jg2f+@andrew.cmu.edu (Jude Anand George) (08/08/90)
[The following is from Eugene Miya, eugene@wilbur.nas.nasa.gov]
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:Jude:Anand:George::%\/::jg2f+@andrew.cmu.edu::%\/::::::jude@nas.nasa.gov:::::
:endanger:judo:age::\/\::::/\:/\::::::/\:::::::\/\::(work-related:email:only):
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---------- Forwarded message begins here ----------
Some one please forward this report to the newsgroups devoted to neural
nets and AI.
Dr. David Kahaner is a numerical analyst visiting Japan for two-years
under the aspice of the Office of Naval Research-Far East (ONRFE).
Back issue of most reports will shortly be available via anonymous FTP.
Host is pending. [ENM]
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.
[DKK]
=======
To: Distribution
From: David K. Kahaner ONRFE [kahaner@xroads.cc.u-tokyo.ac.jp]
Re: Fuzzy Logic and Neural Networks--Takagi paper.
7 August 1990
Iizuka '90, a meeting on Fuzzy Logic and Neural Nets has just ended. We
are working on a summary/evaluation report but this is not ready. One
important paper was presented by Dr. H. Takagi of Matsushita Electric,
surveying the research necessary to merge these two concepts. Takagi's
English is rough in spots, but the paper provides more than 90
references, many to work that is not known outside of Japan. References
to papers in Japanese are carefully noted, although my experience is that
many of these authors read and write English and will respond to queries.
Takagi provided me with a file containing the text of this paper
(slightly revised from that in the Proceedings) in "troff" form, and I
have produced the Ascii version given below. Please contact Takagi for
the typeset paper.
FUSION TECHNOLOGY OF FUZZY THEORY AND NEURAL NETWORKS
- SURVEY AND FUTURE DIRECTIONS -
Hideyuki TAKAGI
Central Research Laboratories,
Matsushita Electric Industrial Co., Ltd.
3-15, Yagumo-Nakamachi, Moriguchi, Osaka 570 JAPAN
TEL <+81>6-909-1121, Facsimile: <+81>6-906-0177
EMAIL: takagi@it4.crl.mei.co.jp
[Presented at Fuzzy Logic and Neural Networks, Izzuka '90, July 24 1990]
[ABSTRACT] This paper describes the trend and research directions for future
development of technology to fuse the neural network theory and fuzzy logic.
Following some background, section II describes two possible fusing
methods. One of which is a method by which individual merits are
combined, and another is a method by which analogies between these are
superposed. Section III introduces a report on the current status of
fusion study. Author analyze them and divide into
(1) initial state,
(2) determination of membership function,
(3) knowledge acquisition or knowledge expression,
(4) fuzzy cognitive map etc.,
(5) clustering and pattern recognition,
(6) serial connection of NN and fuzzy processing, and
(7) other states.
On the bases of these studies, section IV describes the future prospects
and proposals of the author.
I. INTRODUCTION
Studies on the Neural Network (NN) and fuzzy logic particularly in Japan
accomplished substantial advancements in recent years, and by this,
considerable overlap of application fields between these two studies are
presently found in the fields of control and inference problem studies. For
instance, in the field of Japanese security investment, approximate reasoning,
NN, conventional AI, and mathematical approach are actually employed now, and
the levels of these arrived at such a stage that actual fund flotation is
made.
The simultaneous enlargements of these research field have brought not only
the enlargement of individual field of study but the interrelationship between
these fields. That is, compensation of inherent demerits of one field by the
merits of another is now became possible, that is, a fusion of fields of study
is now taking place. The fuzzy theory is generally advantageous in logical
field, and can handle higher-order processing easier. The higher flexibility
is a characteristic feature of NN produced by learning, and therefore, this
fits to data-driven pattern processing better. Therefore, it should be
possible that a powerful flexible knowledge processing tool adorned with a NN
robe on a body structure of fuzzy logic could be produced by fusing these two
fields.
Thus, the following is on the trend of researches and futuristic view prepared
by the author who focused his attention on the fusion of fuzzy logic and NN.
