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Directory: Publications in English
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Xiaozhong Li
Xiaozhong Li, Da Ruan
Novel Neural Algorithms Based on Fuzzy $\delta$ Rules for Solving Fuzzy
Relation Equations: Part I
Fuzzy Sets and Systems 90 (1997) 11-23.
ABSTRACT Although there are some papers on using neural networks to
solve fuzzy relation equations, they have some widespread
problems. For
example, the best learning rate cannot be decided easily and
strict theoretic
analyses on convergence of algorithms are not given due to the
complexity
in a given system. To overcome these problems, we present some novel
neural algorithms in this paper. We first describe such algorithms for
max-min operator networks, then we demonstrate these algorithms
can also
be extended to max-times operator network. Important results
include some
improved fuzzy $\delta$ rules, a convergence theorem and an
equivalence
theorem which reflects fuzzy theory and neural networks can reach the
same goal by different routes. The fuzzy bidirectional associative
memory
network and its training algorithms are also discussed. All important
theorems are well proved and a simulation and a comparision result
with
Blanco and Pedrycz are reported.
Xiaozhong Li, Da Ruan
Fuzzy $\delta$ Rule and Its Simulations in Fuzzy Relation Equations
Int. J. of Fuzzy Mathematics . Accepted.
ABSTRACT After a short review of our previous work, in this paper we
will present a new simplified proof to a lemma which plays an
important role
in proving the convergence theorem of the fuzzy perceptron. The
new proof
is much shorter. Moreover, we give some typical simulation results to
illustrate the power of the fuzzy $\delta$ rule.
Xiaozhong Li, Da Ruan
Novel Neural Algorithms Based on Fuzzy $\delta$ Rules for Solving Fuzzy
Relation Equations: Part II
Fuzzy Sets and Systems , Accepted.
ABSTRACT In this paper, we first design a fuzzy neuron which possesses
some generality. This fuzzy neuron is founded by replacing the
operators of
the traditional neuron with a pair of abstract fuzzy operators as
($\widehat+$, $\widehat\bullet$) which we call fuzzy neuron
operators. For
example, it may be $(+, \bullet)$, $(\bigwedge,\bullet)$,
$(\bigvee,\bullet)$,
or $(\bigwedge,\bigwedge)$, etc. It is an extended fuzzy neuron and a
network composed of such neurons is an extended fuzzy neural network.
Then we discuss the relationship between the fuzzy neuron
operators and
$t$-norm and $t$-conorm, and point out fuzzy neuron operators are
based
on $t$-norm but much wider than $t$-norm. In this paper we will
emphatically discuss a two-layered network and its training
algorithm which
will have to satisfy a set of various operators. This work is very
related to
solving fuzzy relation equations. So it can be used to resolve
fuzzy relation
equations. Furthermore, the new fuzzy neural algorithm is found to be
stronger than other existing methods to some degree. Some simulation
results will be reported in detail.
Xiaozhong Li, Da Ruan
Novel Neural Algorithms Based on Fuzzy $\delta$ Rules for Solving Fuzzy
Relation Equations: Part III
Fuzzy Sets and Systems . Accepted.
ABSTRACT In our previous work, we proposed a max-min operator
network and a series of training algorithms, called fuzzy $\delta$
rules,
which could be used to solve fuzzy relation equations. The most
basic and
important result is the convergence theorem of fuzzy perceptron
based on
max-min operators. This convergence theorem has been extended to the
max-times operator network in the previous paper. In this paper,
we will
further extend the fuzzy $\delta$ rule and its convergence theorem
to the
case of max-* operator network in which * is a t-norm. An equivalence
theorem points out that the neural algorithm in solving this kind
of fuzzy
relation equations is equivalent to the fuzzy solving method
(non-neural) in
\cite{Nol:848,Got:946}. The proof and simulation will be given.
Xiaozhong Li, Da Ruan, Arien J. Van del Wal
Discussions on Soft Computing at FLINS'96
International Journal of Intelligent Systems. , Vol. 13, Nos. 2/3,
Feb./Mar. 1998. pp. 287-300.
ABSTRACT This is a report on the discussion about soft computing (SC)
during FLINS'96. The discussion is based on the 5 questions
formulated by
X. Li, viz. (1) What is SC? (2)What are the characteristics of SC?
(3)What
are the principal achievements of SC? (4)What are the typical
problems of
SC and what are the solutions? and (5)What is the prediction of SC
for the
future. Before and during FLINS'96, these 5 questions have been
sent to
several known specialists for a reply. Among them, Martin
Wildberger, Bart
Kosko, Bo Yuan, Hideyuki Takagi, Takehisa Onisawa, Germano Resconi,
Zhong Zhang and Yasushi Nishiwaki answered these questions with their
opinions. By this report we hope to stimulate some further
discussion on this
topic.
