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  [Dr. David Kahaner is a numerical analyst on sabbatical to the 
   Office of Naval Research-Asia (ONR Asia) in Tokyo from NIST.  The 
   following is the professional opinion of David Kahaner and in no 
   way has the blessing of the US Government or any agency of it.  All 
   information is dated and of limited life time.  This disclaimer should 
   be noted on ANY attribution.]

  [Copies of previous reports written by Kahaner can be obtained using
   anonymous FTP from host cs.arizona.edu, directory japan/kahaner.reports.]

To: Distribution
From: 
 David K. Kahaner
 US Office of Naval Research Asia
 (From outside US):  23-17, 7-chome, Roppongi, Minato-ku, Tokyo 106 Japan
 (From within  US):  Unit 45002, APO AP 96337-0007
  Tel: +81 3 3401-8924, Fax: +81 3 3403-9670
  Email: kahaner@cs.titech.ac.jp
Re: Fuzzy-neural systems research in Asia.
22 Dec 1992
This file is named "fuzzy.92"

ABSTRACT. Overview of fuzzy-neural systems research based on examination
of papers presented at three Asian conferences. A great deal of the
current work is ad hoc and there is a need for more fundamental
research to help explain and direct future activities. (Nguyen)

This report was prepared by
   Prof Hung T. Nguyen
   LIFE Chair of Fuzzy Systems
   Department of Systems Science
   Tokyo Institute of Technology
   4259 Nagatsuta, Midori-ku
   Yokohama 227 JAPAN
    Tel: +81 45-922-1111 ext 2699; Fax: +81 45-922-1385

Prof Nguyen is on leave from the Mathematical Sciences Department of New
Mexico State University.

FUZZY-NEURO SYSTEMS:  MAIN THRUST OF RESEARCH PRESENTED AT THREE
CONFERENCES IN ASIA

          This report describes research trends surrounding the design
of fuzzy-neuro systems as exemplified by works of Asian scientists
presented at The International Symposium on Fuzzy Systems (Iizuka,
Japan, July 1992), The 2nd International Conference on Fuzzy Logic and
Neural Networks (Iizuka, Japan, July 1992) and The Korean Automatic
Control Conference (Seoul, Korea, October 1992).

By Hung T. Nguyen

INTRODUCTION

     The papers presented at the above three Conference are published in

(i)  Proceedings of the International Symposium on Fuzzy Systems (July
12-15, 1992), Kyushu Institute of Technology, Iizuka, Fukuoka, Japan.

Organizers:    Takeshi Yamakawa and Eiji Uchino
               Kyushu Institute of Technology
               680-4 Kawazu, Iizuka, Fukuoka 820, Japan.

(2) Proceedings of the 2nd International Conference on Fuzzy Logic and
Neural Networks (Iizuka '92), two volumes, published by Fuzzy Logic
Systems Institute, 820-1 Yokota, Iizuka, Fukuoka 820, Japan.

Organizer:     Takeshi Yamakawa

(3)     Proceedings of the 1992 Korean Automatic Control Conference
(International sessions), published by Korean Association of Automatic
Control.  General chairman of the Conference: Kyung-Gi Kim, Department
of Electronics Engineering, Hanyang University, 17 Haendang-dong,
Sungdong-ku, Seoul, Korea.

     The majority of papers were concerned with:
         Fuzzy Systems and Neural Networks,
         Fuzzy Logic Control,
         Fuzzy Modeling and
         Approximate Reasoning.

     In the following, we describe the above topics in some detail
together with our comments.  The general observation is this.  Motivated
by the industrial success of the fuzzy methodology in recent years,
especially in Japan, researchers tend to look at practical problems in
which ad-hoc design procedures can be proposed.  We feel that this
indicates a clear need for more basic research concerning general design
methodology.

FUZZY SYSTEMS AND NEURAL NETWORKS

     Neural networks process numerical information and exhibit learning
capability.  Fuzzy systems can process linguistic information and
represent, say, experts' knowledge by fuzzy rules.  Thus, it is not
surprising that the fusion of these two technologies is the current
research trend.  The aim is to be able to create machines with more
intelligent behavior.

     In the mentioned Conferences, one noticed the following motivation
for considering both fuzzy systems and Neural Networks:

(1)  The Knowledge Base of a fuzzy system consists of a collection of
"If...  Then..." rules in which linguistic labels are modeled by
membership functions.

Neural Networks can be used to produce membership functions when
available data are numerical.

(2)  Moreover, one can take advantage of the learning capability of
neural networks to adjust membership functions, say in control
strategies, to enhance control precision.

(3)  Neural Networks can be used to provide learning methods for fuzzy
inference procedures.