Most of these fusion studies are conducted for cases where NN is introduced
into fuzzy logic, and both of these are being actively studied especially in
Japan. Although this review is conducted on a worldwide scale, it is an
author's intention to include the local activities of Japanese academic
associations, and to introduce those to the world through this conference
paper.
II. CONTACT POINTS OF FUSION PROCESS
Both NN and fuzzy theories object the humaneness, and the concerns to each had
been aroused spontaneously and rapidly at a same time. So the similarities
and mutual compensations between these are much discussed. The study of fusion
can be started with the combination of either the individual merits or the
similarities between these two.
Table 1 Contact point of Fusion
Difference Fuzzy logic: Logicality
NN: Learning function
Similarity (1) Output characteristics of NN and membership function
(2) Multiply-add operation of neuron and MAX-MIN operation
of approximate reasoning.
The first fusion pattern is a method combining individual advantages. Fuzzy
logic can express logic explicitly taking a form of rule. NN is helpful when
it is employed for pattern identification because of its learning function.
>From these advantages of view, (a) a method to endow learning function to
fuzzy logic or to conduct pattern processing before fuzzy logic is applied,
and (b) a method to incorporate logics in NN structure etc. could be possible
for combining these two techniques. The employment of former is, however, now
prevailing so far as the reviewed studies are concerned. As for the
difficulty of the latter, it could be attributed for the far less number of NN
researchers who engage in the study of fuzzy logics.
The second fusion method is to superpose similarities. The first similarity
(1) shown in Table 1 is to give a membership function to NN without causing a
crisp boundary between classes formed by a pattern classification type NN.
The reason is that threshold function of its neuron have sigmoid
characteristics to attain continuous values of [0, 1].
The second similarity is that (a) the MIN operation of input and fuzzy
variables conducted at each proposition of IF parts of fuzzy inference rule
corresponds to a product of input to the neuron and synaptic weights, and (b)
the MAX operation to obtain a final inference value from the THEN part of
these plural inference rules corresponds to the input sum within neuron.
There are a number of papers on the fusion of NN and fuzzy theories conducted
at these contact points. For example, the study cited in Sec. 3.2 is an
approximate reasoning logic combined with a learning function of NN on the
bases of similarity (1), and the one mentioned in Sec. 3.3 is the one to
establish a logic by learning function of NN. The one mentioned in Sec. 3.5 is
to use the similarity points (1) and (2) themselves.
The endowment of learning function to the fuzzy logic is one of the major
purpose of fusion with NN. However, we have to be conscious that the learning
function is not a particular characteristics of NN only. One of such reports
is made on a system to reduce the difference between frequency of appearances
and sensation of user who conducted a fuzzy document retrieval by learning
(59). The degree of association between keywords is expressed in a form of
matrix, and the learning is conducted by using the steepest decent method.
Although the matrix in this case could be interpreted as a two-layered NN in a
way, it could apart from the general accepted image of NN.
III. STATUS QUO OF FUSION TECHNOLOGY
Early Stage
In its early stage, introduction of fuzzy logics into NN constituted a core of
those studies. The first paper is concerned "multi-input/multi-output neuron
model" presented by S.C.Lee et al.,(51). They generalized it so that
intermediate values can be dealt, while the output of neuron model proposed by
McCulloch & Pitts was a binary step function, and they also showed
possibilities of fuzzy automata and lambda-fuzzy language recognizer.
The study of correlation to the neural physiology had been further continued
after them. D.Butnariu proposed a model of the eighth sensory nerve (hearing-
vestibuler nerve) by using L-fuzzy automata (8), and A.F.da Rocha et al.,
employed tools such as fuzzy language, fuzzy entropy, and fuzzy automata in
their try to analyze the nerve systems (61-64). Meanwhile, O.G.Chorayan
presented its application to analyze the neuron of the frog visual central
analyzer and the crayfish sixth abdominal ganglion (9). However, very little
report has been made on the application of fuzzy logic to the neural
physiology recently. Instead, L.C.Shiue et al., presented an application of
automata to a fuzzy learning machine constituted of units of fuzzy neuron
(66). If the MAX-MIN operation is substituted by sum of products operation,
stochastic neural automata can be obtained.
