As its name suggests, computing with words (CW) is a methodology
in which words are used in place of numbers for computing and reasoning.
The point of this note is that fuzzy logic plays a pivotal role in CW
and viceversa. Thus, as an approximation, fuzzy logic may be equated to
CW. There are two major imperatives for computing with words. First,
computing with words is a necessity when the available information is
too imprecise to justify the use of numbers, and second, when there is a
tolerance for imprecision which can be exploited to achieve
tractability, robustness, low solution cost, and better rapport with
reality. Exploitation of the tolerance for imprecision is an issue of
central importance in CW. In CW, a word is viewed as a label of a
granule; that is, a fuzzy set of points drawn together by similarity,
with the fuzzy set playing the role of a fuzzy constraint on a variable.
The premises are assumed to be expressed as propositions in a natural
language. In coming years, computing with words is likely to evolve into
a basic methodology in its own right with wideranging ramifications on
both basic and applied levels
Fuzzy system modeling (FSM) is one of the most prominent tools that can be used to identify the behavior of highly nonlinear systems with uncertainty. Conventional FSM techniques utilize type 1 fuzzy sets in order to capture the uncertainty in the system. However, since type 1 fuzzy sets express the belongingness of a crisp value x' of a base variable x in a fuzzy set A by a crisp membership value mu<sub>A</sub>(x'), they cannot fully capture the uncertainties due to imprecision in identifying membership functions. Higher types of fuzzy sets can be a remedy to address this issue. Since, the computational complexity of operations on fuzzy sets are increasing with the increasing type of the fuzzy set, the use of type 2 fuzzy sets and linguistic logical connectives drew a considerable amount of attention in the realm of fuzzy system modeling in the last two decades. In this paper, we propose a blackbox methodology that can identify robust type 2 TakagiSugeno, Mizumoto and Linguistic fuzzy system models with high predictive power. One of the essential problems of type 2 fuzzy system models is computational complexity. In order to remedy this problem, discrete interval valued type 2 fuzzy system models are proposed with type reduction. In the proposed fuzzy system modeling methods, fuzzy Cmeans (FCM) clustering algorithm is used in order to identify the system structure. The proposed discrete interval valued type 2 fuzzy system models are generated by a learning parameter of FCM, known as the level of membership, and its variation over a specific set of values which generate the uncertainty associated with the system structure
Conventional fuzzy inference methodology relates the relevant
subsets of each input universal set to the subsets of the other system
inputs through an intersectionrule configuration. This strategy yields
an exponential growth in the number of rules as inputs are added to the
system, quickly reducing performance to unacceptable levels. A novel
rule configuration and matrix design are presented in this paper that do
not rely on rule multiplication to insure that antecedent elements are
effectively related to their consequent counterparts. This alternative
formulation models the entire system problem space with a simplified
structure that increases linearly as the inference engine grows,
providing significant computational savings to a broad range of
commercial and scientific applications
The digital CMOS 12b fuzzy coprocessor chip SAE 81C991 is
presented. Designed as a fuzzy logic controller, the chip exhibits a
silicon area of 17.9 mm<sup>2</sup> and computation speed in the
submillisecond region. Realtime fuzzy control or classification tasks
in industry electronics, image processing, and automotive are its main
fields of applications. Up to 131072 rules, 4096 inputs, and 1024
outputs with arbitrary membership functions can be processed. The
definition or fuzzy algorithms is facilitated with ten operation modes,
eight inference operators, and four defuzzification methods.
Fuzzification of four 12b inputs, inference of 80 rules, and center of
gravity defuzzification for a 16b output takes only 16 s. This knowledge
base covers only half a kbyte as the memory has to store only the
knowledge base data but almost no operation code for the coprocessor.
Moreover, the membership functions as part of the knowledge base data
are stored with their characteristic values reducing the memory demand
significantly in comparison with a lookup table. Minimized memory
demand and fuzzy algorithms tailored for digital CMOS logic are the key
elements for a small chip area microcontrollers. Interfaces with 8b or
16b microcontrollers are supported
Humancentered information processing has been pioneered by Zadeh through his introduction of the concept of fuzzy sets in the mid 1960s. The insights that were afforded through this formalism have led to the development of the granular computing (GrC) paradigm in the late 1990s. Subsequent research has highlighted the fact that many founding principles of GrC have, in fact, been adopted in other informationprocessing paradigms and, indeed, in the context of various scientific methodologies. This study expands on our earlier research exploring the foundations of GrC and casting it as a structured combination of algorithmic and non algorithmic information processing that mimics human, intelligent synthesis of knowledge from information.
