Systems, Man & Cybernetics - January 2015 - 47

Book Review

by Faa-Jeng Lin

Introduction to Type-2 Fuzzy
Logic Control: Theory and
Applications
by Jerry Mendel, Hani Hagras, WoeiWan Tan, William W. Melek, and Hao
Ying, IEEE Press and Wiley, 2014.
ype-1 fuzzy logic controllers
(FLCs) have proven effective in
dealing with complex nonlinear systems containing uncertainties
that are otherwise difficult to model
or control. However, Type-1 FLCs
have precise membership functions
(MFs), i.e., there is nothing uncertain
in such MFs. Consequently, using
Type-1 FLCs may cause degradation
in the performance of some systems
with noise and uncertainties. On the
other hand, the concept of Type-2
fuzzy sets is an extension of Type-1
fuzzy sets. The Type-2 fuzzy sets have
grades of membership that are also
fuzzy. The primary membership of
Type-2 fuzzy sets can be any subset
in [0, 1]. Moreover, corresponding to
each primary membership, there is a
secondary membership that is also in
[0, 1], which defines the possibilities
for the primary membership.
Both Type-1 fuzzy logic systems
(FLSs) and Type-2 FLSs have the
same four components: the fuzzifier,
rule base, fuzzy inference engine, and
output processor. Furthermore, unlike
Type-1 FLSs, the output processor of
Type-2 FLSs generates a Type-1 fuzzy
set output using the type reducer or a
crisp number using the defuzzifier. A
Type-2 FLS is also characterized by
IF-THEN rules, but its antecedent or
consequent sets are Type 2. Type-2
FLSs can be used when the circumstances are too uncertain to determine membership grades exactly,
such as for imprecise or vague data.
Thus, the Type-2 FLSs have supplant-

Type-2 Fuzzy
Logic Control

Digital Object Identifier 10.1109/MSMC.2015.2395651
Date of publication: 24 April 2015

ed conventional technologies in many
applications, especially in complex
nonlinear systems. However, in general, Type-2 FLSs are computationally intensive due to the complexity of
reducing Type-2 FLSs to Type-1 FLSs.
To simplify the computation, the secondary membership grade can be set
to one, in which case the Type-2 FLSs
become interval Type-2 FLSs. Currently, the most widely used Type-2
fuzzy sets in Type-2 FLCs are interval
Type-2 fuzzy sets.
Introduction to Type-2 Fuzzy
Logic Control: Theory and Applications presents the first unified and
thorough discussion of Type-2 FLCs
and Type-2 fuzzy logic control systems, providing the necessary tools
for the design of the control of complex nonlinear systems. The analysis
includes 1) the mathematical structure
of some Type-2 FLCs, 2) stability of
Type-2 fuzzy logic control systems,
and 3) robustness of the Type-2 fuzzy
logic control systems. This book, the
first one entirely on Type-2 FLCs,
shows the reader how to design Type-2
fuzzy logic control systems based on a
variety of choices for the Type-2 FLC
components and also demonstrates
how to apply Type-2 fuzzy logic control
theory to applications. It is written by
five of the leading experts on Type-2
fuzzy sets, systems, and control.
This book consists of seven chapters. Chapter 1 explains the differences between a Type-1 fuzzy set and a
Type-2 fuzzy set and between a Type-2
Ja nu a r y 2015

FLC and a Type-1 FLC. The chapter also provides many real-world
applications in which Type-2 FLCs
have shown improved performance
over Type-1 FLCs. Chapter 2 presents background material on Type-2
fuzzy sets. In Chapter 3, the Mamdani
and TSK interval Type-2 FLCs are
discussed. Chapter 4 details the analytical structure of various interval
Type-2 fuzzy proportional-integral
(PI) and proportional-derivative
(PD) controllers. Simplifying interval
Type-2 fuzzy PI and PD controllers is
discussed in Chapter 5. The rigorous
design procedure of interval Type-2
TSK fuzzy controllers is provided in
Chapter 6. Finally, the perspectives
of each author about the future of
Type-2 fuzzy logic control are given
in Chapter 7. All of the chapters are
comprehensive and well organized.
This book has been written with an
educational focus rather than a pure
research focus. Each chapter includes
worked examples, and most refer to
computer programs accessible through
the book's Web site, outlining how to
use them at a high level. Therefore,
this book is appropriate for classroom
use in graduate courses in electrical
engineering, computer engineering,
and computer science. This book also
is a self-contained reference suitable
for engineers, researchers, and graduate students who want to gain deep
insights about Type-2 FLCs. Moreover,
the appendix of this book describes
Java-based software that will allow

IEEE SyStEmS, man, & CybErnEtICS magazInE

Table of Contents for the Digital Edition of Systems, Man & Cybernetics - January 2015