Auto-design of Membership Function.
One of the most significant characteristic feature of fuzzy logic attained in
view of the knowledge processing is the separation of its logic and fuzziness
into a rule and a membership function respectively, and another is that the
quantitative expression and processing of fuzziness became possible by this.
Thus, those objects that had been considered highly difficult to deal with
because of their fuzziness can now be dealt easily by using a framework of
conventional knowledge processing. While a considerable time has to be spent
for tuning the rules for dealing those objects having inherent fuzzinesses,
such as talent or skillfulness of expert, by two valued logic based system
wherein the fuzziness affects the logic, there exists no needs to tune the
rules of logical expression when an approximate reason is employed.
However, the method itself for designing this membership function relies much
on the experience now, and this inevitably becomes a bottleneck of system
design. An employment of NN learning function to this is a typical pattern of
fusion study described in this section.
The designing methods of membership function are roughly divided into three
categories shown below.
(a) Manual cut-and-try
(b) Fuzzy clustering (28)
(c) Neural Network.
(a) is a method by which membership function is designed for each of fuzzy
variables, and a fuzzy rule subspace in input variables space obtained by
fuzzy partition is limited within a hypercube shown in Fig a. The method
(b) is free of such a constraint, but it has to take a form such as hyper-
ellipsoid and is constrained by a distance function for clustering. The
method (c) is a first pattern introduced in this section, and by this, the
fuzzy rule partition in an arbitrary hyper curved-surface becomes possible as
shown in Fig b. However, if learning is continued without paying much
attentions, the class boundary become constrained by the sigmoid
characteristics of neuron, producing less ambiguous class boundary region as
shown by a hatched region shown in Fig b. This problem could be
fundamentally solved by changing the sigmoid characteristics according to the
inference object, or by providing learning data considering the inclination of
class boundary plane (the degree of fuzziness), but only a little had been
discussed on this point except a paper telling the effects of learning
iteration (13).
| // // | / /
| // // | // A3 //
| A2 // A3 // | A2 // //
| // // | // //// //
|//////////////////// | ///////// ///
| // | // //
| // | // /// A4
| A1 // A4 | // A1 ///
| // | // //
+------------------------ +---------------------------
Fig a. Fig b.
Ordinary Fuzzy Rule Partition Fuzzy Rule Partition by Neural Network
(Membership function is (Membership function is hypercurve
hypercube surface) surface)
H.Takagi and I.Hayashi proposed a NN-driven Fuzzy Reasoning by which a
membership function of approximate reasoning can be formed by employing a
feed-forward NN (72,17,70,71). This is to cluster the learning data first to
determine the number of fuzzy inference rules, and to form the forms of each
rule boundary in NN. This NN becomes an NN producing all of the membership
functions, and all of the membership functions of each rule are produced by
this. The point is that, by substituting the membership functions given
conventionally in a form of table-look-up or formula by NN, a nonlinearity and
learning function can be endowed the fuzzy system. Furthermore, a reasoning
system can be constituted by using this core NN. This was applied to an
inference problem to confirm the effectiveness of this system (18,19,72).
Regular studies of fusion in Japan began in Spring of 1988 after the above
shown paper was presented, and those have been focused mainly on the design of
inference rule and learning.
T. Furuya et al., also proposed a Neuro Fuzzy System (NFS) employing a feed-
forward NN (10,11,13). The degree of conformity between a pattern that NN
learned in advance and the input vector pattern is used as the membership
values, too. Furthermore, T. Furuya et al., proposed mu-BRAIN as an unit of
knowledge processing to be employed in future (12,14,15). In an architecture
form, this is an knowledge processing unit of which minimum unit is three NNs
consisted of an associative memory NN as memory, a feed-forward NN as
operating director and is mutually linked to the former, and NN as a sequence
controller of these. NFS which conducts approximate reasoning can be used as
NN of operating director. This is a study of knowledge processing unit that
would constitute next generation computer like the modern computer constituted
of logical elements.