We present an approach for MPEG variable bit rate (VBR) video
modeling and classification using fuzzy techniques. We demonstrate that
a type2 fuzzy membership function, i.e., a Gaussian MF with uncertain
variance, is most appropriate to model the logvalue of I/P/B frame
sizes in MPEG VBR video. The fuzzy cmeans (FCM) method is used to
obtain the mean and standard deviation (std) of T/P/B frame sizes when
the frame category is unknown. We propose to use type2 fuzzy logic
classifiers (FLCs) to classify video traffic using compressed data. Five
fuzzy classifiers and a Bayesian classifier are designed for video
traffic classification, and the fuzzy classifiers are compared against
the Bayesian classifier. Simulation results show that a type2 fuzzy
classifier in which the input is modeled as a type2 fuzzy set and
antecedent membership functions are modeled as type2 fuzzy sets
performs the best of the five classifiers when the testing video product
is not included in the training products and a steepest descent
algorithm is used to tune its parameters
We develop simple but effective fuzzyrule based models of complex
systems from inputoutput data. We introduce a simple fuzzyneural
network for modeling systems, and we prove that it can represent any
continuous function over a compact set. We introduce “fuzzy
curves” and use them to: 1) identify significant input variables,
2) determine model structure, and 3) set the initial weights in the
fuzzyneural network model. Our method for input identification is
computationally simple and, since we determine the proper network
structure and initial weights in advance, we can train the network
rapidly. Viewing the network as a fuzzy model gives insight into the
real system, and it provides a method to simplify the neural network
Robust control has long been the purview of quantitative linear
control techniques, while qualitative symbolic control has been deemed
more suitable to obtaining complex control objectives that require only
lowoutput precision. The intelligent techniques of fuzzy control have,
however, shown promise in obtaining results comparable to those obtained
from H<sub>∞</sub> and H<sub>2</sub> robust control techniques.
Often though, these fuzzy control techniques ignore the original intent
of fuzzy logic: implementation of symbolic linguistic control laws based
on qualitative models of the plant and control behaviors. We show that
robust control objectives, even for simple plants, can be achieved by
first developing qualitative behaviors that stabilize the plant and then
superimposing tracking behaviors that achieve control objectives.
Specifically, by superimposing qualitative stability and tracking
behaviors, we can achieve robustness and tracking stability comparable
to the best published linear compensators for the 1992 ACC robust
control benchmark
Software agents are increasingly being used to represent humans in online auctions. Such agents have the advantages of being able to systematically monitor a wide variety of auctions and then make rapid decisions about what bids to place in what auctions. They can do this continuously and repetitively without losing concentration. To provide a means of evaluating and comparing (benchmarking) research methods in this area the trading agent competition (TAC) was established. This competition involves a number of agents bidding against one another in a number of related auctions (operating different protocols) to purchase travel packages for customers. Against this background, this paper describes the design, implementation and evaluation of SouthamptonTAC, one of the most successful participants in both the Second and the Third International Competitions. Our agent uses fuzzy techniques at the heart of its decision making: to make bidding decisions in the face of uncertainty, to make predictions about the likely outcomes of auctions, and to alter the agent's bidding strategy in response to the prevailing market conditions.
This paper describes a method for fuzzy classification and
recognition of 2D shapes, such as handwritten characters, image
contours, etc. A fuzzy model is derived for each considered shape from a
fuzzy description of a set of instances of this shape. A fuzzy
description of a shape instance, in its turn, exploits appropriate fuzzy
partitions of the two dimensions of the shape. These fuzzy partitions
allow us to identify, and automatically associate an importance degree
with the relevant shape zones for classification and recognition
purposes. Two significant applications of the method are described,
namely, recognition of olfactory signals and recognition of isolated,
handwritten characters. In the former case, results are shown concerning
the recognition of three different types of waste waters, collected in
three different dilutions. In the latter case, results are shown
concerning the application of the method to a NIST database, containing
the segmented handprinted characters of 500 writers
Dependentchance programming (DCP) is a new type of stochastic
programming and has been extended to the area of fuzzy programming. This
paper provides a spectrum of DCP and dependentchance multiobjective
programming (DCMOP) as well as dependentchance goal programming (DCGP)
models with fuzzy rather than crisp decisions. The terms of uncertain
environment, event, chance function, and induced constraints are
discussed in the case of fuzzy decisions. A technique of fuzzy
simulation is also designed for computing chance functions. Finally, we
present a fuzzy simulationbased genetic algorithm for solving these
models and illustrate its effectiveness by some numerical examples
This paper will present a novel concept of expected values of fuzzy variables, which is essentially a type of Choquet integral and coincides with that of random variables. In order to calculate the expected value of general fuzzy variable, a fuzzy simulation technique is also designed. Finally, we construct a spectrum of fuzzy expected value models, and integrate fuzzy simulation, neural network, and genetic algorithms to produce a hybrid intelligent algorithm for solving general fuzzy expected value models.
