Database Reference
In-Depth Information
Figure 3. Examples of two soft temporal constraints defined on two timelines with distinct granularity
(months and years, respectively). The constraint “every autumn from 2000 to 2005” is defined as a fuzzy
periodic time element, while “after the second world war” as a fuzzy time interval
Figure 4. Trapezoidal membership function corresponding to a soft constraint representing a fuzzy time
interval
converting the current coarser granule of the
i
i-th node in terms of aggregation of finer granules of the
j
-th node (Figure 5 is a simplification to illustrate how the concept works).
The function F
i,j
:G'→G, where G
∧
G', with
i
i-th node defined on domain G' and
j
i-th defined on G,
defines the mapping of a granule g'
∧
G' into a fuzzy set F
i,j
(g')
∧
G of granules defined on G.
Notice that a precise temporal expression can be converted into a fuzzy temporal expression: for
example a
month
is defined in figure 5 by the following fuzzy set of
days:
month
={0.3/30
days
; 0.08/28
days
, 0.58/31
days
}, meaning that it can consist of 30 days with con-
fidence 0.3, 28 days with confidence 0.08, or 31 days with confidence 0.58.
A temporal indication
t
, defined on a coarser domain G' (e.g., year) can be converted on another
finer domain G (e.g., day) at a distance greater than 1 on the graph, by repeatedly applying the mapping