Xiaozhong Li, Da Ruan
Constructing A Fuzzy Logic Control Demo Model at SCK·CEN
Proceedinds of the 5th European Congress on Intelligent Techniques
and Soft Computing (EUFIT'97) , Aachen, Germany, September 8-11,
1997. Vol. 2, pp. 1408-1412.
ABSTRACT Based on the background of fuzzy logic control application in
nuclear reactors at SCK·CEN, we have made a real fuzzy logic control
demo model. The demo model is suitable for us to test and compare our
new algorithms of fuzzy control, because it is always difficult
and risky to do
all experiments in a real nuclear environment. This paper will
mainly report
the construction of the demo model and its fuzzy logic control system.
Although this demo model is special designed to simulate the working
principle of a nuclear reactor, it can be also used as a general
object or flat
for control experiments. It is much better than an inverted
pendulum system
which is often used as a test flat in imitating the delay of a
real complex
system. The current fuzzy logic control algorithm in this demo
model is a
normal algorithm based on Mamdani model. In our system, triangular
shaped membership functions are used. In order to overcome the well
known dilemma of fast response and no overshot, some parameters, for
instance, fuzzy control rules and universes of discourse, must be
adjusted.
Finally, we have fulfilled this goal, however it is not easy to
choose suitable
parameters. This is the real drawback which has slowed down the wide
applications of fuzzy logic control. Therefore new effective
algorithms must
be further researched, and it is possible to combine other intelligent
technologies, such as the learning of neural network and evolving
of genetic
algorithm, although much work has already been done.
Da Ruan, Xiaozhong Li
Fuzzy Logic Control Applications to Belgian Nuclear Reactor 1 (BR1)
Computers and Artificial Intelligence , Accepted.
ABSTRACT Fuzzy logic applications in nuclear industry present a
tremendous challenge. The main reason for this is the public
awareness of
the risks of nuclear industry and the very strict safety
regulations in force
for nuclear power plants. The very same regulations prevent a
researcher
from quickly introducing novel fuzzy-logic methods into this
field. On the
other hand, the application of fuzzy logic has, despite the
ominous sound of
the word "fuzzy" to nuclear engineers, a number of very desirable
advantages over classical methods, e.g., its robustness and the
capability to
include human experience into the ontroller. In this paper we
report an
on-going R&D project for controlling the power level of the Belgian
Nuclear Reactor 1 (BR1) at the Belgian Nuclear Research Centre
SCK·CEN). The project started in 1995 and aims to investigate the
added
value of fuzzy logic control for nuclear reactors. We first review
some
relevant literature on fuzzy logic control in nuclear reactors,
then present the
state-of-the-art of the BR1 project. After experimenting fuzzy
logic control
under off-line test cases at the BR1 reactor, we now foresee a new
development for a closed-loop fuzzy control as an on-line
operation of the
BR1 reactor. Finally, we present the new development for a closed-loop
fuzzy logic control at BR1 with an understanding of the safety
requirements
for this real fuzzy logic control application in nuclear reactors.
Xiaozhong Li, Da Ruan
Comparative Study of Fuzzy Control, PID control, and Advanced Fuzzy
Control for Simulating a Nuclear Reactor Operation
Intelligent Systems and Soft Computing for Nuclear Science and
Industry , Proceedings of the 3nd International FLINS Workshop, Mol,
Belgium, September 14-16, 1998, Eds. Da Ruan, Pierre D'hondt et
al, World
Scientific Publisher.
ABSTRACT Based on the background of fuzzy control applications at the
BR1 reactor at SCK·CEN, we have made a real fuzzy logic control demo
model. The demo model is suitable for us to test and compare any new
algorithms of fuzzy control and intelligent systems, because it is
always
difficult and time consuming due to safety aspects to do all
experiments in a
real nuclear environment. In this paper, we first briefly report the
construction of the demo model, and then introduce the results of
a fuzzy
control, a PID control, and an advanced fuzzy control, in which the
advanced fuzzy control is a fuzzy control with an adaptive
function which
can self-regulate the fuzzy control rules. Afterwards, we give a
comparative study among those three methods. The results have
shown that
fuzzy control has more advantages in term of flexibility,
robustness, and
easy updated facilities with respect to the PID control of the
demo model,
but PID control has much higher regulation resolution due to its
integration
term. The adaptive fuzzy control can dynamically adjust the rule base,
therefore it is more robust and suitable to those very uncertain
occasions.
_____________________________________________________________________
* Xiaozhong Li. PhD, Currently Young Scientific Researcher *
* Belgian Nuclear Research Centre (SCK.CEN) *----------*
* Boeretang 200, B-2400 Mol, Belgium | _L_ *
* phone: (+32-14) 33 22 30(O); (+32-14) 32 25 52(H) | /\X/\ *
* fax: (+32-14) 32 15 29 | \/Z\/ *
* e-mail:xli@sckcen.be http://www.sckcen.be/people/xli | / \ @ *
*________________________________________________________*----------*
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