(4)  In the opposite direction, one can use fuzzy reasoning architecture
to construct new Neural Networks.

(5)  One can also fuzzify the Neural Networks architecture to enlarge
the domain of applications.

(6)  The fusion of Neural Networks and Fuzzy Systems is essentially
based upon the fact that Neural Networks can learn experts' knowledge
(through numerical data) and Fuzzy Systems can represent experts'
knowledge (through the representation of in-out relation by fuzzy
reasoning).

     As in any science, practical successes call for theoretical
justifications.  While the above technologies have become firmly
established in well defined domains of applications, only few
theoretical results have been obtained.  Theoretical results are needed,
not only for explaining the successful results but also for guiding
general design methodology for systems.  The success of Neural Networks
is explained by the universal approximation property (via
Stove-Weierstrass theorem).  However, there is no standard method for
constructing the most suitable neural network structure, e.g.
determining the number of neural units in hidden layers.  Mathematically
speaking, while the graphical form of Neural Networks indicates that
such input-output maps can approximate continuous functions to any
degree of accuracy, one still faces the practical problem:  which
specific network structure will actually do the job?

     The situation in Fuzzy Systems is the same.  The universal
approximation property of fuzzy systems merely says that their
architecture is on the right track, but says nothing about approximate
designs.  This explains why results are reported in the form of
prototypes with demonstrations of feasibility.  Various approaches to
the same type of problems are given with comparisons based upon
different criteria.

FUZZY LOGIC CONTROL

     The well-defined domain of applications of fuzzy control is the one
in which conventional control techniques, such as PID, cannot be used.
Fuzzy Control is idealistic for cases where mathematical models are not
available or when the controlled plant is highly non-linear and can be
operated by skilled human operators.  The structure of a fuzzy logic
control is similar to that of a general fuzzy system.  The performance
of a fuzzy logic controller depends on the control rules, on membership
functions describing linguistic labels in these rules, and on the
approximate reasoning procedure used.  While the universal approximation
property of fuzzy controls force the designers to stay within its
validity, there is still a very large class of approximate controls for
each situations.  In the face of this situation, results are in general
reported by using simulations, either to demonstrate good performance or
to make comparisons among various alternatives.  The standard design of
a fuzzy logic controller consists of selecting an suitable number of
rules, assigning appropriate membership functions to linguistic labels
(by various empirical techniques) and choosing an approximate reasoning
procedure (i.e.  choosing fuzzy logic connectives to combine evidence
and a defuzzification mode to provide single output).  (Results are also
reported on the problem of stability of fuzzy feedback control).  Some
of the papers in these conferences emphasized the need for a clear
design method for fuzzy controllers.  Recall that when the controlled
plant is too complex to postulate a mathematical model, but skilled
human operators are available, one needs to represent experts' knowledge
and reasoning for the purpose of automation.  The fuzzy logic approach
is attractive because of its ability to handle qualitative information.
Again, various case-studies were reported, such as autonomous mobile
robot, automatic combustion control systems, chemical control processes,
batch culture, driving control of a car, etc.

FUZZY MODELING

     By analogy with stochastic modeling, fuzzy modeling is referred to
the art of systems modeling using Zadeh's theory of fuzzy sets and
logic.  For fuzzy systems in general, the situation is this.  Consider
an input-output map (a black box).  Suppose we wish to describe this box
by a set of "if...  Then..." rules.  Recall that fuzzy If... Then...
rules are widely used in recent industrial applications because of their
flexibility in representing the behavior of a complex system by using
both qualitative experts' knowledge as well as numerical experimental
data.  First we have to identify the input and output variables.  Next,
we construct fuzzy rules.  With regard to a dynamical system, this step
is called identification.  A theoretical question is:  How many rules
are needed to describe faithfully a system?

     Once a number of rules is fixed, one faces the problem of assigning
membership functions to linguistic labels in rules.  Here Neural
Networks can be used to tune membership functions.  From a commonsense
viewpoint, membership functions can be modeled parametrically, i.e. they
are known up to a finite number of numerical parameters.  Thus, after
the structural identification phase, one faces the parameter
identification problem, i.e.  determining (or estimating) the parameters
involved in the membership functions.

     Some ad-hoc methods for identification of systems using fuzzy If...
Then... rules were reported, for example fault diagnosis method,
interior penalty method, fuzzy optimization method, etc....

     Fuzzy modeling is particular important for designing control laws
of dynamical plants without mathematical models.  In such situations,
one needs to identify the plant first and then derive control laws.
This is referred to as fuzzy logic controllers based on fuzzy models (of
the controlled plants).  This important research area is still at its
very beginning.  It is anticipated that without fuzzy dynamical models,
it is not clear how basic concepts such as stability and robustness in
Fuzzy Control theory can be addressed.

