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Simultaneous design of membership functions and rule sets for fuzzy controllers using genetic algorithms
A. Homaifar, E. McCormick
USA
vol. 3, no. 2, pp. 129-39, May 1995

This paper examines the applicability of genetic algorithms (GA's) in the simultaneous design of membership functions and rule sets for fuzzy logic controllers. Previous work using genetic algorithms has focused on the development of rule sets or high performance membership functions; however, the interdependence between these two components suggests a simultaneous design procedure would be a more appropriate methodology. When GA's have been used to develop both, it has been done serially, e.g., design the membership functions and then use them in the design of the rule set. This, however, means that the membership functions were optimized for the initial rule set and not the rule set designed subsequently. GA's are fully capable of creating complete fuzzy controllers given the equations of motion of the system, eliminating the need for human input in the design loop. This new method has been applied to two problems, a cart controller and a truck controller. Beyond the development of these controllers, we also examine the design of a robust controller for the cart problem and its ability to overcome faulty rules.

Fuzzy controllers: synthesis and equivalences
S. Galichet, L. Foulloy
vol. 3, no. 2, pp. 140-8, May 1995

It has been proved that fuzzy controllers are capable of approximating any real continuous control function on a compact set to arbitrary accuracy. In particular, any given linear control can be achieved with a fuzzy controller for a given accuracy. The aim of this paper is to show how to automatically build this fuzzy controller. The proposed design methodology is detailed for the synthesis of a Sugeno or Mamdani type fuzzy controller precisely equivalent to a given PI controller. The main idea is to equate the output of the fuzzy controller with the output of the PI controller at some particular input values, called modal values. The rule base and the distribution of the membership functions can thus be deduced. The analytic expression of the output of the generated fuzzy controller is then established. For Sugeno-type fuzzy controllers, precise equivalence is directly obtained. For Mamdani-type fuzzy controllers, the defuzzification strategy and the inference operators have to be correctly chosen to provide linear interpolation between modal values. The usual inference operators satisfying the linearity requirement when using the center of gravity defuzzification method are proposed.

Advantages of an alternative form of fuzzy logic
J. A. Johnson, H. B. Smartt
vol. 3, no. 2, pp. 149-57, May 1995

A specific implementation of fuzzy logic is described. This implementation uses multiplication rather than finding the minimum to determine the conjunction between antecedents. The fuzzy implication is also determined by the product operator. Crisp membership functions are used for the output fuzzy sets. Thus the product of the antecedents is then multiplied by a crisp output action for that rule and the sum of products determines the net output of the system. Advantages of this method over the "standard" methods include elimination of the defuzzification step, direct control of the shape of the input-to-output mapping surface, and an analytic formulation that can be easily implemented in software or hardware. Conventional controllers are shown to be a special case of the method. The method is also equivalent to a certain class of neural networks and, as such, can be trained to optimum values of the output actions of the system. The method is illustrated with some examples.

Fuzzy basis functions: comparisons with other basis functions
Mun Kim Hyun, J. M. Mendel
USA
vol. 3, no. 2, pp. 158-68, May 1995

Fuzzy basis functions (FBF's) which have the capability of combining both numerical data and linguistic information, are compared with other basis functions. Because a FBF network is different from other networks in that it is the only one that can combine numerical and linguistic information, comparisons are made when only numerical data is available. In particular, a FBF network is compared with a radial basis function (RBF) network from the viewpoint of function approximation. Their architectural interrelationships are discussed. Additionally, a RBF network, which is implemented using a regularization technique, is compared with a FBF network from the viewpoint of overcoming ill-posed problems. A FBF network is also compared with Specht's probabilistic architectural point of view. A FBF network is also compared with a Gaussian sum approximation in which Gaussian functions play a central role. Finally, we summarize the architectural relationships between all the networks discussed in this paper.

A neural fuzzy system with linguistic teaching signals
Teng Lin Chin, Ching Lu Ya
vol. 3, no. 2, pp. 169-89, May 1995

A neural fuzzy system learning with linguistic teaching signals is proposed. This system is able to process and learn numerical information as well as linguistic information. It can be used either as an adaptive fuzzy expert system or as an adaptive fuzzy controller. First, we propose a five-layered neural network for the connectionist realization of a fuzzy inference system. The connectionist structure can house fuzzy logic rules and membership functions for fuzzy inference. We use alpha -level sets of fuzzy numbers to represent linguistic information. The inputs, outputs, and weights of the proposed network can be fuzzy numbers of any shape. Furthermore, they can be hybrid of fuzzy numbers and numerical numbers through the use of fuzzy singletons. Based on interval arithmetics, two kinds of learning schemes are developed for the proposed system: fuzzy supervised learning and fuzzy reinforcement learning. Simulation results are presented to illustrate the performance and applicability of the proposed system.