T. Yamaguchi et al., derived a membership function using Learning Vector
Quantization (LVQ) (85). LVQ has a similarity to the fuzzy clustering, and J.
C. Bezdek identified this relationship to have a high freedom of obtained
boundary form in 2nd NASA Workshop. In contrast to a conventional approximate
reasoning that fuzzy partitions the input space, LVQ maps the input vector on
a new space and, then this new space is fuzzy partitioned. By going through
this mapping step, a non-linear fuzzy partition of the input vector space can
be accomplished.
T. Yamaguchi et al., proposed a learning fuzzy neural network
(87,86,83,34,35,84). This is purposed to control the fuzziness at the
composition of membership function by introducing Bidirectional Associative
Memories (BAM, proposed by B.Kosko), into the approximate reasoning.
While the object of above studies is to control the form of membership
functions using NN at the designing stage, A. Morita et al., proposed a
simplified method by which the gain of membership function of fixed form can
be adjusted by NN (56). Since a system described the knowhow of expert
machinist by approximate reasoning rules is conventionally inferior to the
actual skill of machinist particularly at its initial stage, the membership
function is considered a must to be tuned at the later stage. The method
proposed by A.Morita et al., was to introduce learning to minimize the
difference between the machining instruction given by the system and the
actual machining instructions given by an expert.
H. Ishibuchi et al., carried out an experiment to construct various membership
functions using NN (31), and derived a fuzzy language by which the form of
membership function is transformed into that of instructor (32), and they
further derived an interval-valued membership function of which values are
broadened (75).
N. Watanabe et al., expressed a fuzzy rule by NN that is finely tuned through
learning by allocation of one fuzzy variable to one neuron, and the weighting
factor is so initialized that its sigmoid characteristics comes closer to the
predetermined membership function (79). this is an approach similar to that
of the later which gives a fuzzy expert shell "MORITA", although no paper
concerning this is presently available except technical manual.
C-c. Lee proposed a inference method by which the activity of each fuzzy
inference rule (corresponding to the MIN operation at IF) is determined by the
self-organization by introducing two neurons therein (50).
Although this is unrelated to the determination of membership function,
H.Nomura et al., (58) applied a Hopfield model to determine the controlled
variables of THEN part of a simplified fuzzy inference (30).
Those shown above are the papers that NN is used for determining the
membership function. The following four advantages shown below are noticeable
in these approaches.
(1) Shorter designing time since it is algorithmically determined without
requiring manual works.
(2) Design of nonlinear membership function is possible because of inherent
nonlinearity of NN.
(3) Automatical acquisition of rule from experts using the learning function
of NN.
(4) Dynamical adaptation to inference environment by the learning function
of NN.
As an example of (1), reported is a case where an adjustment conventionally
required 30 to 40 hour manual works was substituted by an NN learning of 30
minutes to one hour conducted on a personal computer. (2) is a point
emphasized in (17,72) and (85), and a cross-section of hyper-curved surface of
nonlinear membership function obtained by this is shown also (17,72).
As for the feature of (3), reports by I. Hayashi et al., (20,21) and the
before-described one by A. Morita et al., (56) can be cited. I. Hayashi et
al., designed an NN-driven fuzzy reasoning from the data acquired from an
experiment conducted on an 1-D pole balancing (inverted pendulum system)
wherein a experimenter tries to swing up a pendulum. In this experiment, the
fuzzy inference rule is automatically determined without providing preliminary
knowledges, since NN acquires the knowhows of experimenter who tried pendulum
inversion automatically. Moreover, as this is related to the term of (2), the
rod supporting a pendulum can be swung up by only two rules because a
nonlinear membership function is employed in this system.
