Computational Intelligence - August 2012 - 15

Abstract-Real world applications are characterized by high levels of linguistic and numerical
uncertainties. Since the inception of Fuzzy Logic Systems (FLSs), they have been applied with
great success to numerous real world applications. The vast majority of FLSs so far have been traditional type-1 FLSs. However, type-1 FLSs cannot fully handle the high levels of uncertainties
available in the vast majority of real world applications. This is because type-1 FLSs employ crisp
and "precise" type-1 fuzzy sets. A type-2 FLS can handle higher uncertainty levels to produce
improved performance. This paper follows on [1] to show how type-2 FLSs are starting to find
their way into a variety of real world applications, promising a continuous growth both in
number and variety of type-2 FLS applications in the next decade.

I. Introduction

ype-1 Fuzzy Logic Systems
(FLSs) have to date been applied
with great success to many different applications. However, for
the vast majority of real-world applications, there is a need to contend with
high levels of uncertainties. Type-1 fuzzy
sets handle the uncertainties associated
with the FLS inputs and outputs by using
"precise" and crisp membership functions
which the user believes would capture
the uncertainties. Once the type-1 membership functions have been chosen, the
fact that the actual degree of membership
itself is uncertain is no longer modelled
in type-1 fuzzy sets. It is assumed that a
given input results in a precise, single
value of membership. However, the linguistic and numerical uncertainties asso© DIGITAL VISION
ciated with dynamic unstructured
environments cause problems in determining the exact and
precise antecedents' and consequents' membership functions
during the FLS design. As a consequence, the designed type-1
fuzzy sets can be sub-optimal under specific environment and
operation conditions. However, because of the environment
changes and the associated uncertainties, the chosen type-1
fuzzy sets may not be appropriate anymore. This can cause degradation in the FLS's performance, which can result in poor
control and inefficiency, and lead to the wastage of resources
spent on frequently redesigning or tuning the type-1 FLS (so
that it can deal with the various uncertainties [1], [2]).
Type-2 fuzzy logic was initially introduced by Lotfi Zadeh
in 1975 [3]. A type-2 fuzzy set is characterized by a fuzzy
membership function, i.e., the membership value (or membership grade); for each element of this set is a fuzzy set in [0,1],
unlike a type-1 fuzzy set where the membership grade is a
crisp number in [0,1] [4]. The membership functions of type-2
fuzzy sets are three dimensional and include a footprint of
uncertainty; it is the third dimension of type-2 fuzzy sets and
the footprint of uncertainty that provide additional degrees of
freedom that make it possible to model and handle uncertainties [4]. Hence, type-2 FLSs have the potential to overcome the

limitations of type-1 FLSs and produce a new generation of
fuzzy systems with improved performance for many applications which require handling high levels of uncertainty [4].
At this point it should be noted that when stating this, we consider FLSs of comparable logical complexity (i.e., number of
rules). As a result, type-2 FLSs have gained significant
popularity in recent years.
In [1], we have published an article summarizing the early
real world applications of type-2 FLSs. Since then, the start
of an increasing spread of type-2 FLSs applications to various
domains has been witnessed. This promises a wide spread of
type-2 FLSs to real world applications similar to that of
type-1 FLSs.
A summary of industrial type-2 FLS applications is given in
[5], however, in order to give an overview of the current level
of application of type-2 FLS, we will present a set of sample
applications of type-2 FLSs in a variety of sectors, including
business and finance, electrical energy, automatic control, networks and the medical/health sector.
II. Type-2 FLSs Applications
in the Business and Finance Domains
A. Type-2 FLSs Application
in Intelligent Business Predictive Analytics

Type-2 FLSs have found their way to real world business and
finance applications where companies are employing type-2
FLSs to handle the linguistic and numerical uncertainties available in the business and finance domains.
For example, Logicalglue Ltd. (http://www.logicalglue.
com) aims to develop intelligent predictive business analytics
which enable the provision of accurate prediction models for
financial and business applications while maintaining a high
level of model transparency, allowing straightforward model
interpretation by the normal user. Logicalglue has filed the first
patent employing type-2 fuzzy logic entitled "An Improved
Neuro Type-2 Fuzzy Based Method for Decision Making"
number PCT/GB2009/001303.
Type-2 FLSs were applied within the Logicalglue products
to handle the linguistic and numerical uncertainties while modelling the group decision making process and using it to make
various automated decisions in financial and business applications [6]. Specifically, the Logicalglue type-2 FLS based product

AUGUST 2012 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE

http://www.logicalglue

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