Neuro-Fuzzy Systems: A Survey

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Abstract
The techniques of artificial intelligence based in fuzzy logic and neural networks are frequently applied together. The reasons to combine these two paradigms come out of the difficulties and inherent limitations of each isolated paradigm. Generically, when they are used in a combined way, they are called Neuro-Fuzzy Systems. This term, however, is often used to assign a specific type of system that integrates both techniques. This type of system is characterised by a fuzzy system where fuzzy sets and fuzzy rules are adjusted using input output patterns. There are several different implementations of neuro -fuzzy systems, where each author defined its own model. This article summarizes a general vision of the area describing the most known hybrid neuro-fuzzy techniques, its advantages and disadvantages.
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Neuro-Fuzzy Systems: A Survey
JOSÉ VIEIRA
*
, ALEXANDRE MOTA
**
* Department of Eng. Electronics and Telecommunications
Polytechnic Superior School of Technology of Castelo Branco
Avenida do Empresario 6000 Castelo Branco, PORTUGAL
zevieira@est.ipcb.pt
**
Department of Eng. Electronics and Telecommunications
University of Aveiro,
Campus Universitário de Santiago, 3810 Aveiro, PORTUGAL
alex@det.ua.pt
Abstract: The techniques of artificial intelligence based in fuzzy logic and neural networks are many times
applied together. The reasons to combine these two paradigms come out of the difficulties and inherent
limitations of each isolated paradigm. Generically, when they are used in a combined way, they are called
Neuro-Fuzzy Systems. This term, however, is many times used to assign a specific type of system that integrates
both techniques. This type of system is characterised for a fuzzy system where fuzzy sets and fuzzy rules are
adjusted using input output patterns. There are several different implementations of neuro-suzzy systems,
therefore each author defined its own model. This article summarizes a general vision of the area describing the
most known hybrid neuro-fuzzy techniques, its advantages and disadvantages.
Key Words Hybrid Systems, Cooperative Systems, Concurrent Systems, Neuro-Fuzzy Architectures, Non-
Linear Modelling.
1 Introduction
The modern techniques of artificial intelligence have
found application in almost all the fields of the
human knowledge. However, a great emphasis is
given to the accurate sciences areas, perhaps the
biggest expression of the success of these techniques
is in engineering field. These two techniques neural
networks and fuzzy logic are many times applied
together for solving engineering problems where the
classic techniques do not supply an easy and
accurate solution. The neuro-fuzzy term was born of
course by the fusing of these two techniques. As
each investigator combines these two tools in
different way, then, some confusion was created on
the exact meaning of this term. Still there is no
absolute consense but in general, the neuro-fuzzy
term means a type of system characterized for a
similar structure of a fuzzy controller where the
fuzzy sets and rules are adjusted using neural
networks tuning techniques in an iterative way with
data vectors (input and output systems data).
Such systems show two distinct ways of behaviour.
In a first phase, called learning phase, it behaves like
neural networks learning its internal structure
parameters off-line. Later, in the execution phase, it
behaves like a fuzzy logic system.
Separately, each one of these techniques possesses
advantages and disadvantages that, when mixed
together, theirs cooperage providing better results
than the ones achieved with the use of any one
isolated technique.
1.1 Fuzzy Systems
Fuzzy systems propose a mathematic calculus to
translate the subjective human knowledge of the real
processes. This is a way to manipulate practical
knowledge with some level of uncertainty. The
fuzzy sets theory was initiated by Lofti Zadeh [16],
in 1965. The behaviour of such systems is described
through a set of fuzzy rules, like:
IF <premise> THEN <consequent>
that uses linguistics variables with symbolic terms.
Each term represents a fuzzy set. The terms of the
input space (typically 5-7 for each linguistic
variable) compose the fuzzy partition.
The fuzzy inference mechanism consists of three
stages: in the first stage, the values of the numerical
inputs are mapped by a function according to a
degree of compatibility of the respective fuzzy sets,
this operation can be called fuzzyfication. In the
second stage, the fuzzy system processes the rules in
accordance with the firing strengths of the inputs. In
the third stage, the resultant fuzzy values are
transformed again into numerical values, this
operation can be called defuzzyfication. Essentially,
this procedure makes possible the use fuzzy
categories in representation of words and abstracts
ideas of the human beings in the description of the
decision taking procedure.