As for (4), no report proving it is so far available, and this is a task left
to be done in future, but this could be executed without bringing up
complexity since its fundamental is similar to that of (3). However, since
the learning method that a well learnt NN is reinitialized and the learning is
restarted by the data acquired in an independent inference environment, this
can not be employed in the currently operating fuzzy system, and an additional
learning has to be introduced therein, but the problem of additional learning
that uses only additional data is not completely solved yet in the field of
NN.
Knowledge Acquisition, Knowledge Expression
There are many cases where the approximate reasoning is combined with an
expert system (ES) because the approximate reasoning is rule-based. When NN
has to be incorporated therein, it takes a form of knowledge acquisition or
knowledge expression. In a case of knowledge expression, the knowledge NN
acquires is incorporated in the system as it is. In a case where knowledge
acquisition is mainly employed, the inference rules are derived from the
analysis made on the learnt NN. This derivation of knowledge is conducted
mostly from a statistical analysis of the hidden layer, but the acquisition of
new knowledge from the distributed expressions is considered fairly difficult.
However, it could be done slightly easier if a linguistic meaning is assigned
to neurons of I/O layers, and by determining causal relationship.
K. Saitoh et al., constructed a muscular contractive headache diagnostic ES by
a simple NN, and tried to derive rules out of the causal relationship of I/O
(65). They extracted 443 rules from this experiment. Those were inference
rules based on the binary logic, and thus, the certainty of rule and
importance of proposition were unknown. Though a extracted rules were
evaluated, it is certain that a lot of points to be improved were left.
As a method to improve this point, Y. Hayashi et al., conducted an experiment
to acquire fuzzy inference rules from the causal relationship of I/O of NN
(26,22). To acquire knowledge easier, a layered network of which each unit
outputs only three values (True (1), Unknown (0), False (-1)) were supervised
trained by a pocket algorithm developed by S. I. Gallant. This is to extract
not only a casual relationship of I/O, but to determine the linguistic truth
values included in each fuzzy proposition in a relation to its membership
function, and to determine the certainty of each rule itself from the value of
output unit at the last. This method is meaningful in considering the
importance of individual rule as a criterion for selecting only essential
rules. As an application of this method, diagnosis of four hepatobiliary
disorder on the bases of a blood analysis on the nine biochemical items and
sex distinction is conducted (23,90). >From the results of this, an accuracy
of inference that is 10% higher than a ordinal discriminant function was
obtained. Furthermore, an inference method suited for inference rule
containing a fuzzy proposition having linguistic truth values was proposed
(24). They proved that the inference using the acquired rule was superior
than the original NN (25).
The knowledge expression is incorporated in the self-organized fuzzy
controller developed by T. Takagi et al.(69,57). As the two types of NN are
included in this system, the first NN is used as an identifier of control
pattern, and the second NN is used as a knowledge expression of dynamic
characteristics of control system for controlling the fuzzy controller.
D. L. Hundson et al., reported an experiment where the rule-based knowledge of
fuzzy ES for lung cancer diagnosis is combined with NN for eliminating
interviews with specialists (29). Beside these shown above, although this may
not be proper to mention in this section, C. G. Looney proposed an expansion
of approximate reasoning to petri nets (52), and as an application of this,
an algorithm to be applied to the inference of new NN was also proposed.
For those who interested in this field, it would be profitable to see
Reference (73) wherein the description of review and analysis of NN+ES is
included.
Fuzzy Cognitive Maps etc.
B. Kosko proposed a Fuzzy Cognitive Maps (FCM) (41) which is derived by
expanding the cognitive maps proposed by R. Axelrod (4). The cognitive map is
an oriented graph showing a causal relationship between different factors,
wherein the causal relationship is expressed by either the positive or
negative sign for knowledge expressions. FCM expresses the degree of this
relationship. Comparing with the tree-structured inference knowledge
expression employed in conventional ES, this is advantageous in respect of
higher process speed attainable by its parallel processing capability, easy
adaptability to the inferences containing feedback, and easy system
unification by employing matrix expression. As for the problem of how to
determine the degree of causal relationship, a differential Hebbian learning
developed by improving self-organized learning of NN is proposed (42).