Autonomous mobile robots navigating in changing and dynamic unstructured environments like the outdoor environments need to cope with large amounts of uncertainties that are inherent of natural environments. The traditional type1 fuzzy logic controller (FLC) using precise type1 fuzzy sets cannot fully handle such uncertainties. A type2 FLC using type2 fuzzy sets can handle such uncertainties to produce a better performance. In this paper, we present a novel reactive control architecture for autonomous mobile robots that is based on type2 FLC to implement the basic navigation behaviors and the coordination between these behaviors to produce a type2 hierarchical FLC. In our experiments, we implemented this type2 architecture in different types of mobile robots navigating in indoor and outdoor unstructured and challenging environments. The type2based control system dealt with the uncertainties facing mobile robots in unstructured environments and resulted in a very good performance that outperformed the type1based control system while achieving a significant rule reduction compared to the type1 system.
The automation of complex industrial batch processes is a
difficult problem due to the extremely nonlinear and variable system
behavior or the conflicting goals within the different process phases.
The introduction of a single multipleinput multipleoutput controller
is not useful because of the rather high design effort and the low
transparency of its complex structure. A more suitable hierarchical
fuzzylogic (FL) based supervisory control concept is proposed. It
permits the decomposition of the complex control problem into a series
of smaller and simpler ones. In the upper level of the hierarchy the
FLbased supervisory controller classifies the actual process phase in
terms of the available process sensor signals and activates dynamically
the appropriate situation specific lowlevel controllers. The paper
presents the generic concept of the FL supervisory controller that
comprises both a FL process diagnosis and a control mode selection as
well as experiences with the industrial application
This paper presents some novel results for stabilizing singularly perturbed (SP) nonlinear systems with guaranteed control performance. By using TakagiSugeno fuzzy model, we construct the SP fuzzy (SPF) systems. The corresponding fuzzy slow and fast subsystems of the original SPF system are also obtained. Two fuzzy control designs are explored. In the first design method, we propose the composite fuzzy control to stabilize the SPF subsystem with H<sup>∞</sup> control performance. Based on the Lyapunov stability theorem, the stability conditions are reduced to the linear matrix inequality (LMI) problem. The composite fuzzy control will stabilize the original SP nonlinear systems for all ε∈(0,ε<sup>*</sup>) and the upper bound ε<sup>*</sup> can be determined. For the second design method, we present a direct fuzzy control scheme to stabilize the SP nonlinear system with H<sup>∞</sup> control performance. By utilizing the Lyapunov stability theorem, the direct fuzzy control can guarantee the stability of the original SP nonlinear systems for a given interval ε∈[ε_,ε~]. The stability conditions are also expressed in the LMIs. Two SP nonlinear systems are adopted to demonstrate the feasibility and effectiveness of the proposed control schemes.
The fuzzy linguistic approach has been applied successfully to
many problems. However, there is a limitation of this approach imposed
by its information representation model and the computation methods used
when fusion processes are performed on linguistic values. This
limitation is the loss of information; this loss of information implies
a lack of precision in the final results from the fusion of linguistic
information. In this paper, we present tools for overcoming this
limitation. The linguistic information is expressed by means of
2tuples, which are composed of a linguistic term and a numeric value
assessed in (0.5, 0.5). This model allows a continuous representation
of the linguistic information on its domain, therefore, it can represent
any counting of information obtained in a aggregation process. We then
develop a computational technique for computing with words without any
loss of information. Finally, different classical aggregation operators
are extended to deal with the 2tuple linguistic model
This paper introduces a new approach for fuzzy interpolation and
extrapolation of sparse rule base comprising of membership functions
with finite number of characteristic points. The approach calls for
representing membership functions as points in highdimensional
Cartesian spaces using the locations of their characteristic points as
coordinates. Hence, a fuzzy rule base can be viewed as a set of mappings
between the antecedent and consequent spaces and the interpolation and
extrapolation problem becomes searching for an image in the consequent
space upon given an antecedent observation. The present approach divides
observations into two groups: 1) observations within the antecedent
spanning set contain the same geometric properties as the given
antecedents; and 2) observations lying outside the antecedent spanning
set contain new geometric properties beyond those of the given rules.
Heuristic reasoning must therefore be applied. In this case, a twostep
approach with certain flexibility to accommodate additional criteria and
design objectives is formulated
The most often used operator to aggregate criteria in decision
making problems is the classical weighted arithmetic mean. However, in
many problems the criteria considered interact and a substitute to the
weighted arithmetic mean has to be adopted. We show that, under rather
natural conditions, the discrete Choquet integral is an adequate
aggregation operator that extends the weighted arithmetic mean by taking
into consideration of the interaction among criteria. The axiomatic that
supports the Choquet integral is presented and an intuitive approach is
proposed as well
This paper makes type2 fuzzy logic systems much more accessible to fuzzy logic system designers, because it provides mathematical formulas and computational flowcharts for computing the derivatives that are needed to implement steepestdescent parameter tuning algorithms for such systems. It explains why computing such derivatives is much more challenging than it is for a type1 fuzzy logic system. It provides derivative calculations that are applicable to any kind of type2 membership functions, since the calculations are performed without prespecifying the nature of those membership functions. Some calculations are then illustrated for specific type2 membership functions.
