Collective Classification for Spam Filtering - Computational Intelligence in Security for Information Systems - page 36

Fig. 1. Fuzzification Function of SD and TD
when considering clusters for aggregation. Before the implementation of the sys-
tem, and depending on the particular application, it is possible to identify other
possible parameters apart from spatial and temporal location, with possible in-
fluence on the decision of aggregation, such as distance between agents or speeds.
The input values corresponding to all influential parameters are real numbers,
which the system has to assign to adjectives. The next step is to formulate rules
that express the combination of the chosen influential parameters. In particular,
according to such rules, the degrees of the influential parameters adjectives are
combined using fuzzy Boolean operators such as AND, OR and NOT, defined
as the minimum, maximum, and complement, respectively. The output of the
application of every rule is defined as two possible values: YES and NO. This
fuzzy decision making process allows combining all possible influential parame-
ters in order to conclude whether two received warnings refer to the same event
because the complexity of the original real values of such parameters are hidden
behind the mapping to adjectives.
As an example of fuzzy decision making based on rules we propose to choose
and combine the influential parameters of spatial and temporal location denoted
Space-Distance (SD) and Time-Distance (TD). Fig. 1 exemplifies this process
for both variables representing the influence of both parameters considering as
x-coordinate respectively SD in meters or TD in minutes, and the y-coordinate
is the probability corresponding to the adjectives LOW, MEDIUM and HIGH.
Each of these adjectives is described by a membership function that maps the
real valued input value of the corresponding influence factor to a membership
degree corresponding to the adjective described by the function. In the depicted
example, according to the fact that a typical error in normal GPS is about 23
meters of ambiguity, an input SD of less than 3 meters is fuzzified as being LOW
with a degree of 1. For example, the output of the function for a SD of about 9
meters is classified at the same time as LOW and as MEDIUM with a degree of
0.5. From 27 meters on, SD is considered HIGH with probability 1. The same is
considered for TD in minutes.