The advantages of the fuzzy systems are:
capacity to represent inherent uncertainties of
the human knowledge with linguistic variables;
simple interaction of the expert of the domain
with the engineer designer of the system;
easy interpretation of the results, because of the
natural rules representation;
easy extension of the base of knowledge
through the addition of new rules;
robustness in relation of the possible
disturbances in the system.
And its disadvantages are:
incapable to generalize, or either, it only
answers to what is written in its rule base;
not robust in relation the topological changes
of the system, such changes would demand
alterations in the rule base;
depends on the existence of a expert to
determine the inference logical rules;
1.2 Neural Networks
The neural networks try to shape the biological
functions of the human brain. This leads to the
idealisation of the neurones as discrete units of
distributed processing. Its local or global
connections inside of a net also are idealized, thus
leading to the capacity of the nervous system in
assimilating, learning or to foresee reactions or
decisions to be taken. W. S. McCulloch, W. Pits,
described the first Neural Network model and F.
Rosenblatt (Perceptron) and B. Widrow (Adaline)
develop the first training algorithm. The main
characteristic of the neural networks is the fact of
these structures could learn with examples (training
vectors, input and output samples of the system).
The neural networks modify’s its internal structure
and the weights of the connections between its
artificial neurones to make the mapping, with a level
of acceptable error for the application, of the relation
input/output that represent the behaviour of the
modelled system.
The advantages of the neural networks are:
learning capacity;
generalization capacity;
robustness in relation to disturbances.
And its disadvantages are:
impossible interpretation of the functionality;
difficulty in determining the number of layers
and number of neurons.
2 Neuro Fuzzy Systems
Since the moment that fuzzy systems become
popular in industrial application, the engineers
designer perceived that the development of a fuzzy
system with good performance is not an easy task.
The problem of finding membership functions and
appropriate rules are frequently a tiring process of
attempt and error. Thus, appears the idea of applying
learning algorithms to the fuzzy systems. The neural
networks, that have efficient learning algorithms,
had been presented as an alternative to automates or
to support the development of tuning fuzzy systems.
The first studies of the neuro-fuzzy systems date of
the beginning of the 90’s decade, with Jang, Lin and
Lee in 1991, Berenji in 1992 and Nauck from 1993,
etc. The majority of the first applications were in
process control. Gradually, its application spread for
all the areas of the knowledge like, data analysis,
data classification, imperfections detention and
support to decision-making, etc.
The neural networks and the fuzzy systems can be
combined to join its advantages and to cure its
individual illness. The neural networks introduce its
computational characteristics of learning in the
fuzzy systems and receive from them the
interpretation and clearity of systems representation.
Thus, the disadvantages of the fuzzy systems are
compensated by the capacities of the neural
networks. These techniques are complementary,
which justifies its.
3 Types of Neuro-Fuzzy Systems
In a general way, all the combinations of techniques
based on neural networks and fuzzy logic can be
called neuro-fuzzy systems. The different
combinations of these techniques can be divided, in
accordance with [10], in the following classes:
Cooperative Neuro-Fuzzy System: In the cooperative
systems there is a pre-processing phase where the
neural networks mechanisms of learning determine
some sub-blocks of the fuzzy system with the
patterns . For instance, the fuzzy sets and/or fuzzy
rules (fuzzy associative memories [8] or the use of
clustering algorithms to determine the rules and
fuzzy sets position [3]). After the fuzzy sub-blocks
are calculated the neural network is taken away
executing only the fuzzy system.
Concurrent Neuro-Fuzzy System: In the concurrent
system the neural network and the fuzzy system
work continuously together. In general, the neural
networks pre-processes the inputs (or pos-processes
the outputs) of the fuzzy system.
Hybrid Neuro-Fuzzy System: In this category, a
neural network is used to learn some parameters of
the fuzzy system (parameters of the fuzzy sets, fuzzy
rules and weights of the rules) of a fuzzy system in
an iterative way. The majority of the investigators
uses the neuro-fuzzy term to assign only hybrid
neuro-fuzzy system.
