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13.1 Business Process Maps 327

proportionally varying the width of the arcs. If the threshold is set to 0.3, then all
activities are included. When the threshold is increased to 0.4, then activities c and
d and their connections disappear. When the threshold is increased to 0.6, also ac-
tivities b, g, and l and their connections disappear. If the threshold is set to 1, then
only the most frequent activities are included. The left-hand side of Fig. 13.5 shows
atomic activities and their relations. The right-hand side of the figure shows the
connections if we assume that the activities are aggregated as shown in the orig-
inal WF-net (cf. Fig. 13.3). It is important to note that the connection between z
and x disappears when the threshold is higher than 0.4. If we abstract from the
infrequent activities b and l, then we should also remove this connection. For the
same reason the connection between z and y is not shown when the threshold is set
to 1.
Figure 13.5 shows how one can seamlessly zoom in and zoom out to show more
or less detail. This is very different from providing a static hierarchical decompo-
sition and showing a particular level in the hierarchy as is done by the graphical
editors of BPM systems, WFM systems, simulation tools, business process model-
ing tools, etc.
Thus far, we assumed a static partitioning of atomic activities over three subpro-
cesses. Depending on the desired view this partitioning may change. To illustrate
this, we use an example event log consisting of 100 cases and 3730 events. This
event log contains events related to the reviewing process of journal papers. Each
paper is sent to three different reviewers. The reviewers are invited to write a report.
However, reviewers often do not respond. As a result, it is not always possible to
make a decision after a first round of reviewing. If there are not enough reports, then
additional reviewers are invited. This process is repeated until a final decision can
be made (accept or reject). Figure 13.6 shows the process model discovered by the
α-algorithm.
The α-algorithm does not allow for seamlessly zooming in and out. One would
need to filter out infrequent activities from the log and subsequently apply the
α-algorithm to different event logs. The Fuzzy Miner of ProM allows for seam-
lessly zooming in and out as is shown in Fig. 13.7 [49, 50]. The three fuzzy
models shown in Fig. 13.7 are all based on the event log also used by the
α-algorithm. Figure 13.7(a) shows the most detailed view. All activities are in-
cluded. The color and width of the connections indicate their significance (like
in Fig. 13.5). Figure 13.7(b) shows the most abstract view. The decision activ-
ity is typically executed multiple times per paper. Therefore, it is most frequent.
The other 18 activities are partitioned over 4 so-called cluster nodes. Each clus-
ter node aggregates multiple atomic activities. Using a threshold similar to the
one used in Fig. 13.5, the Fuzzy Miner can seamlessly show more or less de-
tails. Figure 13.7(c) shows a model obtained using an intermediate threshold value.
The top-level model shows the six most frequent activities. The other activities
can be found in the three cluster nodes. Figure 13.7(d) shows the inner struc-
ture of an aggregate node consisting of 10 atomic activities. Note that the in-
ner structure of an aggregate node shows the connections to nodes at the higher
level.