APPROXIMATE REASONING

     The inference engine of a fuzzy system is constructed using a
logical process known as approximate reasoning.  It is a generalization
of classical deduction reasoning process.  Basically an approximate
reasoning procedure consists of the selection of an interpretation of
"If... Then..." statements and a way to "fire" such rules.  Unlike
classical two-valued logic, a fuzzy implication can have various
different interpretations, i.e. different mathematical "truth tables".
Also, there are different ways to generalize the classical Modus Ponens.
Even Zadeh's compositional rule of inference leaves room for various
choices of fuzzy logical connectives.  Thus the designer of a particular
system always faces a choice problem.  Papers presented in the area of
approximate reasoning contained new methods such as fuzzy entropy
method, linear revising method, approximate reasoning method with
certainty factor, and Neural Networks based methods.

OVERVIEW AND COMMENTS

     The papers presented at the three conferences covered a large
spectrum of results obtained as well as problems in Neural Networks and
Fuzzy technologies:  Fuzzy Neural Networks, Chaos fuzzy systems, fuzzy
neural computing, learning algorithms for fuzzy systems, approximate
reasoning, fuzzy modeling, fuzzy logic control, neural chips, fuzzy
hardware, fuzzy clustering....

     Although Neural Networks and Fuzzy systems can be investigated
separately, the majority of papers focused on the fusion of the two
technologies in order to tackle more complex problems, and hence to
create more intelligent machines.  So far, empirical evidence is
convincing for more research in this direction.

     In my view, the variety of design techniques is due to a lack of
firm theoretical foundation.  Of course, this is the area of "soft
computing", and one should not expect a rigid theory like a conventional
mathematical theory.  However, theoretical results are already useful as
general guide lines, namely specifying the structures of Neural Networks
and fuzzy systems, the classes of inference procedures used in
approximate reasoning.  More basic research is needed in order to
provide foundations for design methodology.  In the near future, we will
continue to see more applications of the fuzzy approach to the so-called
friendly systems.  Several questions remain:  if a system is
"successfully" designed, how to make it "better"?, can one specify a
design technique for a class of systems rather than just for one given
system?

     It was apparent that the Asian scientists pursued more research
than US scientists in the fields of chaotic fuzzy systems and fuzzy
measures and integrals for decision-making.  The chaos in general
systems results from non-linear dynamical systems and exhibits
complicated and unpredictable behavior.  Applications are considered for
control problems, especially for systems sensitive to oscillations and
chaostic instability.  Typical papers to be looked at are:

(1)  "Chaos and Information loss in Fuzzy dynamical Systems" (P.
Diamond, Australia, Proceedings of the International Symposium in Fuzzy
Systems, p.17- 20)

(2)  "A chaostic chip for analyzing non-linear discrete dynamical
systems" (T. Yamakawa, T. Miki and E. Uchino, Proceedings of the Second
International Conference on Fuzzy Logic and Neural Networks, Vol. 1,
p.563-566)

     As for the development of the mathematical theory of measures and
integrals in a fuzzy setting is concerned, typical paper is:

     "Non-additivity of fuzzy measures representive preferential
dependence" (T. Murofushi and M. Sugeno, Proceedings of the Second
International Conference Fuzzy Logic and Neural Networks, Vol. 2,
p.617-620)

     The invited section on this topic was devoted to new results and
applications to reasoning in decision and control problems.  Dealing
with uncertainty in humanistic systems is a crucial problem.  Besides
the random uncertainty which can be captured by probabilistic laws (with
the analytic tools of the well-established statistical decision theory),
it has been recognized that other types of uncertainty, such as
imprecision and ambiguity (vagueness), have also to be dealt with.  The
main feature of these uncertainties is the non-additivity property.  In
the Bayesian approach to reasoning in intelligent machines, upper and
lower probabilities, or some more general axiomatic measures of
imprecision, are non-additive.  In a related vein, the concept of
degrees of belief in the so-called theory of evidence exhibits also
non-additivity.  It turns out that a general framework for measuring
non-additive uncertainties is the theory of fuzzy measures proposed by
M. Sugeno in 1974.  As a typical example of applications, the Choguet
integral of utility functions, with respect to some fuzzy measure, can
be used as a generalization of the ordinary concept of expected
utilities in decision- making problems.  Thus, in my view. a general
theory of decisions based upon fuzzy measures and integrals will be
useful for systems exhibiting various kinds of uncertainties.

-------------------------------END OF REPORT----------------------------