4 Cooperative Neuro-Fuzzy Systems
In a cooperative system the neural networks are only
used in an initial phase. In this case, the neural
networks determine sub-blocks of the fuzzy system
using training data, after this, the neural networks
are forget and only the fuzzy system is executed. In
the cooperative neuro-fuzzy systems, the structure is
not total interpretable what can be considered a
disadvantage.
FUZZY
SYSTEM
NEURAL
NETWORK
F UZZY
SETS
F UZZY
R ULES
Figure 1. Cooperative Systems
5 Concurrent Neuro-Fuzzy Systems
A concurrent system is not a neuro-fuzzy system in
the strict sense, because the neural network works
together with the fuzzy system. This means that the
inputs enters in the fuzzy system, are pre-processed
and then the neural network processes the outputs of
the concurrent system or in the reverse way. In the
concurrent neuro-fuzzy systems, the results are not
completely interpretable, what can be considered a
disadvantage.
FUZZY
SYSTEM
NEURAL
NETWORK
NEURAL
NETWORK
FUZZY
SYSTEM
Figure 2. Concurrent Systems
6 Hybrid Neuro-Fuzzy Systems
In Nauck [10] definition: “A hybrid neuro-fuzzy
system is a fuzzy system that uses a learning
algorithm based on gradients or inspired by the
neural networks theory (heuristical learning
strategies) to determine its parameters (fuzzy sets
and fuzzy rules) through the patterns processing
(input and output)”.
A neuro-fuzzy system can be interpreted as a set of
fuzzy rules. This system can be total created from
input output data or initialised with the à priori
knowledge in the way of fuzzy rules. The resultant
system by fusing fuzzy systems and neural networks
has as advantages of learning through patterns and
the easy interpretation of its functionality.
There are several different ways to develop hybrid
neuro-fuzzy systems, therefore, for being a recent
research subject, each investigator has defined its
own particular models. These models are similar in
its essence, but they present basic differences.
Many types of neuro-fuzzy systems are represented
by neural networks that implement logical functions.
This is not necessary for the application of an
learning algorithm in to a fuzzy system, however,
the representation trouth a neural networks is more
convenient because it allows to visualise the flow of
data through the system and the error signals that are
used to update its parameters. The aditional benefit
is to allow the comparison of the different models
and visualise its structural differences. There are
several neuro-fuzzy architectures like:
Fuzzy Adaptive Learning Control Network
(FALCON) C. T. Lin and C. S. Lee [9];
Adaptive Network based Fuzzy Inference System
(ANFIS) R. R. Jang [5];
Generalized Approximate Reasoning based
Intelligence Control (GARIC) H. Berenji [2];
Neuronal Fuzzy Controller (NEFCON) D. Nauck &
Kruse [11];
Fuzzy Inference and Neural Network in Fuzzy
Inference Software (FINEST) Tano, Oyama and
Arnould [15];
Fuzzy Net (FUN) S. Sulzberger, N. Tschichold and
S. Vestli [14];
Self Constructing Neural Fuzzy Inference Network
(SONFIN) Juang and Lin [6].
Fuzzy Neural Network (NFN) Figueiredo and
Gomide [4];
Dynamic/Evolving Fuzzy Neural Network (EFuNN
and dmEFuNN) Kasabov and Song [7];
A summarise description of the five most popular
neuro-fuzzy architectures is made in next section.
6.1 FALCON Architecture
The Fuzzy Adaptive Learning Control Network
FALCON [9] is an architecture of five layers as it is
shown in figure 3. There are two linguistics nod es
for each output. One is for the patterns and the other
is for the real output of the FALCON. The first
hidden layer is responsible for the mapping of the
input variables relatively to each membership
functions. The second hidden layer defines the
antecedents of the rules followed of the consequents
in the third hidden layer. FALCON uses an hybrid
learning algorithm composed by a unsupervised
learning to define the initial membership functions
and initial rule base and it uses a learning algorithm
based on the gradient descent to optimise/adjust the
final parameters of the membership functions to
produce the desired output.