Beside a digital version of FCM proposed by W. Zhang (91), W. R. Taber et
al., proposed a method of such employed to infer the expert weights. As an
application of such, K. Gotoh et al., employed this for supporting a plant
control system (16). K. Gotoh et al., constructed four kinds of FCMs from the
causal relationship acquired from four specialists who conducted pumping
operations judging the conditions of rain precipitation per unit time, water
level, and change of water level, and unified these to construct a final
system. An easy unification of knowledges is accomplished by superposing
plural small systems.
Moreover, B. Kosko, centering around ABAM (Adaptive BAM) which takes
intermediate values from the binary output BAM by Hebbian law, developed CABAM
(Competitive ABAM; BAM which conducts competitive learning) (45), FAM (Fuzzy
Associate Memories; ABAM to express a fuzzy proposition) (46), and RABAM
(Random ABAM: ABAM to conduct annealing by giving a noise) (48) and its model
of NN, and discussed these with a new aspect of geometric interpretation of
fuzzy entropy in n-cube space.
Clustering and Pattern Recognition
The similarities (1) shown in Table 1 is to separate a class, and those could
be related with the clustering. One of such examples is a fuzzy clustering M.
Izumida et al., (36,37) conducted by employing a Hopfield model. The
relationship with the fuzzy clustering is described for a multi-input and
multi-output NN model developed by Y. Tan (76,77), and as an application of
this, Y. Katoh et al applied this model to an alphanumeric character
recognition (38).
The model of Y. Tan et al., should be regarded as a multi-NNs with inhibition
learning. They weren't conscious about the relation with the fuzzy theory in
their development process, and their model also has no relationship with the
multi-input/multi-output neuron model of S. C. Lee et. al., shown in Sec. 3.1.
A direct expression of similarities (2) shown in Table 1 is a fuzzy neuron
developed by T. Yamakawa, and this is applied to a numeric character
recognition (88,89). The region wherein the line segment of hand-written
character should cross, region wherein the line-segment should not cross, and
the region which can be ignored because of large deviations, are expressed in
terms of membership functions in this model. These membership functions can
be regarded as synapses of neuron.
As for the studies other than those of above, W. Pedrycz commented on a
pattern recognition method that introduces two NNs and uses a fuzzy level
(60). G. Bortolan et al. who developed an identification of ECG Fuzzy pattern
are studying the relationship of it also (5). M. Katoh et al., studied on the
hand-written numeric character recognition (39). It unifies plural outputs of
NN by using a combination rule developed by A. P. Dempster. J. M. Keller et
al., reported on an experiment to accomplish a fast convergence of linear
discrimination problem by perceptron . They gave a higher learning priority
according to the distance from the center of class (40).
Cascade Connection of NN and Fuzzy Processing
One of the generally practiced sharing of roles between so-called NN and fuzzy
logic is that NN performs the pattern processing at first, and the later part
is processed by fuzzy logic on the logic base. Viewing from this meaning, the
cases of such a system would become more popular as the more complicated
system has to be dealt in near future.
Although this can not be said as the rule-based fuzzy control, the air-
conditioner control developed by F. Matsuoka et al., is the first case having
keywords of NN and fuzzy control in Japan (53,54,55). Therein, the three
variables of actuators that interact each other is controlled by system
command for each actuators and correlation command for cooperation of
actuators, and a time-weighting (this was said to correspond to a membership
function) is given to these two types of commands to composite a final
control.
A. Amano et al., applied NN to consonant recognition, and attained a final
judgment by inputting the output of NN into approximate reasoning. The errors
of NN are restored by this (3,2,1).
W. R. Taber et al., reduced the influence of noise by conducting fuzzy post-
processing after the recognition of orca call with the neuron ring {nothing
sup (68).
Nihon Unisys Ltd., exhibited a stockbroking judging ES at "International
Symposium Computer World '88" held in Kobe. This ES was constructed by
inputting the results of technical analysis into NN, and utilizing the output
of it that is a dealing command as a partial input to the approximate
reasoning.