A new approach to fuzzy-neural system modeling
Lin Yinghua, G. A. Cunningham III
vol. 3, no. 2, pp. 190-8, May 1995

We develop simple but effective fuzzy-rule based models of complex systems from input-output data. We introduce a simple fuzzy-neural 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 fuzzy-neural 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.

Fuzzy learning control for a flexible-link robot
V. G. Moudgal, W. A. Kwong, K. M. Passino, S. Yurkovich
vol. 3, no. 2, pp. 199-210, May 1995

There are two main drawbacks in fuzzy control: 1) the design of fuzzy controllers is usually performed in an ad hoc manner where it is often difficult to choose some of the controller parameters; and 2) the fuzzy controller constructed for the nominal plant may later perform inadequately if significant and unpredictable plant parameter variations occur. In this paper we illustrate these two problems on a two-link flexible robot testbed by: 1) developing, implementing, and evaluating a fuzzy controller for the robotic mechanism, and 2) illustrating that payload variations can have negative effects on the performance of a well designed fuzzy control system. Next, we show how to develop and implement a fuzzy model reference learning controller for the flexible robot and illustrate that it can automatically synthesize a rule-base for a fuzzy controller that will achieve comparable performance to the case where it was manually constructed, and automatically tune the fuzzy controller so that it can adapt to variations in the payload.

Fuzzy logic for digital phase-locked loop filter design
D. Simon, H. El-Sherief
vol. 3, no. 2, pp. 211-18, May 1995

The problem of robust phase-locked loop design has attracted attention for many years, particularly since the advent of the global positioning system. This paper proposes and demonstrates the use of a fuzzy PLL to estimate the time-varying phase of a sinusoidal signal. It is shown via simulation results that fuzzy PLL's offer performance comparable to analytically derived PLL's (e.g. Kalman filters and H/sub infinity / estimators) when the phase exhibits high dynamics and high noise. The fuzzy PLL rules are optimized using a gradient descent method and a genetic algorithm.

Approximation theory of fuzzy systems-MIMO case
Jun Zeng Xiao, M. G. Singh
vol. 3, no. 2, pp. 219-35, May 1995

In this paper, the approximation properties of MIMO fuzzy systems generated by the product inference are discussed. We first give an analysis of fuzzy basic functions (FBF's) and present several properties of FBF's. Based on these properties of FBF's, we obtain several basic approximation properties of fuzzy systems: 1) basic approximation property which reveals the basic approximation mechanism of fuzzy systems; 2) uniform approximation bounds which give the uniform approximation bounds between the desired (control or decision) functions and fuzzy systems; 3) uniform convergent property which shows that fuzzy systems with defined approximation accuracy can always be obtained by dividing the input space into finer fuzzy regions; and 4) universal approximation property which shows that fuzzy systems are universal approximators and extends some previous results on this aspect. The similarity between fuzzy systems and mathematical approximation is discussed and an idea to improve approximation accuracy is suggested based on uniform approximation bounds.

Characterization of the ordered weighted averaging operators
J. Fodor, J. L. Marichal, M. Roubens
vol. 3, no. 2, pp. 236-40, May 1995

This paper deals with the characterization of two classes of monotonic and neutral (MN) aggregation operators. The first class corresponds to (MN) aggregators which are stable for the same positive linear transformations and presents the ordered linkage property. The second class deals with (MN)-idempotent aggregators which are stable for positive linear transformations with the same unit, independent zeroes and ordered values. These two classes correspond to the weighted ordered averaging operator (OWA) introduced by Yager in 1988. It is also shown that the OWA aggregator can be expressed as a Choquet integral.

Optimization of clustering criteria by reformulation
R. J. Hathaway, J. C. Bezdek, USA.
vol. 3, no. 2, pp. 241-5, May 1995

Various hard, fuzzy and possibilistic clustering criteria (objective functions) are useful as bases for a variety of pattern recognition problems. At present, many of these criteria have customized individual optimization algorithms. Because of the specialized nature of these algorithms, experimentation with new and existing criteria can be very inconvenient and costly in terms of development and implementation time. This paper shows how to reformulate some clustering criteria so that specialized algorithms can be replaced by general optimization routines found in commercially available software. We prove that the original and reformulated versions of each criterion are fully equivalent. Finally, two numerical examples are given to illustrate reformulation.

A fuzzy logic system for channel equalization
P. Sarwal, M. D. Srinath
vol. 3, no. 2, pp. 246-9, May 1995

We present a new method for channel equalization using fuzzy logic. The membership functions are derived from the training data set, and a method to estimate the delay of the communication channel is proposed. The performance of the fuzzy equalizer is compared with that of a transversal filter equalizer. It is shown using simulations that the transversal filter requires a much larger training set to achieve the same error rate. It is also shown, using simulations, that the fuzzy equalizer performs better in the presence of channel nonlinearities.