6.2 ANFIS Architecture
The Adaptive Network based Fuzzy Inference
System ANFIS [5] implements a Takagi Sugeno
fuzzy inference system and it has five layers as
shows in figure 4. The first hidden layer is
responsible for the mapping of the input variable
relatively to each membership functions. The
operator T-norm is applied in the second hidden
layer to calculate the antecedents of the rules. The
third hidden layer normalizes the rules strengths
followed by the fourth hidden layer where the
consequents of the rules are determined. The output
layer calculates the global output as the summation
of all the signals that arrive to this layer.
ANFIS uses backpropagation learning to determine
the the input membership functions parameters and
the least mean square method to determine the
consequents parameters. Each step of the iterative
learning algorithm has two parts. In the first part, the
input patterns are propagated and the parameters of
the consequents are calculated using the iterative
minimum squared method algorithm, while the
parameters of the premises are considered fixed. In
the second part, the input patterns are propagated
again and in each iteration, the learning algorithm
backpropagation are used to modify the parameters
of the premises, while the consequents remain fixed.
6.3 GARIC Achitecture
The Generalized Approximate Reasoning based
Intelligence Control GARIC [2] implements a
neuro-fuzzy system using two neral netwoks
modules, ASN (Action Selection Network) and AEN
(Action State Evaluation Network). The AEN is an
adaptative evaluator of ASN actions. The ASN of
the GARIC is an advanced network of five layers.
Figure 5 illustrates GARIC-ASN structure. The
connections between the layers are not weighted.
The first hidden layer stores the linguistics values of
all input variables. Each input can only connect to
the first layer, which represent its associates
linguistics values. The second hidden layer
represents the fuzzy rules nodes that determine the
compatibility degree of each rule using a softmin
operator. The third hidden layer represents the
linguistics values of the output variables. The
conclusions of each rule are calculated depending on
the strength of the rules antecedents calculated in the
rules nodes. GARIC uses the mean of local mean of
maximum method to calculate the output of the
rules. This method needs for a numerical value in
the exit of each rule. Thus, the conclusions should be
transformed from fuzzy values for numerical values
before being accumulated in the final output value of
the system. GARIC uses a mixture of the gradient
descending with a reinforcement learning for a fine
adjustment of its internal parameters.
Figure 3. FALCON achitecture.
Figure 4. ANFIS achitecture.
Figura 5. GARIC achitecture.
6.4 NEFCON Architecture
The Neural Fuzzy Controller NEFCON [11] was
drawn to implement a Mamdani type inference fuzzy
system as illustrated in figure 6. The connections in
this architecture are weighted with fuzzy sets and
rules using the same antecedents (called shared
weights), which are represented by the drawn
ellipses. They assure the integrity of the base of
rules. The input units assume the function of
fuzzyfication interface, the logical interface is
represented by the propagation function and the
output unit is responsible for the defuzzyfication
interface. The process of learning in architecture
NEFCON is based on the mixture of reinforcement
learning with the backpropagation algorithm. This
architecture can be used to learn the rule base from
the beginning, if there is no à priori knowledge of
the system, or to optimise an initial manually
defined rule base. NEFCON has two variants
NEFPROX (for function approximation) and
NEFCLASS (for classification tasks) [14].
6.5 EFuNN Architecture
In Evolving Neural Fuzzy Network EFuNN [10] all
nodes are created during the learning phase. The first
layer passes data to the second layer that calculates
the degrees of compatibility relate to the predefined
membership functions. The third layer contains
fuzzy rule nodes representing prototypes of input-
output data as an association of hyper-spheres from
the fuzzy input and fuzzy output spaces. Each rule
node is defined by two vectors of connection
weights, which are adjusted through a hybrid
learning technique. The fourth layer calculates the
degree to which output membership functions are
matched the input data and the fifth layer carries out
the defuzzyfication and calculates the numerical
value for the output variable. Dynamic Evolving
Neural Fuzzy Network (dmEFuNN) [10] is a
modified version of the EFuNN with the idea of not
only the winning rule node’s activation is
propagated but a group of rule nodes that is dynamic
selected for every new input vector and their
activation values are used to calculate the dynamical
parameters of the output function. While EFuNN
implements Mamdani type fuzzy rules, dmEFuNN
implements Takagi Sugeno fuzzy rules.
