Showing papers in "IEEE Transactions on Fuzzy Systems in 1996"

Fuzzy logic = computing with words

Abstract: 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 vice-versa. 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 wide-ranging ramifications on both basic and applied levels.

An approach to fuzzy control of nonlinear systems: stability and design issues

Abstract: Presents a design methodology for stabilization of a class of nonlinear systems. First, the authors represent a nonlinear plant with a Takagi-Sugeno fuzzy model. Then a model-based fuzzy controller design utilizing the concept of the so-called "parallel distributed compensation" is employed. The main idea of the controller design is to derive each control rule so as to compensate each rule of a fuzzy system. The design procedure is conceptually simple and natural. Moreover, the stability analysis and control design problems can be reduced to linear matrix inequality (LMI) problems. Therefore, they can be solved efficiently in practice by convex programming techniques for LMIs. The design methodology is illustrated by application to the problem of balancing and swing-up of an inverted pendulum on a cart.

Comments on "Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: quadratic stabilizability, H/sup /spl infin// control theory, and linear matrix inequalities"

Abstract: This paper presents stability analysis for a class of uncertain nonlinear systems and a method for designing robust fuzzy controllers to stabilize the uncertain nonlinear systems, First, a stability condition for Takagi and Sugeno's fuzzy model is given in terms of Lyapunov stability theory. Next, new stability conditions for a generalized class of uncertain systems are derived from robust control techniques such as quadratic stabilization, H/sup /spl infin// control theory, and linear matrix inequalities. The derived stability conditions are used to analyze the stability of Takagi and Sugeno's fuzzy control systems with uncertainty which can be regarded as a generalized class of uncertain nonlinear systems, The design method employs the so-called parallel distributed compensation, important issues for the stability analysis and design are remarked. Finally, three design examples of fuzzy controllers for stabilizing nonlinear systems and uncertain nonlinear systems are presented.

H/sup /spl infin// tracking design of uncertain nonlinear SISO systems: adaptive fuzzy approach

Abstract: A fuzzy logic controller equipped with a training (adaptive) algorithm is proposed in this work to achieve H/sup /spl infin// tracking performance for a class of uncertain (model free) nonlinear single-input single-output (SISO) systems with external disturbances. An attempt is also made to create a bridge between two important control design techniques, i.e., H/sup /spl infin// control design and fuzzy control design, so as to supply H/sup /spl infin// control design with more intelligence and fuzzy control design with better performance. The perfect matching of parameters in an adaptive fuzzy logic system is generally deemed impossible. Therefore, a desired tracking performance cannot be guaranteed in the conventional adaptive fuzzy control systems. In this study, the influence of both fuzzy logic approximation error and external disturbance on the tracking error is attenuated to a prescribed level. Both indirect and direct adaptive fuzzy controllers are employed to treat this H/sup /spl infin// tracking problem. The authors' results indicate that arbitrarily small attenuation level can be achieved via the proposed adaptive fuzzy control algorithm if a weighting factor of control variable is adequately chosen. The proposed design method is also useful for the robust tracking control design of the nonlinear systems with external disturbances and a large uncertainty or unknown variation in plant parameters and structures. Furthermore, only smooth control signals are needed via the proposed control designs. Two simulation examples are given finally to illustrate the performance of the proposed methods. Computer simulation results confirm that the effect of both the fuzzy approximation error and external disturbance on the tracking error can be attenuated efficiently by the proposed method.

The possibilistic C-means algorithm: insights and recommendations

Abstract: Recently, the possibilistic C-means algorithm (PCM) was proposed to address the drawbacks associated with the constrained memberships used in algorithms such as the fuzzy C-means (FCM). In this issue, Barni et al. (1996) report a difficulty they faced while applying the PCM, and note that it exhibits an undesirable tendency to converge to coincidental clusters. The purpose of this paper is not just to address the issues raised by Barni et al., but to go further and analytically examines the underlying principles of the PCM and the possibilistic approach, in general. We analyze the data sets used by Barni et al. and interpret the results reported by them in the light of our findings.

