Database Reference
In-Depth Information
R
= {(
p
= {( ,
c
)∈
D
×
D
| ∃((( ,
cs
)∈
O
:
c
∈
cs
} is connected and acyclic.
= {(
p
Using the example introduced already, examples of data elements are 'claimant has not
issued a claim earlier in the same year' (i1), 'damage is covered according to the policy' (i2),
and 'claim is acceptable' (i3). An example of an operation is (i3, {i1, i2}). As said, the issue
we consider is how to fi nd a set of activities that partition the total set of operations. For a
proper division, we introduce the notion of a
valid activity
and a
valid activity ordering
.
Defi nition 2. (Valid activity).
Given an operations structure (
D
Given an operations structure ( ,
O
), any subset
t
⊆
O
Given an operations structure (
D
is a
valid activity
on the operations structure, or simply an
activity
.
Defi nition 3. (Valid activity ordering).
Given an operations structure (
D
Given an operations structure ( ,
O
), the tuple
Given an operations structure (
D
(
T
,
T
,
T F
) is a valid activity ordering on that operations structure if:
F
) is a valid activity ordering on that operations structure if:
T
is a set of valid activities,
T
⊆Π(
O
), such that:
•
1. ∀
o
∈
O
: (∃
t
∈
T
:
o
∈
t
}.
F
is a partial ordering on
F
,
F F
⊆
T
×
T
, such that for each
•
F
,
t
∈
TTT
2. ∀
t, u
∈
T
: ((
T
: (
T
∃((( ,
cs
) ∈
t
, (
q
,
ds
) ∈
u
:
q
∈
cs
)⇒(
u
,
t
) ∈
F'
).
F'
).
Within this defi nition it is expressed by 1 that all operations from the operation struc-
ture should appear at least once in one activity. This seems a reasonable requirement if we
assume that in an earlier stage it has been decided that all remaining operations are essential
to be performed. Condition 2 of Defi nition 3 enforces that when one operation depends on
the output of another, then the respective tasks they are part of are ordered such that they
respect this dependency. In other words, all information that is produced by an operation
can only be consumed by a later activity.
The defi nition of our cohesion metric, then, depends on two important parts: the rela-
tion cohesion and the information cohesion. The relation cohesion gives a measure on how
much the different operations within one activity are related. We will fi rst give the formal
defi nitions, after which we explain these notions with some examples.
Defi nition 4. (Activity relation cohesion).
For a valid activity
t
on an operation
t
structure (
D
structure ( ,
O
), its relation cohesion λ(
t
) is defi ned as follows:
structure (
D
To compute the activity relation cohesion, for each operation it should be determined
with how many other operations it overlaps, i.e., it shares an input or output. The
average
overlap per operation over all operations within an activity is then divided by the maximal
overlap, i.e., the number of operations minus 1, to get a relative measure between 0 and 1.
The other component of our cohesion metric, the activity information cohesion, focuses
on the sharing of information elements.