While fuzzy processing follows NN in these four examples, H. Takahashi
employed these in a reversed order (74). The input unit performs statistical
processing of vehicle data, and this output is fed into the feature extraction
unit to which fuzzy inference rules based on multi-variable analysis are
incorporated for the analysis. The NN part delivers the output of human
subjective judgment on the relative difficulties based on these features'
values.
Studies other than the above-mentioned include the reports made on the
employment of NN for identifying the system having fuzzy I/O (e.g. lecture of
L. A. Zadeh at Kyoto and the 2nd NASA Workshop), wherein the learning of NN
was so conducted to input a membership function and to output a membership
function. R. R. Yager proposed an OWA (Ordered Weighted Averaging
Aggregation) operator (81) to be used in the fields where decision making is
performed based on plural criterions. >From the similarities of this
application field to the multi-input neuron, his paper discussed the
relationship with NN (82). D. C. Kuncisky et al., presented a discussion made
from a view point defining that the inputs to neuron are the elements of a
fuzzy set and the output of neuron is a fuzzy measure of truth (49), in
addition to their comment on the prospects on the learning algorithm. F. J.
Bremner et al., presented nonparametric methods of analyzing fuzzy-set data
using transforming neuron polarization values (7).
As for the relationship between NN and fuzzy logic, it was reported first at
the NASA workshop held in May 1988. Although the proceedings of meeting was
not published, a report of the meeting prepared by K. Hirota is available
(27). According to this, four people presented papers with two key-words. It
was told that B. Kosko reported on the analysis and design of fuzzy
associative memory with fuzzy entropy, and M. Togai on the fuzzy-NN processor
using an approximate reasoning chip, and W. R. Taber and R. R. Yager reported
on the similarities between sum of products operation of neuron and MAX-MIN
operation of approximate reasoning. At the 2nd NASA Workshop held in April of
this year, the number of papers having two key-words is found doubled over
those at the first workshop.
IV. FUTURE DIRECTIONS
As seen from the trend of these commented papers, current fusion study is to
bring NN into fuzzy logic. From the author's future view, importance of the
itemized developments as future research directions shown below would be
increasing.
(a) "Automatic Acquisition of Fuzzy Inference Rules Using NN." The learning
function of NN is recently introduced in the field of fuzzy control succeeding
to the fuzzy adaptive control, recurrent fuzzy control, and the leaning fuzzy
control. Whereas cases like exercises had been considered so far, automatic
tuning and acquisition of inference rule structure will be applied to
practical applications more often to prove its effectiveness to upgrade the
development efficiency and performances. Plural corporations that already put
fuzzy ES in the market are trying to incorporate NN into their development
tools aiming their applications probably in auto-tuning or knowledge
acquisition.
ESs employing NN for knowledge expression that was described in Sec. 3.3 would
be increasing. However, as for the method by which knowledges are acquired in
a form of production rule from NN, an accomplishment of break-through in
future seems essential.
(b) "Adaptation of Fuzzy Inference Rule to Inference Environment." The
development of new learning method by which the inference rules can be
modifyed according to the changes of inference environment is now necessary.
Ultimately, this would lead to the day when we develop "equipments of which
handling easiness is improved as it is used more". At the present age of
"Individuality", the control used to be adapted mainly for a large system has
to be now shifted to a control adapted to individual character and need for
the mass produced products. Therefore, the additional learning problem that
requires partial rewriting of the function formed in NN, discarding the past
learning data, has to be developed. Presently, this can be accomplished only
either by complete re-learning or by adding new learning data to the whole
past learning data which are held.
(c) "Development Started From Similarities of Processing." Considering an
expanded operator capable of unified handing of two similarities (2) shown in
Table 1, there could be a probability to develop a new processing form based
on this. Were this realized, highly effective results could be expected to
both fields.
(d) "Fast Approximation by Introducing Network Structure" The form of
inference rule that is capable of both parallel processing and multistage
inference is a very structure of NN. While the parallel processings are
popular at present in the field on NN such as the silicon system and optical
neuro devices, the efforts to develop higher speed NN will surely affect the
approximate reasoning.