To get a more detail description of this architectures,
beyond the specific pointed references made in this
paper, a detailed survey was made by Abraham [1]
in 2000 where it can be found a detailed description
of several well known neuro-fuzzy architectures
theirs respective learning algorithms.
7 Discussion and Application
The hybrid neuro-fuzzy systems present a
intepreteble model and they have learning capacities
in a supervised way. In FALCON, GARIC, ANFIS,
NEFCON, SONFIN and FINEST the learning
process only worried with the adaptation of internal
parameters of a fixed structure of the system. For
complex problems, it will be computational
demanding to determine all the parameters (of
premises parameters, consequents parameters,
number of rules, etc) because the parameters will
grow exponentially.
An important characteristic of the architecture
dmEFuNN and EFuNN is to make the training only
in one iteration. This characteristic will allowed the
implementation of on-line adaptation in a simple
way.
Abraham proposed [1] a evolutionary approach
based on genetic algorithms for the optimisation of
all parameters of the structure of a neuro-fuzzy
system (type of fuzzy system, number of rules,
parameters, inference operators, rules and
membership functions).
Fuzzyfica-
tion Layer
Defuzzyfi-
cation Layer
Figure 6. NEFCON architecture.
Figure 7. EfuNN architecture.
In the industrial field, initially these architectures
were applied in modelling non-linear systems and
control engineering. Actually, however these
architectures are used in almost all knowledge areas
where a non-linear function should be approximated.
The actual neuro fuzzy systems application areas are
medicine, economy, control, mechanics, physics,
chemistry, etc.
8 Conclusions
In this article it is presented, in a summarize way,
the last decade of investigation in the area of the
modelling non-linear functions through neuro-fuzzy
systems. Duo to the vast number of common tools it
continues to be difficult to compare conceptual the
different architectures and to evaluate comparatively
its performances. In generic terms the bibliography
points that neuro fuzzy systems that implement
Takagi-Sugeno type fuzzy inference systems get
accurate results than the approaches that implement
neuro fuzzy inference systems of Mamdani type,
although its bigger computational demanding. As a
guide line for implementing highly efficient neuro-
fuzzy systems they should have the following
characteristics; fast learning; adaptability on-line; to
adjust itself with the aim of obtaining the small
global error possible; small computational
complexity.
The data acquisition and the pre-processing of input
training data are also very important for the success
of the application of the neuro-fuzzy architectures.
All the neuro-fuzzy architectures use the gradient
descent techniques of for the learning its internal
parameters. For a faster convergence of the
calculation of these parameters it would be
interesting to explore other efficient algorithms of
neural networks learning as the conjugated gradient
search in spite of the backpropagation algorithm.
References
[1] A. Abraham and Baikunth Nath, “ Hybrid
Intelligent Systems: A Review of a decade of
Research”, School of Computing and
Information Technology, Faculty of Information
Technology , Monash University, Autralia,
Technical Report Series, 5/2000, 2000, pp. 1-55.
[2] H. R. Berenji and P. Khedkar, “Learning and
Tuning Fuzzy Logic Controllers through
Reinforcements”, IEEE Transactions on Neural
Networks, 1992, Vol. 3, pp. 724-740.
[3] E. Czogala and J. Leski, “Neuro-Fuzzy
Intelligent Systems, Studies in Fuzziness and
Soft Computing”, Springer Verlag, Germany,
2000.
[4] M. Figueiredo and F. Gomide; "Design of Fuzzy
Systems Using Neuro-Fuzzy Networks", IEEE
Transactions on Neural Networks, 1999, Vol.
10, no. 4, pp.815-827.
[5] R. Jang, “Neuro-Fuzzy Modelling:
Architectures, Analysis and Applications”, PhD
Thesis, University of California, Berkley, July
1992.
[6] F. C. Juang, T. Chin Lin, “An On-Line Self
Constructing Neural Fuzzy Inference Network
and its applications”, IEEE Transactions on
Fuzzy Systems, 1998, Vol. 6, pp. 12-32.
