implementation of fuzzy sistem (PART 1)

I. INTRODUCTION
In the 1960s, Zadeh [1,2] developed a linguistic approach to deal with linguistic
vague information based on fuzzy sets and fuzzy logic. Since then there
have been a number of applications of the approach to a variety of fields including
meteorology, engineering, medicine, management, computer science, expert
systems, and systems science.
In the field of systems science, many complex plants are difficult to deal with
by the conventional approach (precise mathematical equations) because of their
nonlinear, time-varying behavior and imprecise measurement information. Nevertheless,
human operators can handle these complex plants by their practical experience.
They only need imprecise system states and a set of imprecise linguistic
if-then rules. The fuzzy system theory developed by Zadeh [3] based on fuzzy
sets and fuzzy logic can be used to deal with such complex systems.
Fuzzy systems accept numeric inputs from the outside world and convert these
into linguistic values that can be manipulated by using fuzzy logic operations
with Hnguistic if-then rules given by human operators. The linguistic outputs, theresult of the fuzzy logic operations, are converted into numeric outputs which arethen delivered to the outside world. Thus, fuzzy systems provide a framework ofrepresenting human expert rules with fuzzy logic to infer human decision. Basedon this ability, fuzzy systems can approximate human reasoning and achieve some intelligence.
Fuzzy systems can be used for different kinds of purposes such as modeling,
prediction, classification, and control in the field of systems science. In particular,
the possible use of fuzzy systems in modeling and control has generated great
attention. Fuzzy systems for modeling and control have emerged as one of the
most active and fruitful areas for research in the appUcation of fuzzy set theory.
The application was pioneered by Mamdani [4], who successfully carried out a
pilot study on a model steam engine using fuzzy systems. His study showed that
fuzzy systems may profitably and easily be used by control engineers. A number
of successful control applications have also been reported. These included heat
exchange process control [5], steam engine control [6, 7], traffic junction control
[8], cement kiln control [9], model car parking control [10], automobile speed
control [11], robot control [12,13], aircraft autopilot control [14], camera autofocus
control, and automobile transmission control [15].
However, at present there is no systematic procedure for the design of fuzzy
systems. Usually the linguistic rules are generated by converting the human operator’s
experience into linguistic form directly or by summarizing the sampled
input-output pairs of the systems to be dealt with. Unfortunately, it is difficult
for systems designers to obtain optimal fuzzy rules because these are most likely
to be influenced by the intuitiveness of the operators and the systems designers.
Moreover, some information will be lost when human operators express their experience
by linguistic rules. This results in a set of less than optimal linguistic
rules. Therefore, fuzzy systems capable of developing and improving the linguistic
rules and structures automatically are highly desired [16-18].
Neural network implementation of fuzzy systems has been proposed as a possible
approach for fuzzy systems design [19-29]. The resulting systems, which are
sometimes called fuzzy neural networks or neural-network-based fuzzy systems,
will possess the advantages of both types of systems and overcome the difficulties
of each type of system. In fact, the resulting systems not only support numerical
mathematical analysis, hardware implementation, distributed parallel processing,
and self-learning but are also capable of deaUng with difficulties arising from uncertainty,
imprecision, and noise.
Another aim of developing neural-network-based fuzzy systems is to enhance
fuzzy systems with higher intelligence. Fuzzy systems simulate human reasoning
to achieve intelligence by manipulating a set of heuristic rules given by a human
expert. Thus, the inteUigence is totally limited by the given set of rules. There will
be neither chance for the fuzzy system to improve nor useful rules to be added. To make fuzzy systems more intelligent, fuzzy systems with learning and adaptation are desired.
The fuzzy neural network discussed in this chapter is a hybrid system which
functions as a fuzzy system with the processing mechanism realized by a neural
network. Thus, the capability of learning imposed upon a fuzzy system can be
achieved by the learning algorithm of a neural network. In principle, a fuzzy neural
network is a fuzzy system implemented within the framework of neural networks
so as to achieve the capability of learning using input-output data which
will lead to improvement of the fuzzy rules and fuzzy system intelligence.
In general, there are two approaches to the integration of fuzzy systems and
neural networks. In the first approach, one may incorporate the concept of fuzzy
logic into the neural network. A fuzzy neuron is designed to function in much the
same way as a nonfuzzy neuron, except that it reflects the fuzzy nature and has
the ability to cope with fuzzy information [23-26].
The other approach [19-22, 27-29] is to realize the process of fuzzy reasoning
by the structure of a neural network and to express the parameters of fuzzy
reasoning by the connection weights of the neural network. The resulting fuzzy
neural network can automatically identify the fuzzy rules and tune membership
functions by modifying the connection weights of the network using some learning
algorithm. This second approach is closer to dealing with the problem of fuzzy
systems design. This chapter will deal mainly with the second approach to fuzzy
neural networks. This approach has been discussed by a number of researchers
[19-22].
Horikawa et al [22] described three general structures of fuzzy neural networks
in accordance with the structure of the consequences of fuzzy rules. The
first type is concerned with the consequence being a crisp constant, the second
one with the consequence being a function of input variables, and the third one
with the consequence being a fuzzy value. The error back-propagation algorithm
was used for training.
Lin and Lee [20, 30] proposed a neural-network-based fuzzy logic control system.
This work considered finding centers/widths of membership functions by
self-organized clustering and finding fuzzy logic rules by competitive learning.
The fuzzy logic control system implemented was of a conventional type, and error
back propagation was applied to tune the consequence parameters of output
membership functions and premise parameters of input membership functions.
The system was enhanced with a reinforcement learning method when obtaining
exact training data became expensive [31].
Jang [19] implemented the Sugeno-Takagi fuzzy logic system using an adaptive
network (which can be regarded as a neural network) that utilized hybrid
learning rules. A gradient descent techniques was applied to tune premise
parameters, and the least-squares estimation techniques was used to estimate consequence parameters. The membership functions were chosen to be bellshaped functions (highly nonlinear functions; e.g., of the Gaussian type). It was shown that the system was functionally equivalent to a radial basis function network[32].
The fuzzy neural networks proposed in the aforementioned papers suffered
from the Umitation that if the number of input fuzzy partitions is large, the required
number of consequence parameters will be very large, and the least-squares
estimation algorithm cannot be implemented easily because the calculation of
very large matrices is required. Thus, the application of the networks is limited to
some low-dimensional systems. Moreover, the learning processes were typically
slow.
This chapter discusses the neural network implementation of fuzzy systems
based on Takagi-Sugeno fuzzy systems [33] because they have many advantages
for modeling and control. Takagi-Sugeno fuzzy systems differ from conventional
fuzzy systems in that linear systems instead of fuzzy sets are formed in the consequences
of the fuzzy rules. The output of the fuzzy systems is a “fuzzy” combination
of a set of linear systems. In what follows, the basic concepts of fuzzy sets,
fuzzy logic, and structure of fuzzy systems are presented first, and fuzzy neural
network designs are then discussed in the latter part of this chapter.