Semantic Knowledge Representations for Soft Data Fusion - Efficient Decision Support Systems: Practice and Challenges from Current to Future - page 19

,G 1 = G 1 and G 2 = •f

|

C 1

|≤|

C 2

|

G 2

• else G 1 = G 2 and G 2 = G 1

C 1 (resp. C 2 ) is the set of concepts of G 1 (resp. G 2 ).
sim Graph (

G 1 , G 2 )=

C 1 (

max c 2 ∈ C 2 p

(

t 1,2 ) ∗ sim

| (

c 1 , c 2 ))

∑
c 1 ∈

gene

( ) p t 1,2

∑

C 1 × C 2 |

( c 1 , c 2 ) ∈

C 2 , c 3 = ∀ c 3 ∈ c 2 ∧

sim | ( c 1 , c 3 ) < sim | ( c 1 , c 2 )

gene gene

where p is the weight associated with the conceptual type t 1,2 and that allows giving more or less

importance to some of the concepts, according to the application domain;

(

t 1,2

)

As a matter of example, let us consider the two graphs g 1 and g 2 depicted on figure 10. To
compute their similarity, we process the similarities of the different possible pairs of concepts.
The table on figure 11 shows the similarity scores, using sim

| gene , of all the pairs of concepts

that can be matched between the two graphs.

Fig. 10. Processing similarity - input graphs

The matching surrounded in red continuous line has a similarity score of 0,92 and is the best
that can be found.

5.4 Multi-source synthesis
The multi-source information synthesis phase relies on a fusion process that is an extension of
the maximal join operation initially described by John Sowa (Sowa (1984)). The structures
and contents of the two graphs to be fused are compared relying on homomorphism search.
Redundant parts are fused (i.e. added only once) into the resulting fused graph and
complementary elements are all added.

5.4.1 Projection based operations on conceptual graphs and maximal join
To fuse two graphs, we first have to find all the couples of nodes of the two graphs that
represent the same parts of the TV program description. Doing so, one should look, not only
at the identical nodes, but also at the ones that represent the same thing, potentially with
different levels of precision. For instance, in Figure 12 the [Program] and [Entity:

P1]

concepts represent the same object of the world, (a TV program which referent is P1 ).