Stable adaptive control using fuzzy systems and neural networks

Abstract: Stable direct and indirect adaptive controllers are presented, which use Takagi-Sugeno fuzzy systems, conventional fuzzy systems, or a class of neural networks to provide asymptotic tracking of a reference signal for a class of continuous-time nonlinear plants with poorly understood dynamics The indirect adaptive scheme allows for the inclusion of a priori knowledge about the plant dynamics in terms of exact mathematical equations or linguistics while the direct adaptive scheme allows for the incorporation of such a priori knowledge in specifying the controller We prove that with or without such knowledge both adaptive schemes can "learn" how to control the plant, provide for bounded internal signals, and achieve asymptotically stable tracking of a reference input In addition, for the direct adaptive scheme a technique is presented in which linguistic knowledge of the inverse dynamics of the plant may be used to accelerate adaptation The performance of the indirect and direct adaptive schemes is demonstrated through the longitudinal control of an automobile within an automated lane

Validity-guided (re)clustering with applications to image segmentation

Abstract: When clustering algorithms are applied to image segmentation, the goal is to solve a classification problem. However, these algorithms do not directly optimize classification duality. As a result, they are susceptible to two problems: 1) the criterion they optimize may not be a good estimator of "true" classification quality, and 2) they often admit many (suboptimal) solutions. This paper introduces an algorithm that uses cluster validity to mitigate problems 1 and 2. The validity-guided (re)clustering (VGC) algorithm uses cluster-validity information to guide a fuzzy (re)clustering process toward better solutions. It starts with a partition generated by a soft or fuzzy clustering algorithm. Then it iteratively alters the partition by applying (novel) split-and-merge operations to the clusters. Partition modifications that result in improved partition validity are retained. VGC is tested on both synthetic and real-world data. For magnetic resonance image (MRI) segmentation, evaluations by radiologists show that VGC outperforms the (unsupervised) fuzzy c-means algorithm, and VGC's performance approaches that of the (supervised) k-nearest-neighbors algorithm.

Adaptive fuzzy rule-based classification systems

Abstract: This paper proposes an adaptive method to construct a fuzzy rule-based classification system with high performance for pattern classification problems. The proposed method consists of two procedures: an error correction-based learning procedure, and an additional learning procedure. The error correction-based learning procedure adjusts the grade of certainty of each fuzzy rule by its classification performance. That is, when a pattern is misclassified by a particular fuzzy rule, the grade of certainty of that rule is decreased. On the contrary, when a pattern is correctly classified, the grade of certainty is increased. Because the error correction-based learning procedure is not meaningful after all the given patterns are correctly classified, we cannot adjust a classification boundary in such a case. To acquire a more intuitively acceptable boundary, we propose an additional learning procedure. We also propose a method for selecting significant fuzzy rules by pruning unnecessary fuzzy rules, which consists of the error correction-based learning procedure and the concept of forgetting. We can construct a compact fuzzy rule-based classification system with high performance.

Comments on "A possibilistic approach to clustering"

Abstract: In this comment, we report a difficulty with the-application of the possibilistic approach to fuzzy clustering (PCM) proposed by Keller and Krishnapuram (1993). In applying this algorithm we found that it has the undesirable tendency to produce coincidental clusters. Results illustrating this tendency are reported and a possible explanation for the PCM behavior is suggested.

Approximation accuracy analysis of fuzzy systems as function approximators

Abstract: 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 center-average defuzzifier has better approximation accuracy and properties than the class of fuzzy systems generated by the min inference and the center-average 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.

A parametric model for fusing heterogeneous fuzzy data

Abstract: Presented is a model that integrates three data types (numbers, intervals, and linguistic assessments). Data of these three types come from a variety of sensors. One objective of sensor-fusion models is to provide a common framework for data integration, processing, and interpretation. That is what our model does. We use a small set of artificial data to illustrate how problems as diverse as feature analysis, clustering, cluster validity, and prototype classifier design can all be formulated and attacked with standard methods once the data are converted to the generalized coordinates of our model. The effects of reparameterization on computational outputs are discussed. Numerical examples illustrate that the proposed model affords a natural way to approach problems which involve mixed data types.

Handling uncertainty with possibility theory and fuzzy sets in a satellite fault diagnosis application

Abstract: The fault mode effects and criticality analyses (FMECA) describe the impact of identified faults. They form an important category of knowledge gathered during the design phase of a satellite and are used also for diagnosis activities. This paper proposes their extension, allowing a finer representation of the available knowledge, at approximately the same cost, through the introduction of an appropriate representation of uncertainty and incompleteness based on Zadeh's possibility theory and fuzzy sets. The main benefit of the approach is to provide a qualitative treatment of uncertainty where we can for instance distinguish manifestations which are more or less certainly present (or absent) and manifestations which are more or less possibly present (or absent) when a given fault is present. In a second step, the proposed approach is extended to handle fault impacts expressed as event chronologies. Efficient, real-time compatible discrimination techniques exploiting uncertain observations are introduced, and an example of satellite fault diagnosis illustrates the method. A brief rationale for the choice of possibility theory and fuzzy sets is provided.