[7] N. Kasabov e Qun Song, “Dynamic Evolving
Fuzzy Neural Networks with ‘m-out-of-n’
Activation Nodes for On-Line Adaptive
Systems”, Technical Report TR99/04,
Departement of Information Science, University
of Otago, 1999.
[8] B. Kosko, “Neural Networks and Fuzzy
Systems: A Dynamical System Approach to
Machine Intelligence”, Prentice Hall,
Englewood Cliffs, New Jersey, 1992.
[9] T. C. Lin, C. S. Lee, “Neural Network Based
Fuzzy Logic Control and Decision System”,
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[10] D. Nauck, F. Klawon; R. Kruse,
“Foundations of Neuro-Fuzzy Systems”, J.
Wiley & Sons, 1997.
[11] D. Nauck, R, Kurse, “Neuro-FuzzySystems
for Function Approximation”, 4
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International
Workshop Fuzzy-Neuro Systems, 1997.
[12] D. Nauck, “Beyond Neuro-Fuzzy Systems:
Perspectives and Directions”. Proc. of the Third
European Congress on Intelligent Techniques
and Soft Computing (EUFIT’95), Aachen, 1995.
[13] D. Nauck; “A Fuzzy Perceptron as a
Generic Model for Neuro-Fuzzy Approaches”.
Proc. Fuzzy-Systems, 2
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GI-Workshop,
Munich, 1994.
[14] S. Sulzberger, N. Tschichold e S. Vestli,
“FUN: Optimization of Fuzzy Rule Based
Systems Using Neural Networks”, Proceedings
of IEEE Conference on Neural Networks, San
Francisco, March 1993, pp. 312-316.
[15] S. Tano, T. Oyama, T. Arnould, “ Deep
Combination of Fuzzy Inference and Neural
Network in Fuzzy Inference”, Fuzzy Sets and
Systems, 1996, Vol. 82(2), pp. 151-160.
[16] L. A. Zadeh; “Fuzzy Sets”, Information and
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    In classification and prediction of different types of medical disorders the neuro-fuzzy systems (NFS) are playing vital and significant role. To avoid false diagnosis the NFS assists medical practitioners to a greater extent in automating the domain dealing with medical disorders. With the passage of time the NFS approach has become apparent to enhance accuracy in dealing with a wide range of complicated research problems in the field of medical diagnosis. In this paper the author presents the literature review of the research done in implementing NFS in the field of medical diagnosis for current decade. Total of 100 publications in chronological advancement and up-gradation in models are considered for the time period of 10 years. A detailed study of each disease is carried out to discuss how NFS methodologies have been applied for classification and prediction in the diagnosis of different types of medical disorders. Ten (10) most severe medical disorders i.e. cancer, cardiovascular, depression and anxiety, diabetes, communicable, kidney, liver, neuro-degenerative, respiratory and thyroid has been undertaken for the study. Based on the study carried out it has been observed that NFS found to be effective as compared to the application of other AI techniques in medical diagnosis. Study reveals that effectiveness of NFS increases significantly when integrated with other AI approaches. This review adds into the knowledge of different researchers working in the field of medical diagnosis and will also give the comprehensive view of the effectiveness of the NFS techniques being used in medical diagnosis. The paper also incorporates a few research publications that were submitted in 2019 to incorporate the latest advances in medical science implementation of NFS.
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    Molecular communication (MC) nanonetworks, the interconnection of biological nanomachines (Bio-NMs), are envisaged to significantly expand the applications of nano-technology in the areas of the biomedical, material science, and electrical engineering. In this paper, we consider the scenario of diffusion-based molecular communication (DMC) system that is a promising bio-inspired approach to implementing nanonetwork systems. Considering the limited computation capability, ultra-low energy assumption, and expensive information exchange cost among Bio-NMs, this paper proposes a pulse-based demodulation scheme in three biologically inspired techniques for the detection of the molecular pulses: a multivariate polynomial approximation (MPA) scheme, an adaptive fuzzy threshold-based detection (AFTD) scheme, and an adaptive neuro-fuzzy based multivariate polynomial approximation (ANF-MPA) scheme. These methods are suitable for binary On-OFF keying (BOOK signaling), where the Rx Bio-NM adapts the 1/0-bit detection threshold based on the previously received bits that help to alleviate the inter-symbol interference (ISI) problem resulting from residual (tail) diffusion molecules arriving at the receiver due to past bit transmissions and reception noise. To evaluate the performance of DMC systems, the essential communication metrics in each detection schemes are identified, and the numerical results are obtained and validated by MATLAB simulation. Moreover, the complexity of the proposed schemes is calculated, and the performance evaluation in various noisy channel sources shows a promising improvement in the un-coded bit error rate (BER) performance compared with the threshold detection schemes in the literature. These results provide insights that may guide the implementation of future DMC nanonetworks.