We developed three linguistic statements to describe user information desires in a battlefield information environment. These rules are based on enduser interest in each track report generated from radars across the battlefield. Along with these rules of user interest, a linguistic statement describing communications systems capabilities at each node was created. These linguistic statements were converted to fuzzy variables and these variables were used as network control devices in a simulation model. The model results show that effective communications control can be exercised by these simple rules
Antiblocking system (ABS) brake controllers pose unique
challenges to the designer: a) For optimal performance, the controller
must operate at an unstable equilibrium point, b) Depending on road
conditions, the maximum braking torque may vary over a wide range, c)
The tire slippage measurement signal, crucial for controller
performance, is both highly uncertain and noisy, d) On rough roads, the
tire slip ratio varies widely and rapidly due to tire bouncing, and e)
The braking system contains transportation delays which limit the
control system bandwidth. A digital controller design was chosen which
combines a fuzzy logic element and a decision logic network. The
controller identifies the current road condition and generates a command
braking pressure signal, based on current and past readings of the slip
ratio and brake pressure. The controller detects wheel blockage
immediately and avoids excessive slipping. The ABS system performance is
examined on a quarter vehicle model with nonlinear elastic suspension.
The parallelity of the fuzzy logic evaluation process ensures rapid
computation of the controller output signal, requiring less time and
fewer computation steps than controllers with adaptive identification.
The robustness of the braking system is investigated on rough roads and
in the presence of large measurement noise. This paper describes design
criteria, and the decision and rule structure of the control system. The
simulation results present the system's performance on various road
types and under rapidly changing road conditions
In literature, the optimization model with a linear objective function subject to fuzzy relation equations has been converted into a 01 integer programming problem by Fang and Li (1999). They proposed a jumptracking branchandbound method to solve this 01 integer programming problem. In this paper, we propose an upper bound for the optimal objective value. Based on this upper bound and rearranging the structure of the problem, we present a backward jumptracking branchandbound scheme for solving this optimization problem. A numerical example is provided to illustrate our scheme. Furthermore, testing examples show that the performance of our scheme is superior to the procedure in the paper by Fang and Li. Several testing examples show that our initial upper bound is sharp.
This paper addresses the problem of integrated robust fault estimation (FE) and accommodation for discretetime TakagiSugeno (TS) fuzzy systems. First, a multiconstrained reducedorder FE observer (RFEO) is proposed to achieve FE for discretetime TS fuzzy models with actuator faults. Based on the RFEO, a new fault estimator is constructed. Then, using the information of online FE, a new approach for fault accommodation based on fuzzydynamic output feedback is designed to compensate for the effect of faults by stabilizing the closedloop systems. Moreover, the RFEO and the dynamic output feedback faulttolerant controller are designed separately, such that their design parameters can be calculated readily. Simulation results are presented to illustrate our contributions.
This paper describes how we applied a fuzzy technique to a datamining task involving a large database that was provided by an international bank with offices in Hong Kong. The database contains the demographic data of over 320,000 customers and their banking transactions, which were collected over a sixmonth period. By mining the database, the bank would like to be able to discover interesting patterns in the data. The bank expected that the hidden patterns would reveal different characteristics about different customers so that they could better serve and retain them. To help the bank achieve its goal, we developed a fuzzy technique, called fuzzy association rule mining II (FARM II). FARM II is able to handle both relational and transactional data. It can also handle fuzzy data. The former type of data allows FARM II to discover multidimensional association rules, whereas the latter data allows some of the patterns to be more easily revealed and expressed. To effectively uncover the hidden associations in the bankaccount database, FARM II performs several steps which are described in detail in this paper. With FARM II, the bank discovered that they had identified some interesting characteristics about the customers who had once used the bank's loan services but then decided later to cease using them. The bank translated what they discovered into actionable items by offering some incentives to retain their existing customers.
In our opinion, there are two main concerns in Roubos and Babugka's note, that are summarized as follows. 1) The kinds of problems used in our paper to test the algorithm proposed in "A proposal to improve the accuracy of linguistic modeling" and other studies. The authors claim that they are very simple to be considered as benchmarks for nonlinear modeling techniques. 2) The interpretability of the different kinds of models considered. Roubos and Babuska think that there is no difference between the interpretability of fuzzy linguistic models, TakagiSugenoKang (TSK) fuzzy models, and mathematical formulations (linear models, in this case). We agree with some of the opinions of the authors of the note but not with some others.