Design and application of an analog fuzzy logic controller

Abstract: In this paper, we present an analog fuzzy logic hardware implementation and its application to an autonomous mobile system. With a simple structure the fabricated fuzzy controller shows good performance in processing speed and area consumption. Accomplished with 13 reconfigurable rules, a speed of up to 6 MFLIPS has been achieved. To stress the advantages of the new architecture, speed and flexibility, the same control strategy is implemented on the new analog fuzzy controller and on a digital multipurpose microcontroller in software. The results of the two implementations show that the analog approach is not only faster but also flexible enough to compete with digital fuzzy approaches.

Digital fuzzy logic controller: design and implementation

Abstract: In this paper, various aspects of digital fuzzy logic controller (FLC) design and implementation are discussed, Classic and improved models of the single-input single-output (SISO), multiple-input single-output (MISC), and multiple-input multiple-output (MIMO) FLCs are analyzed in terms of hardware cost and performance. A set of universal parameters to characterize any hardware realization of digital FLCs is defined. The comparative study of classic and alternative MIMO FLCs is presented as a generalization of other controller configurations. A processing element for the parallel FLC architecture realizing improved inferencing of MIMO system is designed, characterized, and tested. Finally, as a case feasibility study, a direct data stream architecture for complete digital fuzzy controller is shown as an improved solution for high-speed, cost-effective, real-time control applications.

A reasoning algorithm for high-level fuzzy Petri nets

Abstract: We introduce an automated procedure for extracting information from knowledge bases that contain fuzzy production rules. The knowledge bases considered here are modeled using the high-level fuzzy Petri nets proposed by the authors in the past. Extensions to the high-level fuzzy Petri net model are given to include the representation of partial sources of information. The case of rules with more than one variable in the consequent is also discussed. A reasoning algorithm based on the high-level fuzzy Petri net model is presented. The algorithm consists of the extraction of a subnet and an evaluation process. In the evaluation process, several fuzzy inference methods can be applied. The proposed algorithm is similar to another procedure suggested by Yager (1983), with advantages concerning the knowledge-base searching when gathering the relevant information to answer a particular kind of query.

Uncertainty management issues in the object-oriented data model

Abstract: This paper fully develops a previous approach by George et al. (1993) to modeling uncertainty in class hierarchies. The model utilizes fuzzy logic to generalize equality to similarity which permitted impreciseness in data to be represented by uncertainty in classification. In this paper, the data model is formally defined and a nonredundancy preserving primitive operator, the merge, is described. It is proven that nonredundancy is always preserved in the model. An object algebra is proposed, and transformations that preserve query equality are discussed.

On fuzzy associative memory with multiple-rule storage capacity

Abstract: Kosko's fuzzy associative memory (FAM) is the very first neural network model for implementing fuzzy systems. Despite its success in various applications, the model suffers from very low storage capacity, i.e., one rule per FAM matrix. A lot of hardware and computations are usually required to implement the model and, hence, it is limited to applications with small fuzzy rule-base. In this paper, the inherent property for storing multiple rules in a FAM matrix is identified. A theorem for perfect recalls of all the stored rules is established and based upon which the hardware and computation requirements of the FAM model can be reduced significantly. Furthermore, we have shown that when the FAM model is generalized to the one with max-bounded-product composition, single matrix implementation is possible if the rule-base is a set of semi-overlapped fuzzy rules. Rule modification schemes are also developed and the inference performance of the established high capacity models is reported through a numerical example.

Fuzzy modeling and analytic hierarchy processing to quantify risk levels associated with occupational injuries. I. The development of fuzzy-linguistic risk levels

Abstract: This paper presents the Part I in a two-phase research project to develop a fuzzy-linguistic expert system for quantifying and predicting the risk of occupational injury, specifically, cumulative trauma disorders of the forearm and hand. This aspect of the research focuses on the development and representation of linguistic variables to qualify risk levels. These variables are then quantified using fuzzy-set theory, thus allowing the model to evaluate qualitative and quantitative data. These linguistic risk variables may be applied to other potentially hazardous environments. The three phases of the knowledge acquisition and variable development are covered, as well as the feasibility of the linguistic variables.

A 12b general-purpose fuzzy logic controller chip

Abstract: 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/ and computation speed in the submillisecond region. Real-time 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 look-up 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.

