Semantic Knowledge Representations for Soft Data Fusion - Efficient Decision Support Systems: Practice and Challenges from Current to Future - page 17

• The types of the relations are equals: x

)
• one element of R 1 is related to at most one element of R 2 :

R

y

⇔

l

(

x

)=

l

(

y

∀

x

∈

R 1 ,

( ∃

! y

∈

R 2 , such that x

R

y

) ∨

R ∅
• one element of R 2 is related to at most one element of R 1 :

x

∀

y

∈

R 2 ,

( ∃

! x

∈

R 1 , such that x

R

y

) ∨

y
To define the similarity measure regarding the context of two concepts, we use the two sets INTERSEC
and COMPL , defined as follows as follows.
INTERSEC is a set of couples of relations nodes of R 1 and R 2 that are related through the

∅ R

R

relation.

x , y ) ∈ Let INTERSEC

= { (

x , y

) ∈

R 1 × R 2 | x

R

y with

∀ (

x , y

) ∈

R 1 × R 2 ,

(

R 1 × R 2 ,ifx

R

y

∧

x R y ,x x ⇔ y }

.
COMPL is the set of relations that could not be related through

=

y

=

R

R 1 × R 2 | y x , y ) ∈ x = { ( ) ∈ ∈ ( ∧ ∈ Let COMPL x , y R 2 such that INTERSEC

x , y ) ∈ = ∅) }

The similarity of the context of c 1 and c 2 is then defined according to the cardinality of the two sets
INTERSEC and COMPL :

( ∧ ( = ∅ ⊕ R 1 such that INTERSEC x y

| | INTERSEC

( )=

sim context c 1 , c 2

| | + | | INTERSEC COMPL

5.3.1.4 Similarity of concepts
To compare two concepts, now, we use a similarity measure that combines all the measures
described above.
The order of importance of the component of two concepts, when processing their similarity
is the following one:
1. their concept types
2. their referents
3. the context in which they are used
To account for this hierarchy of importance, within the similarity measure sim

gene , we apply
different coefficients to the individual similarity (and dissimilarity) measures: a coefficient
of 4 is applied to the part accounting for the similarity of the concept types, 2 to the part
accounting for the referents and 1 for the contexts. In order to keep a normalized similarity,
the the similarity score processed as described above is divided by 7.

|

2

Definition 5.6. The similarity measure sim

| gene : C → [

0, 1

]

, where

C

is a set of concepts defined

on the same vocabulary, is expressed as follows:
∀ (

2 such that c 1 =[

c 1 , c 2 ) ∈C t 1 : v 1 ] and c 2 =[ t 2 : v 2 ] ,

• If the most specific common parent of t 1 and t 2 is the root of the type hierarchy, we have
sim

| (

c 1 , c 2 )= 0 .

gene

• Otherwise, we have
sim

( −

diss type ( t 1 , t 2 ))+

∗

sim ref ( v 1 , v 2 )+ sim context ( c 1 , c 2 ) 4 1 2

| (

c 1 , c 2 )=

gene

7
where diss type , sim ref and sim context are the similarity and dissimilarity measures defined above.