Many methods have been proposed in the literature for designing
fuzzy systems from inputoutput data (the socalled neurofuzzy
methods), but very little was done to analyze the performance of the
methods from a rigorous mathematical point of view. In this paper, we
establish approximation bounds for two of these methods  the table
lookup scheme proposed by Wang et al. (1992) and the clustering method
studied by Wang (1993, 1997). We derive detailed formulas of the error
bounds between the nonlinear function to be approximated and the fuzzy
systems designed using the methods based on inputoutput data. These
error bounds show explicitly how the parameters in the two methods
influence their approximation capability. We also propose modified
versions for the two methods such that the designed fuzzy systems are
welldefined over the whole input domain
Although the induction of fuzzy decision tree (FDT) has been a
very popular learning methodology due to its advantage of
comprehensibility, it is often criticized to result in poor learning
accuracy. Thus, one fundamental problem is how to improve the learning
accuracy while the comprehensibility is kept. This paper focuses on this
problem and proposes using a hybrid neural network (HNN) to refine the
FDT. This HNN, designed according to the generated FDT and trained by an
algorithm derived in this paper, results in a FDT with parameters,
called weighted FDT. The weighted FDT is equivalent to a set of fuzzy
production rules with local weights (LW) and global weights (GW)
introduced in our previous work (1998). Moreover, the weighted FDT, in
which the reasoning mechanism incorporates the trained LW and GW,
significantly improves the FDTs' learning accuracy while keeping the FDT
comprehensibility. The improvements are verified on several selected
databases. Furthermore, a brief comparison of our method with two
benchmark learning algorithms, namely, fuzzy ID3 and traditional
backpropagation, is made. The synergy between FDT induction and HNN
training offers new insight into the construction of hybrid intelligent
systems with higher learning accuracy
We propose accurate linguistic modeling, a methodology to design
linguistic models that are accurate to a high degree and may be suitably
interpreted. This approach is based on two main assumptions related to
the interpolative reasoning developed by fuzzy rulebased systems: a
small change in the structure of the linguistic model based on allowing
the linguistic rule to have two consequents associated; and a different
way to obtain the knowledge base based on generating a preliminary fuzzy
rule set composed of a large number of rules and then selecting the
subset of them best cooperating. Moreover, we introduce two variants of
an automatic design method for these kinds of linguistic models based on
two wellknown inductive fuzzy rule generation processes and a genetic
process for selecting rules. The accuracy of the proposed methods is
compared with other linguistic modeling techniques with different
characteristics when solving of three different applications
In the above paper by Cordon and Herrara (IEEE Trans. Fuzzy Syst., vol. 8, p. 33544, 2000), the socalled accurate linguistic modeling (ALM) method was proposed to improve the accuracy of linguistic fuzzy models. A number of examples are given to demonstrate the benefits of the approach. We show that: 1) these examples are not suitable as benchmarks or demonstrators of nonlinear modeling techniques and 2) better results can be obtained by using both standard regression tools as well as other fuzzy modeling techniques. We argue that benchmark examples that are used in articles to demonstrate the effectiveness of fuzzy modeling techniques should be selected with great care. Critical analysis of the results should be made and linear models should be regarded as a lower bound on the acceptable performance.
Typical digit recognizers classify an unknown digit pattern by
computing its distance from the cluster centers in a feature space. In
this paper, we propose a methodology that has many salient aspects.
First, the classification rule is dependent on the
“difficulty” of the unknown sample. Samples
“far” from the center, which tend to fall on the boundaries
of classes are error prone and, hence, “difficult”. An
“overlapping zone” is defined in the feature space to
identify such difficult samples. A table is precomputed to facilitate an
efficient lookup of the class corresponding to all the points in the
overlapping zone. The lookup function itself is defined by a
modification of the KNN rule. A characteristic function defining the new
boundaries is computed using the topology of the set of samples in the
overlapping zones. Our twopronged approach uses different
classification schemes with the “difficult” and
“easy” samples. The method described has improved the
performance of the gradient structural concavity digit recognizer
described by Favata et al. (1996)
This paper establishes the approximation error bounds for various
classes of fuzzy systems (i.e., fuzzy systems generated by different
inferential and defuzzification methods). Based on these bounds, the
approximation accuracy of various classes of fuzzy systems is analyzed
and compared. It is seen that the class of fuzzy systems generated by
the product inference and the centeraverage defuzzifier has better
approximation accuracy and properties than the class of fuzzy systems
generated by the min inference and the centeraverage defuzzifier, and
the class of fuzzy systems defuzzified by the MoM defuzzifier. In
addition, it is proved that fuzzy systems can represent any linear and
multilinear function and explicit expressions of fuzzy systems generated
by the MoM defuzzified method are given
Clustering is a useful approach in image segmentation, data mining, and other pattern recognition problems for which unlabeled data exist. Fuzzy clustering using fuzzy cmeans or variants of it can provide a data partition that is both better and more meaningful than hard clustering approaches. The clustering process can be quite slow when there are many objects or patterns to be clustered. This paper discusses the algorithm brFCM, which is able to reduce the number of distinct patterns which must be clustered without adversely affecting the partition quality. The reduction is done by aggregating similar examples and then using a weighted exemplar in the clustering process. The reduction in the amount of clustering data allows a partition of the data to be produced faster. The algorithm is applied to the problem of segmenting 32 magnetic resonance images into different tissue types and the problem of segmenting 172 infrared images into trees, grass and target. Average speedups of as much as 59290 times a traditional implementation of fuzzy cmeans were obtained using brFCM, while producing partitions that are equivalent to those produced by fuzzy cmeans.
