Majalah Ilmiah UNIKOM
Vol.9, No. 1
45
H a l a m a n
gleton fuzzification), type-1 or Interval
Type2 Fuzzy Systems, which then activate
the inference engine and the rule base to
produce output Interval Type 2 Fuzzy Sys-
tems. These Interval Type-2 Fuzzy Systems
are then processed by a type-reducer
(which combines the output sets and then
performs a centroid calculation), leading to
an interval Type 1 Fuzzy System called the
type-reduced set. A defuzzifier then de-
fuzzifies the type-reduced set to produce
crisp outputs.
Rules are the heart of an FLS. They
may be provided by expert or extracted
from numerical data. The rules can be ex-
pressed as a collection of IF-THEN state-
ments. The IF-part of a rule is its antece-
dent, and the THEN-part of a rule is its
consequent.
The type-reduced set provides an inter-
val of uncertainty for the output of an In-
terval Type 2 Fuzzy Logic System, in much
the same way that a confidence interval
provides an interval of uncertainty for a
probabilistic system. The more uncertain-
ties that occur in an Interval Type 2 Fuzzy
Logic System, which translate into more
uncertainties about its Membership Func-
tions, the larger will be the type-reduced
set, and vice-versa.
Five different type-reduction methods
are described in [5]. Each is inspired by
what we do in a Type 1 Fuzzy Logic System
and are based on computing the centroid
of an Interval Type 2 Fuzzy System.
INTERVAL TYPE-2 FUZZY LOGIC SYSTEM
TOOLBOX
The Interval Type-2 files contain the
functions to create Mamdani and TSK In-
terval type-2 Fuzzy Inference Systems (FD
newfis.vi), functions to add input-output
variabels and their ranges (FD addvar.vi), it
has functions to add 8 types of Interval
Type-2 Membership functions for input-
outpus (FD addmf.vi), functions to add the
rule matrix (FD addrule.vi), it can evaluate
the Interval Type-2 Fuzzy Inference Sys-
tems (FD evalfis.vi), it can generate the
initial parameters of the Interval Type-2
Membership Functions (FD Generate FIS
from data.vi), it can plot the Interval type-2
Membership functions with the input-
output variables (FD plotmftype.vi), it can
generate the solution surface of the Fuzzy
Inference System (gensurftype.vi).
Figure 2 show the main view of the In-
terval Type-2 Fuzzy Inference Systems
Structure Editor.
Fig. 2 Front Panel of IT2 FLS Toolbox
The Interval Type-2 Toolbox are arranged
in six layers : FIS Editor, Membership Func-
tion Editor, Rule Editor, Surface Viewer,
Simulation and FIS Array. In the FIS Editor
the user must define how many input and
output variablesand what are their
names ? The Interval Type-2Toolbox does-
n’t limit the number of inputs. However,
the number of inputs may be limited by
available memory in the machine. If the
number of inputs is too large, or the num-
ber of membership functions is too big,
then it may also be difficult to analyze the
Interval Type-2 using this toolbox. Figure 3
show the FIS Editor of the Interval Type-2
Fuzzy Inference Systems. In the left of the
front panel is the type of inference used.
The default is Mamdani-type inference.
Another slightly different type of inference
is Sugeno-type inference. Below the name