Majalah Ilmiah UNIKOM
Vol.9, No. 1
43
H a l a m a n
INTERVAL TYPE-2 FUZZY LOGIC SYSTEMS TOOLBOX
MUHAMMAD ARIA
Electrical Engineering Department
Faculty of Technic and Computer Science
Abstract –
search in the field of fuzzy logic in recent years. Comparing with type-1 systems,
type-2 fuzzy systems are more complex and relatively more difficult to under-
stand and implement. In this paper we presents the design and development of
a software tool for for construction, edition and observation of Interval Type-2
Fuzzy Inference Systems. The Toolbox’s best qualities are the capacity to de-
velop complex systems and the flexibility that permits the user to extend the
availability of functions for working with the use of type-2 fuzzy operators, lin-
guistic variables, interval type-2 membership functions, defuzzification metods
and the evaluation of Interval Type-2 Fuzzy Inference Systems.
Index Terms –
Fuzzy Logic Toolbox, Karnik-Mendel algorithms, Membership Functions
On the past decade, fuzzy systems
have displaced conventional technology in
different scientific and system engineering
applications, especially in pattern recogni-
tion and control systems. The same fuzzy
technology, in approximation reasoning
form, is resurging also in the information
technology, where it is now giving support to
decision making and expert systems with
powerful reasoning capacity and a limited
quantity of rules.
The fuzzy sets were presented by L.A.
Zadeh in 1965 to process/manipulated
data and information affected by unprob-
abilistic uncertainty. There were designed to
mathematically represent the vagueness
and uncertainty of linguistic problems;
thereby obtaining formal tools to work with
intrinsic imprecision in different type of
problems; it is considered a generalization
of the classic set theory.
Intelligent systems based on fuzzy
logic are fundamental tools for nonlinear
complex system modeling. The fuzzy sets
and fuzzy logic are the base for fuzzy sys-
tems, where their objective has been to
model how the brain manipulates inexact
information.
Type-2 fuzzy sets are used for model-
ing uncertainty and imprecision in a better
way. These type-2 fuzzy sets were originally
presented by Zadeh in 1975 and are essen-
tially ―fuzzy fuzzy‖ sets where the fuzzy de-
gree of membership is a type-1 fuzzy set.
The new concepts were introduced by Men-
del and Liang allowing the characterization
of a type-2 fuzzy set with a superior mem-
bership functions and an inferior member-
ship function. These two functions can be
represented each one by a type-1 fuzzy set
membership function. The interval between
these two functions represent the footprint
of uncertainty (FOU), which is used to char-
acterize a type-2 fuzzy set.
The uncertainty is the imperfection of
knowledge about the natural process or
natural state The statistical uncertainty is
the randomness or error that comes from
different sources as we use it in a statistical
methodology.
There are different sources of uncertainty in
the evaluation process. The five
bidang
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