A novel thresholdingbased segmentation approach for accurate segmentation of pigmented skin lesion images regarding malignant melanoma diagnosis has been proposed. The presented approach utilizes type2 fuzzy logic techniques for automatic threshold determination. The method is applied on various clinically obtained lesion images, and the results are compared with those obtained with two other popular methods from the literature. It is observed that the presented method exhibits superior performance over competing methods and is very successful at handling the uncertainty encountered in determining the border between the lesion and the skin.
In this paper, we demonstrate, through the multicategory classification of battlefield ground vehicles using acoustic features, how it is straightforward to directly exploit the information inherent in a problem to determine the number of rules, and subsequently the architecture, of fuzzy logic rulebased classifiers (FLRBC). We propose three FLRBC architectures, one nonhierarchical and two hierarchical (HFLRBC), conduct experiments to evaluate the performances of these architectures, and compare them to a Bayesian classifier. Our experimental results show that: 1) for each classifier the performance in the adaptive mode that uses simple majority voting is much better than in the nonadaptive mode; 2) all FLRBCs perform substantially better than the Bayesian classifier; 3) interval type2 (T2) FLRBCs perform better than their competing type1 (T1) FLRBCs, although sometimes not by much; 4) the interval T2 nonhierarchical and HFLRBCseries architectures perform the best; and 5) all FLRBCs achieve higher than the acceptable 80% classification accuracy
In this paper, we develop a technique for acquiring the finite set of attributes or variables which the expert uses in a classification problem for characterising and discriminating a set of elements. This set will constitute the schema of a training data set to which an inductive learning algorithm will be applied. The technique developed uses ideas taken from psychology, in particular from Kelly's Personal Construct Theory. While we agree that Kelly's repertory grid technique is an efficient way to do this, it has several disadvantages which we shall try to solve by using a fuzzy repertory table. With the suggested technique, we aim to obtain the set of attributes and values which the expert can use to "measure" the object type (class) on the classification problem in some way. We will also acquire some general rules to identify the expert's evident knowledge; these rules will comprise concepts belonging to their conceptual structure.
Knowledge acquisition is a longstanding problem in fuzzyrulebased systems. In spite of the existence of several approaches, much effort is still required to increase the efficiency of the learning process. This study introduces a new method for the fuzzyrule evolution that forms an expert system knowledge: the knowledge acquisition with a swarmintelligence approach (KASIA). Specifically, this strategy is based on the use of particleswarm optimization (PSO) to obtain the antecedents, consequences, and connectives of the rules. To test the feasibility of the suggested method, the invertedpendulum problem is studied, and results are compared for two of the most extensively used methodologies in machine learning: the geneticbased Pittsburgh approach and the Qlearningbased strategy, i.e., stateactionrewardstateaction (SARSA). Moreover, KASIA is analyzed as a learning strategy in fuzzyrulebased metascheduler design for grid computing, and performance is compared with other scheduling strategies based on genetic learning and existing scheduling approaches, i.e., EASYbackfilling and ESG+local periodical search. To be more precise, simulation results prove the fact that the proposed strategy outperforms classical learning approaches in terms of final results and computational effort. Furthermore, the main advantage is the capability to control convergence and its simplicity.
