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Majalah Ilmiah UNIKOM

Vol.9, No. 1


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


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.



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