Generalized defuzzification strategies and their parameter learning procedures

Abstract: Defuzzification is a procedure of crucial importance for fuzzy systems because a final crisp output (control) action is required in many theoretical and practical applications. The choice of defuzzification strategy, therefore, can directly affect the success of such applications. Among the existing strategies, neither the center of area (COA) nor the mean of maximum (MOM) emerges as the better defuzzification strategy. A compromise strategy that combines the two methods may offer a synergetic solution. In this paper, the authors introduce two new objective defuzzification strategies, Gaussian distribution transformation-based defuzzification (GTD) and polynomial transformation-based defuzzification (PTD), which are based on a discrete universe of discourse. Both strategies can perform better than the existing strategies and the PTD strategy offers a generalized defuzzification tool for a wide class of practical problems. Both strategies include the COA and MOM strategies as special cases, and both are based on parameter learning processes using the extended Kalman filter as their iterative improvement algorithms on sample database containing fuzzy sets and the associate defuzzified values. The proposed parameter learning procedures are capable of either off-line or on-line processing.

A unifying approach to defuzzification and comparison of the outputs of fuzzy controllers

Abstract: This paper addresses the defuzzification of the fuzzy set outputs of fuzzy controllers from a comparison or ranking perspective. This is done by emphasizing the fuzzy controller as a decision-making system. Based on the extensive study and justification of the fuzzy-set comparison criteria that were developed and published elsewhere by the author, a ranking and, thus, a defuzzification index is introduced. This index is shown to overcome the disadvantages of the commonly used defuzzification methods whose attempted justifications based on probabilistic arguments have not been successful. In addition, the proposed index is based on the generalization of the Hurwicz criterion that is usually adopted in decision making under nonprobabilistic uncertainty and it encompasses the pessimistic maximin and the optimistic maximax criteria as special cases.

ID3-derived fuzzy rules and optimized defuzzification for handwritten numeral recognition

Abstract: Presents a technique to produce fuzzy rules based on the ID3 approach and to optimize defuzzification parameters by using a two-layer perceptron. The technique overcomes the difficulties in a conventional syntactic approach to handwritten character recognition, including problems of choosing a starting or reference point, scaling, and learning by machines. The authors' technique provides: a way to produce meaningful and simple fuzzy rules; a method to fuzzify ID3-derived rules to deal with uncertain, noisy, or fuzzy data; and a framework to incorporate fuzzy rules learned from the training data and those extracted from human recognition experience. The authors' experimental results on NIST Special Database 3 show that the technique out-performs the straight forward ID3 approach. Moreover, ID3-derived fuzzy rules can be combined with an optimized nearest neighbor classifier, which uses intensity features only, to achieve a better classification performance than either of the classifiers. The combined classifier achieves a correct classification rate of 98.6% on the test set.

Computer-aided design of fuzzy systems based on generic VHDL specifications

Abstract: In this paper, three types of fuzzy systems and related hardware architectures are discussed: standard fuzzy controllers, FuNe I fuzzy systems, and fuzzy classifiers based on a neural network structure. Two computer-aided design (CAD) packages for automatic hardware synthesis of standard fuzzy controllers are presented: a hard-wired implementation of a complete fuzzy system on a single or multiple field programmable gate arrays (FPGA) and a modular toolbox called fuzzyCAD for synthesis of reprogrammable fuzzy controllers with architectures due to specified designer constraints. In the fuzzyCAD system, an efficient design methodology has been implemented which covers a large design space in terms of signal representations and component architectures as well as system architectures. Very high speed integrated-circuits hardware-description language (VHDL) descriptions and usage of powerful synthesis tools allow different technologies to be targeted easily and efficiently. Properties and hardware realizations of fuzzy classifiers based on a neural network are introduced. Finally, future perspectives and possible enhancements of the existing toolkits are outlined.

A multirule-base controller using the robust property of a fuzzy controller and its design method

Abstract: This paper suggests a new fuzzy adaptive controller, which is able to solve the problems of classical adaptive controllers and conventional fuzzy adaptive controllers. It explains the architecture of a fuzzy adaptive controller using the robust property of a fuzzy controller. The basic idea of new adaptive control scheme is that an adaptive controller can be constructed with parallel combination of robust controllers. This new adaptive controller uses a multirule-base architecture which has several independent fuzzy controllers in parallel, each with different robust stability area. Out of several independent fuzzy controllers, the most suited one is selected by a system identifier which observes variations in the controlled system parameter. Here, we propose a design procedure which can be carried out mathematically and systematically from the model of a controlled system; related mathematical theorems and their proofs are also given. The performance of the proposed adaptive control algorithm is analyzed through a design example and a DC motor control simulation.