While the studies of network reasoning and multistage inference are active in
the field of fuzzy theory, These studies are made also in People's Republic of
China (78), and it is being incorporated in a system {nothing sup (80). This
may give an affect to NN field. Since very little about the studies of fuzzy
mathematics is known in Japan except its titles, the author would like to
expect fruits of technical exchange at "Sino-Japan Joint Meeting on Fuzzy Sets
and Systems" which will be held in October this year.
(e) "Introduction of Fuzzy Logic into NN. It is said that the improvement of
functions of NN could not be obtained by starting with cut-and-try, but it
depends on how to incorporate the preparatory knowledge into NN. Conventional
knowledge incorporation had been done either by (1) conduct a preprocessing
according to the statistical information of input data, (2) prewiring for
units connection, (3) combination of functional NNs, or by others. It seems
that a higher order processing could be attained by incorporating fuzzy
inference rule thereto.
As the one of such efforts, the NN-type ES "MORITA" of Brains Co., is
automatically manufactured by using production rules of fuzzy ES "NORIO"(6)
wherein a fuzzy proposition in the inference rules is allocated to one of the
NN units, and thus the relationship between IF and THEN parts is expressed by
a connection between units. The final value of weighting factor of NN is
determined by the learning made after the initial value setting made on the
degree of confidence of inference rule. This approach is to incorporate an
approximate reasoning structure into NN.
In the field of NN study, a number of structurized NNs have been proposed. In
the field of fuzzy theory study also, excluding the paper presented this
conference, the NN-driven fuzzy reasoning, NFS, and the learning fuzzy neural
network described in Sec. 2.3 are the models related to structurized NN. Thus,
the positive employments of fuzzy logic structure for NN designing is a
definite trend in future.
(f) "Introduction of Fuzzy Theory into Fast NN Learning. There exists a high
expectation on the effects of introducing the fuzzy theory into NN learning to
make it higher speed. However, unlike the study fields of above, even the
starting of this has not been made yet except the related one made by J. M.
Keller et. al., mentioned before.
The employment of NN by fuzzy theory researchers was made in an early date,
and many of them have continued concerns to NN as a tool. However, since there
are very little who are versed very well in the fuzzy theory, the development
of this study may take some more time. The reason of this is that fuzzy theory
gave an vague impression since it combined with many fields and is diversified
too much although NN offered a tool that can be used as a black box. The
advancement of fuzzy researchers into the fields of NN could be one of
possible solutions. If an advancement in such fields were made, and the high-
speed learning became a promising prospect, this is what the author wished to
see.
V. CONCLUSION
An analytical pattern of the studies to fuse NN and fuzzy logic, and the
survey of status quo of fusion studies divided into seven fields are carried
out. And based on these, the author derives and describes the future
prospects and the research directions to be taken.
As laboratories advocating the fuzzy and NN themes are being established in
Japan and France, and the first and second workshop meeting in NASA and the
conference in Iizuka have been held, the author would like to expect this
trend would be largely expanded to create revolutional fusion technologies in
near future.
Whereas the provision of conversational humane environments such as
gentleness, warmness and friendliness are essential to conduct successful
communication between human beings. The future age where such environment is
provided even for the man-machine communication so that the nonspecialist can
establish a friendly communication with machine, is at around the corner, the
author would like to see the study of NN and fuzzy logic would become a key
technology to realize such society.
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IEICE: The Institute of Electronics, Information and Communication Engineers
(Japan)
IEE Japan: The Institute of Electrical Engineers of Japan
IPSJ: Information Processing Society of Japan
SICE: The Society of Instrument and Control Engineers
ISCIE: Institute of Systems, Control and Information Engineers (Japan)
SOFT: Japan Society for Fuzzy Theory and Systems
ICNN: IEEE International Conference on Neural Networks
IJCNN: IEEE & INNS International Joint Conference on Neural Networks
IIZUKA-88: International Workshop on Fuzzy System Applications
Fuzzy Syst. Symp.: sponsor was IFSA Japan Chapter
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