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    A fuzzy set is a class of objects with a continuum of grades of membership. Such a set is characterized by a membership (characteristic) function which assigns to each object a grade of membership ranging between zero and one. The notions of inclusion, union, intersection, complement, relation, convexity, etc., are extended to such sets, and various properties of these notions in the context of fuzzy sets are established. In particular, a separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.
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    At the Laboratory for International Fuzzy Engineering Research in Japan (LIFE), we are now developing FINEST (Fuzzy Inference Environment Software with Tuning). The special features are (1) improved generalized modus ponens, (2) mechanism which can tune the inference method as well as fuzzy predicates and (3) software environment for debugging and tuning. In this paper, we give an outline of the software, and describe an important concept, a deep combination of the fuzzy inference and the neural network in FINEST, which enables FINEST to tune the inference method itself. FINEST is now being used as a tool for quantification of the meaning of natural language sentences as well as a tool for fuzzy modelling and fuzzy control.
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    Introduces a systematic approach for fuzzy system design based on a class of neural fuzzy networks built upon a general neuron model. The network structure is such that it encodes the knowledge learned in the form of if-then fuzzy rules and processes data following fuzzy reasoning principles. The technique provides a mechanism to obtain rules covering the whole input/output space as well as the membership functions (including their shapes) for each input variable. Such characteristics are of utmost importance in fuzzy systems design and application. In addition, after learning, it is very simple to extract fuzzy rules in the linguistic form. The network has universal approximation capability, a property very useful in, e.g., modeling and control applications. Here we focus on function approximation problems as a vehicle to illustrate its usefulness and to evaluate its performance. Comparisons with alternative approaches are also included. Both, non-noisy and noisy data have been studied and considered in the computational experiments. The neural fuzzy network developed here and, consequently, the underlying approach, has shown to provide good results from the accuracy, complexity, and system design points of view
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    A method for learning and tuning a fuzzy logic controller based on reinforcements from a dynamic system is presented. It is shown that: the generalized approximate-reasoning-based intelligent control (GARIC) architecture learns and tunes a fuzzy logic controller even when only weak reinforcement, such as a binary failure signal, is available; introduces a new conjunction operator in computing the rule strengths of fuzzy control rules; introduces a new localized mean of maximum (LMOM) method in combining the conclusions of several firing control rules; and learns to produce real-valued control actions. Learning is achieved by integrating fuzzy inference into a feedforward network, which can then adaptively improve performance by using gradient descent methods. The GARIC architecture is applied to a cart-pole balancing system and demonstrates significant improvements in terms of the speed of learning and robustness to changes in the dynamic system's parameters over previous schemes for cart-pole balancing.
