

2.2. *FCA and Adverse Drug Event Exploration* The intent of some formal concepts shows that some patients took a same set of drugs and had the same set of AEs. In , four patients took the drug and have the adverse event . We also observe in the context that , among others, also took but is the only drug that the four patient took. Thanks to the closure operators used to build the concepts, the lattice gives all the drugs-AEs relationships that exist in the data and no more. Among all the concepts, we distinguish potential **signals**, when the intent includes only one drug and one AE (see and ); 
potential **drug interactions**, when the intent includes two drugs and one AE (see and ); and potential **syndrome**, when the intent includes one drug and several AEs 
(see ).

Compared to extraction of {drug, AE } couples without FCA, the lattice - with its formal concepts built using the closure operators - reduces the number of situations drugs-AEs to study. In figure 1(b), patients share the attributes . While disproportionality measures would propose two potential signals to study 
( and ), the lattice keeps only one ( ) as is not 