A comparison of fuzzy shell-clustering methods for the detection of ellipses

Abstract: In this paper, we introduce a shell-clustering algorithm for ellipsoidal clusters based on the so-called "radial distance" which can be easily extended to superquadric clusters. We compare our algorithm with other algorithms in the literature that are based on the algebraic distance, the approximate distance, the normalized radial distance, and the exact distance. We evaluate the performance of each algorithm on two-dimensional data sets containing "scattered" ellipses, partial ellipses, outliers, and ellipses of disparate sizes, and summarize the relative strengths and weaknesses of each algorithm.

Fuzzy sets of rules for system identification

Abstract: The synthesis of fuzzy systems involves the identification of a structure and its specialization by means of parameter optimization. In doing this, symbolic approaches which encode the structure information in the form of high-level rules allow further manipulation of the system to minimize its complexity, and possibly its implementation cost, while all-parametric methodologies often achieve better approximation performance. In this paper, we rely on the concept of a fuzzy set of rules to tackle the rule induction problem at an intermediate level. An online adaptive algorithm is developed which almost surely learns the extent to which inclusion of a rule in the rule set significantly contributes to the reproduction of the target behavior. Then, the resulting fuzzy set of rules can be defuzzified to give a conventional rule set with similar behavior. Comparisons with high-level and low-level methodologies show that this approach retains the most positive features of both.

Neuro-fuzzy hybrid control system of tank level in petroleum plant

Abstract: Shown in this paper is a practical method of control using neural network and fuzzy control techniques, where a neural network estimates the target of fuzzy control. The neural network is used to estimate the transient state of a plant which has nonlinear processes such as refrigerating and filtering. The suitable control target pattern for fuzzy control is selected according to this estimation. This method is applied to control the tank level of a solvent dewaxing plant for: 1) changing the tank outflow rate smoothly, and 2) keeping the tank level stable. The results show that this system can control the tank level effectively in both steady state and transient state.

Decomposition property of fuzzy systems and its applications

Abstract: This paper presents the decomposition property of fuzzy systems using a simple, constructive, decomposition procedure. That is, by properly dividing the input space into sub-input spaces, a general fuzzy system is decomposed into several sub-fuzzy systems which are the simplest fuzzy systems in the sub-input spaces. Based on the decomposition property of fuzzy systems, the analysis of fuzzy systems can be divided into two steps: first, analyze the properties of the simplest fuzzy systems, and then, use the decomposition property to extend the results to general fuzzy systems. Using this idea, two applications of the decomposition property are given. The first is the application to the representation capability analysis of fuzzy systems. The second is the application to the analysis of a class of nonlinear control systems. Then, based on the piecewise affine fuzzy-system model, the existence condition and the design of a stable control for a class of single-input single-output (SISO) nonlinear systems are presented.

Fuzzy modeling and analytic hierarchy processing-means to quantify risk levels associated with occupational injuries. II. The development of a fuzzy rule-based model for the prediction of injury

Abstract: This paper presents the second phase in a two-part research project to develop a fuzzy rule-based expert system for predicting occupational injuries of the forearm and hand. Analytic hierarchy processing (AHP) is used to assign relative weights to the identified risk factors. A fuzzy rule base is constructed with all of the potential combinations for the given factors. The input parameters are linguistic variables obtained in the first part of the research. These inputs are fuzzified and defuzzified to provide two system outputs: a linguistic value and a numeric value as a prediction of injury. The system provides linguistic risk levels as well as quantified risks in assessing the overall risk of injury. The system evaluation was conducted resulting in calculations for Type I and Type II errors. The contributions and limitations of the system are discussed.

Designing fuzzy logic controllers using a multiresolutional search paradigm

Abstract: A multiresolutional search paradigm is employed to design optimal fuzzy logic controllers in a variable structure simulation environment. The initial search space is evaluated with a coarse resolution and some of the subspaces are selected as candidate regions for global optimum. New optimization processes are then created to investigate the candidate search spaces in detail, a process which continues until a solution is found. This search paradigm was implemented using hierarchical distributed genetic algorithms (HDGAs)-search agents solving different degrees of abstracted problems. Creation/destruction of agents is executed dynamically during the operation based on their performance. In the application to fuzzy systems, the HDGA investigates design alternatives such as different types of membership functions and the number of the fuzzy labels, as well as their optimal parameter settings, all at the same time. This paradigm is demonstrated with an application to the design of a fuzzy controller for an inverted pendulum.