Proposes a fourlayered adaptive fuzzy command acquisition network
(AFCAN) for adaptively acquiring fuzzy command via interactions with the
user or environment. It can catch the intended information from a
sentence (command) given in natural language with fuzzy predicates. The
intended information includes a meaningful semantic action and the fuzzy
linguistic information of that action. The proposed AFCAN has three
important features. First, we can make no restrictions whatever on the
fuzzy command input, which is used to specify the desired information,
and the network requires no acoustic, prosodic, grammar, and syntactic
structure, Second, the linguistic information of an action is learned
adaptively and it is represented by fuzzy numbers based on αlevel
sets. Third, the network can learn during the course of performing the
task. The AFCAN can perform offline as well as online learning. For the
offline learning, the mutualinformation (MI) supervised learning
scheme and the fuzzy backpropagation (FBP) learning scheme are employed
when the training data are available in advance. The former learning
scheme is used to learn meaningful semantic actions and the latter learn
linguistic information. The AFCAN can also perform online learning
interactively when it is in use for fuzzy command acquisition. For the
online learning, the MIreinforcement learning scheme and the fuzzy
reinforcement learning scheme are developed for the online learning of
meaningful actions and linguistic information, respectively. An
experimental system is constructed to illustrate the performance and
applicability of the proposed AFCAN
The procedure for acquiring control rules to improve the
performance of control systems has received considerable attention
previously. This paper deals with a collision avoidance problem in which
the controlled object is a ship with inertia which must avoid collision
with a moving object. It has proven to be difficult to obtain collision
avoidance rules, i.e., steering rules and speed control rules, which
coincide with the operator's knowledge. This paper shows that rules of
this type can be acquired directly from observational data using fuzzy
neural networks (FNNs). This paper also shows that the FNN can obtain
portions of the fuzzy rules for the inferences of the static and dynamic
degrees of danger and the decision table based on the degrees of danger
to avoid the moving obstacle
Intelligent congestion control is vital for encoded video streaming of a clip or film, as network traffic volatility and the associated uncertainties require constant adjustment of the bit rate. Existing solutions, including the standard transmission control protocol (TCP) friendly rate control equationbased congestion controller, are prone to fluctuations in their sending rate and may respond only when packet loss has already occurred. This is a major problem, because both fluctuations and packet loss affect the enduser's perception of the delivered video. A type1 (T1) fuzzy logic congestion controller (FLC) can operate at video display rates and can reduce packet loss and rate fluctuations, despite uncertainties in measurements of delay arising from congestion and network traffic volatility. However, a T1 FLC employing precise T1 fuzzy sets cannot fully cope with the uncertainties associated with such dynamic network environments. A type2 FLC using type2 fuzzy sets can handle such uncertainties to produce improved performance. This paper proposes an interval type2 FLC that achieves a superior delivered video quality compared with existing traditional controllers and a T1 FLC. To show the response in different network scenarios, tests demonstrate the response both in the presence of typical Internet crosstraffic as well as when other video streams occupy a bottleneck on an AllInternet protocol (IP) network. As AllIP networks are intended for multimedia traffic, it is important to develop a form of congestion control that can transfer to them from the mixed traffic environment of the Internet. It was found that the proposed type2 FLC, although it is specifically designed for Internet conditions, can also successfully react to the network conditions of an AllIP network. When the control inputs were subject to noise, the type2 FLC resulted in an order of magnitude performance improvement in comparison with the T1 FLC. The type2 FLC also showed reduced pa

cket loss when compared with the other controllers, again resulting in superior delivered video quality. When judged by established criteria, such as TCPfriendliness and delayed feedback, fuzzy logic congestion control offers a flexible solution to network bottlenecks. These findings offer the type2 FLC as a way forward for congestion control of video streaming across packetswitched IP networks.
This paper provides the first convergence proof for fuzzy reinforcement learning (FRL) as well as experimental results supporting our analysis. We extend the work of Konda and Tsitsiklis, who presented a convergent actorcritic (AC) algorithm for a general parameterized actor. In our work we prove that a fuzzy rulebase actor satisfies the necessary conditions that guarantee the convergence of its parameters to a local optimum. Our fuzzy rulebase uses TakagiSugenoKang rules, Gaussian membership functions, and product inference. As an application domain, we chose a difficult task of power control in wireless transmitters, characterized by delayed rewards and a high degree of stochasticity. To the best of our knowledge, no reinforcement learning algorithms have been previously applied to this task. Our simulation results show that the ACFRL algorithm consistently converges in this domain to a locally optimal policy.
In this paper, a TakagiSugenoKangtype fuzzyneuralnetwork control (TFNNC) scheme is constructed for an nlink robot manipulator to achieve highprecision position tracking. According to the concepts of mechanical geometry and motion dynamics, the dynamic model of an nlink robot manipulator including actuator dynamics is introduced initially. However, it is difficult to design a suitable modelbased control scheme due to the uncertainties in practical applications, such as friction forces, external disturbances and parameter variations. In order to cope with this problem, a TFNNC system without the requirement of prior system information and auxiliary control design is investigated to the joint position control of an nlink robot manipulator for periodic motion. In this modelfree control scheme, a fivelayer fuzzyneuralnetwork is utilized for the major control role, and the adaptive tuning laws of network parameters are established in the sense of projection algorithm and Lyapunov stability theorem to ensure the network convergence as well as stable control performance. In addition, experimental results of a twolink robot manipulator actuated by dc servomotors are provided to verify the effectiveness and robustness of the proposed TFNNC methodology.
