Page 1Page 2Page 3Page 4Page 5Page 6Page 7Page 8

Page 1 of 8
next >

Majalah Ilmiah UNIKOM

Vol.9, No. 1


H a l a m a n



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


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


There are different sources of uncertainty in

the evaluation process. The five