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conflict was detected between these two concepts (Fig. 9) and the customer's
softgoal was aligned to the “Learnability” concern by grid analysis (Fig. 10).
Thus, in the reconciled view, occurrences of terminological interference are iden-
tified and managed, and distinct early aspects are represented using distinct
lexicons.
4.1
Formal Concept Analysis
Formal concept analysis (FCA) is a mathematical technique for analyzing bi-
nary relations. The mathematical foundation of concept analysis was laid by
Birkhoff [3] in 1940. For more detailed information on FCA, we refer to [12],
where the mathematical foundation is explored.
FCA deals with a relation
I⊆O×A
between a set of objects
O
and a set
of attributes
A
. The tuple
C
=(
O, A, I
) is called a
formal context
. For a set of
objects
O ⊆O
, the set of common attributes
σ
(
O
) is defined as:
σ
(
O
)=
{a ∈ A |
(
o, a
)
∈I
for all
o ∈ O}.
(1)
Analogously, the set of common objects
τ
(
A
) for a set of attributes
A ⊆A
is
defined as:
τ
(
A
)=
{o ∈ O |
(
o, a
)
∈I
for all
a ∈ A}.
(2)
A formal context can be represented by a relation table, where columns hold
the objects and the rows hold the attributes. An object
o
i
and attribute
a
j
are
in the relation
I
if and only if the cell at column
i
and row
j
is marked by
“
”. As an example related to the media shop, a binary relation between a set
of objects
×
{
CD, MAGAZINE, NEWSPAPER, VIDEOTAPE, BOOK
}
and a set
of attributes
{
free-distribution, timely, paper, sound
}
is shown in Fig. 11a. For
that formal context, we have:
σ
(
{
CD
}
)=
{
free-distribution
,
sound
},
τ
(
{
timely
,
paper
}
)=
{
MAGAZINE
,
NEWSPAPER
}.
A tuple
c
=(
O, A
) is called a
concept
if and only if
A
=
σ
(
O
)and
O
=
τ
(
A
),
i.e., all objects in
c
share all attributes in
c
. For a concept
c
=(
O, A
),
O
is called
the
extent
of
c
, denoted by
extent
(
c
), and
A
is called the
intent
of
c
, denoted by
intent
). Informally speaking, a concept corresponds to a maximal rectangle of
filled table cells modulo row and column permutations. In Fig. 11b, all concepts
for the relation in Fig. 11a are listed.
The set of all concepts of a given formal context forms a partial order via the
superconcept-subconcept ordering
(
c
≤
:
(
O
1
,A
1
)
≤
(
O
2
,A
2
)
⇐⇒ O
1
⊆ O
2
,
(3)
or, dually, with
(
O
1
,A
1
)
≤
(
O
2
,A
2
)
⇐⇒ A
1
⊇ A
2
.
(4)
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