  • Conference Paper
    A method for optimization of fuzzy rule based systems using neural networks is described. A neural network model with special neurons has been developed so that the translation of fuzzy rules and membership functions into the network is possible. The performance of this network, and hence the quality of the original rule base, is then improved by training the network using a combination of neural network learning algorithms. The optimized rules and membership functions can be extracted from the net and used in normal fuzzy inference tools. This net has been tested on the WallJumperOver and the problem of local navigation for mobile robots
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    A self-constructing neural fuzzy inference network (SONFIN) with online learning ability is proposed in this paper. The SONFIN is inherently a modified Takagi-Sugeno-Kang (TSK)-type fuzzy rule-based model possessing neural network learning ability. There are no rules initially in the SONFIN. They are created and adapted as online learning proceeds via simultaneous structure and parameter identification. In the structure identification of the precondition part, the input space is partitioned in a flexible way according to an aligned clustering-based algorithm. As to the structure identification of the consequent part, only a singleton value selected by a clustering method is assigned to each rule initially. Afterwards, some additional significant terms selected via a projection-based correlation measure for each rule will be added to the consequent part incrementally as learning proceeds. The combined precondition and consequent structure identification scheme can set up an economic and dynamically growing network, a main feature of the SONFIN. In the parameter identification, the consequent parameters are tuned optimally by either least mean squares or recursive least squares algorithms and the precondition parameters are tuned by a backpropagation algorithm. To enhance the knowledge representation ability of the SONFIN, a linear transformation for each input variable can be incorporated into the network so that much fewer rules are needed or higher accuracy can be achieved
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    A general neural-network (connectionist) model for fuzzy logic control and decision systems is proposed. This connectionist model, in the form of feedforward multilayer net, combines the idea of fuzzy logic controller and neural-network structure and learning abilities into an integrated neural-network-based fuzzy logic control and decision system. A fuzzy logic control decision network is constructed automatically by learning the training examples itself. By combining both unsupervised (self-organized) and supervised learning schemes, the learning speed converges much faster than the original backpropagation learning algorithm. The connectionist structure avoids the rule-matching time of the inference engine in the traditional fuzzy logic system. Two examples are presented to illustrate the performance and applicability of the proposed model
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    Full-text available
    The paper introduces a new type of evolving fuzzy neural networks (EFuNNs), denoted as mEFuNNs, for on-line learning and their applications for dynamic time series analysis and prediction. mEFuNNs evolve through incremental, hybrid (supervised/unsupervised), on-line learning, like the EFuNNs. They can accommodate new input data, including new features, new classes, etc. through local element tuning. New connections and new neurons are created during the operation of the system. At each time moment the output vector of a mEFuNN is calculated based on the m-most activated rule nodes. Two approaches are proposed: (1) using weighted fuzzy rules of Zadeh-Mamdani type; (2) using Takagi-Sugeno fuzzy rules that utilise dynamically changing and adapting values for the inference parameters. It is proved that the mEFuNNs can effectively learn complex temporal sequences in an adaptive way and outperform EFuNNs, ANFIS and other neural network and hybrid models. Rules can be inserted, extracted and adjusted continuously during the operation of the system. The characteristics of the mEFuNNs are illustrated on two bench-mark dynamic time series data, as well as on two real case studies for on-line adaptive control and decision making. Aggregation of rule nodes in evolved mEFuNNs can be achieved through fuzzy C-means clustering algorithm which is also illustrated on the bench mark data sets. The regularly trained and aggregated in an on-line, self-organised mode mEFuNNs perform as well, or better, than the mEFuNNs that use fuzzy C-means clustering algorithm for off-line rule node generation on the same data set.
  • Article
    The emerging need for Hybrid Intelligent Systems (HIS) is currently motivating important research and development work. The integration of different learning and adaptation techniques, to overcome individual limitations and achieve synergetic effects through hybridization or fusion of these techniques, has in recent years contributed to a large number of new intelligent system designs. Soft Computing (SC) introduced by Lotfi Zadeh [1] is an innovative approach to construct computationally intelligent hybrid systems consisting of Artificial Neural Network (ANN), Fuzzy Logic (FL), approximate reasoning and derivative free optimization methods such as Genetic Algorithm (GA), Simulated Annealing (SA) and Tabu Search (TS). Most of these approaches, however, follow an ad hoc design methodology, further justified by success in certain application domains. Due to the lack of a common framework it remains often difficult to compare the various hybrid systems conceptually and evaluate their performance comparatively. It has been over a decade since HIS were first applied to solve complicated problems. In this paper, we first aim at classifying state--of--the--art intelligent systems, which have evolved over the past decade in the HIS community. Some theoretical concepts of ANN, FL and Global Optimization Algorithms (GOA) namely GA, SA and TS are also presented. We further attempt to summarize the work that has been done and present the current standing of our vision on HIS and future research directions.