This paper is concerned with the design of reliable H<sub>infin </sub> fuzzy controllers for continuoustime nonlinear systems with actuator failures. The Takagi and Sugeno fuzzy model is employed to represent a nonlinear system. The objective is to find a stabilizing statefeedback fuzzy controller such that the nominal H<sub>infin</sub> performance is optimized while satisfying a prescribed H<sub>infin</sub> performance constraint in the actuator failure cases. Based on the linear matrix inequality (LMI) techniques, two efficient methods for the design of a suboptimal reliable H<sub>infin</sub> fuzzy controller are proposed. Different Lyapunov functions are used during the design for the nominal and actuator failure cases, which lead to a less conservative controller design. In the first method, a single Lyapunov function is used for the actuator failure cases. The second method adopts a parameterdependent Lyapunov function for the actuator failure cases, which further reduces the conservatism of the design. Finally, numerical simulations on the chaotic Rossler system are given to illustrate the effectiveness of the proposed design methods
This paper addresses the problem of robust fault estimation and fault tolerant control (FTC) for TakagiSugeno (TS) fuzzy systems. A fuzzyaugmented fault estimation observer (AFEO) design is proposed to achieve fault estimation of TS models with actuator faults. Furthermore, based on the information of online fault estimation, an observerbased dynamic output feedbackfault tolerant controller (DOFFTC) is designed to compensate for the effect of faults by stabilizing the closedloop system. Sufficient conditions for the existence of both AFEO and DOFFTC are given in terms of linear matrix inequalities. Simulation results of an inverted pendulum system are presented to illustrate the effectiveness of the proposed method.
In this paper, a piezoelectric actuator (PEA) system is approximated by N subsystems, which are described by pulse transfer functions. The approximation error between the PEA system and the fuzzy linear pulse transfer function system is represented by additive nonlinear timevarying uncertainties in every subsystem. First, a deadbeat to the switching surface for every ideal subsystem is designed. It is called the "variable structure tracking control". The output disturbance of the ith subsystem is caused by the approximation error of fuzzymodel and the interaction dynamics resulting from other subsystems. In general, it is not small. Then, the H<sup>∞</sup>norm of the sensitivity function between the switching surface and the output disturbance is minimized. It is the "optimal robustness". Although the effect of the output disturbance is attenuated, a better performance can be reinforced by a switching control which is based on the Lyapunov redesign. This is the final step for the robustness design of control, which is "reinforced robustness". The stability of the overall system is verified by Lyapunov stability theory. Experimental work of a PEA system was carried out to confirm the validity of the proposed control.
This paper extends the possibilistic approach to instancebased
reasoning that has recently been developed in a companion paper. Within
the framework of this approach, the similarityguided extrapolation
principle underlying instancebased learning is formalized by means of
socalled possibility rules, a special type of fuzzy rules. Proceeding
from this idea, a methodology has been outlined, which allows a human
expert to specify a model of the inference mechanism in a linguistic
way. In this paper, a method for adapting a linguistic model
automatically to observed data is proposed. This extension frees the
expert from specifying mathematical concepts such as similarity measures
and membership functions of fuzzy sets precisely. Rather, the expert
determines only the qualitative structure of the model, which is then
"calibrated" bit using the cases stored in memory
This paper presents an adaptive control architecture, where
evolutionary learning is applied for initial learning and realtime
tuning of a fuzzy logic controller. The initial learning phase involves
identification of an artificial neural network model of the process and
subsequent development of a fuzzy controller with parameters obtained
via a genetic search. The neural network model is utilized for
evaluating trial fuzzy controllers during the genetic search. The
proposed adaptive mechanism is based on the concept of perpetual
evolution, where parameters of the fuzzy controller are updated at each
time step with solutions extracted from a continuously evolving
population of trials. There are two mechanisms that accommodate the
realtime changes in the control task and/or the process into the
continuous genetic search: a scheme that dynamically modifies the
fitness evaluation criteria of the genetic algorithm, and an online
learning of the neural network model used for evaluating the trial
controllers. The potential of using evolutionary learning for realtime
adaptive control is illustrated through computer simulations, where the
proposed technique is applied to a chemical process control
problem
In this study, a novel fuzzy controller, which is able to selfdesign from scratch, while working online, is proposed. The controller does not use the information regarding the differential equations that govern the plant's behavior or any of their bounds. The algorithm presented is able to determine the mostadequate topology for the fuzzy controller based on the data obtained during the system's normal operation. Therefore, the controller can start operating with an empty set of fuzzy rules and needs no offline training. The proposed methodology comprises two phases: adaptation of the consequents for every selected topology and online addition of new membership functions (MFs). Some of the main advantages of this method are its robustness under changes on the plant's dynamics, good performance in noisy situations, and the ability to perform variable selection among a group of candidate variables. Unlike other online methods, the modification of the topology is based on the analysis of the whole operating region of the plant, thus providing higher robustness. Several simulation examples are used to show these features.
In this paper, an evolutionbased approach to design of neural
fuzzy networks is presented. The proposed strategy optimizes the whole
fuzzy system with minimum rule number according to given specifications,
while training the network parameters. The approach relies on an
optimization tool, which combines evolution strategies and simulated
annealing algorithms in finding the global optimum solution. The
optimization variables include membership function parameters and rule
numbers which are combined with genetic parameters to create diversity
in the search space due to selfadaptation. The optimization technique
is independent of the topology under consideration and capable of
handling any type of membership function. The algorithmic details of the
optimization methodology are discussed in detail, and the generality of
the approach is illustrated by different examples