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A fuzzy logic controller for an ABS braking system
G. F. Mauer
vol. 3, no. 4, pp. 381-8, Nov. 1995

Anti-blocking 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.

A general axiomatic theory of intrinsically fuzzy mathematical morphologies
D. Sinha, E. R. Dougherty
vol. 3, no. 4, pp. 389-403, Nov. 1995

Intrinsic fuzzification of mathematical morphology is grounded on an axiomatic characterization of subset fuzzification. The result is an axiomatic formulation of fuzzy Minkowski algebra. Part of the Minkowski algebra results solely from the axioms themselves and part results from a specific postulated form of a subsethood indicator function. There exists an infinite number of fuzzy morphologies satisfying the axioms; in particular, there are uncountably many indicators satisfying the postulated form. This paper develops fuzzy Minkowski algebra, with special emphasis on fitting characterizations of fuzzy erosion and opening, examines key properties of the indicator function, and provides fuzzy extensions of the basic binary Matheron representations for openings and increasing, translation-invariant operators.

A design methodology for fuzzy system interfaces
J. Valente de Oliveira
vol. 3, no. 4, pp. 404-14, Nov. 1995

Conceptually, a fuzzy system interacting with a numerical environment has three components: a numeric/linguistic interface, a linguistic processing unit, and a linguistic/numeric interface. At these interfaces, membership functions representing linguistic terms play a top role both for the linguistic meaning provided and for the pre/post information processing introduced to the fuzzy system. Considering these issues, a set of membership function properties is postulated. Furthermore, an expert-free interface design methodology able to meet these properties, and based on the concept of optimal interfaces, is proposed. This concept simply states an equivalence between information format (numeric and linguistic), thereby making the methodology appealing from the applicational point of view. An algorithm is developed, and brief notes on selected applications are outlined stressing relevant issues of the proposed methodology.

A neuro-fuzzy system for chemical agent detection
P. Vuorimaa, T. Jukarainen, E. Karpanoja
vol. 3, no. 4, pp. 415-24, Nov. 1995

The authors previously introduced a fuzzy version of Kohonen's well-known self-organizing map neural network model. In this novel neuro-fuzzy system, the neurons of Kohonen's original model are replaced by fuzzy rules. Each fuzzy rule is composed of fuzzy sets and an output singleton. Since the fuzzy self-organizing map is a modified version of Kohonen's original model, the self-organizing map and the learning vector quantization learning laws can be used to tune the neuro-fuzzy system. Originally, the fuzzy self-organizing map was intended to be used as an unknown function approximator, while Kohonen's self-organizing map is primarily used as a neural classifier. In this paper, the authors show how the fuzzy self-organizing map can also be used as a neuro-fuzzy classifier. Simulation results show that, in chemical agent detection, the fuzzy self-organizing map not only gives better classification results than Kohonen's model, but it also has smaller number of fuzzy rules than the corresponding neurons required by Kohonen's self-organizing map.

Interval-valued fuzzy backward reasoning
T. Arnould, S. Tano
vol. 3, no. 4, pp. 425-37, Nov. 1995

The importance and efficiency of backward reasoning in nonfuzzy reasoning has been stressed for a long time, especially in the case of expert systems and decision-support systems. The extension of this reasoning method to fuzzy theory, however, has never been considered. In this paper, the authors propose a definition of fuzzy backward reasoning based on the generalized modus ponens and show the necessity of considering interval-valued fuzzy backward reasoning. Then, the authors propose solving methods for fuzzy backward reasoning in the case of a rule with one or several conditions as well as in the case of several rules.

Stability and stabilizability of fuzzy-neural-linear control systems
K. Tanaka
vol. 3, no. 4, pp. 438-47, Nov. 1995

This paper discusses stability analysis of fuzzy-neural-linear (FNL) control systems which consist of combinations of fuzzy models, neural network (NN) models, and linear models. The authors consider a relation among the dynamics of NN models, those of fuzzy models and those of linear models. It is pointed out that the dynamics of linear models and NN models can be perfectly represented by Takagi-Sugeno (T-S) fuzzy models whose consequent parts are described by linear equations. In particular, the authors present a procedure for representing the dynamics of NN models via T-S fuzzy models. Next, the authors recall stability conditions for ensuring stability of fuzzy control systems in the sense of Lyapunov. The stability criteria is reduced to the problem of finding a common Lyapunov function for a set of Lyapunov inequalities. The stability conditions are employed to analyze stability of FNL control systems. Finally, stability analysis for four types of FNL control systems is demonstrated.

Applicability analysis of fuzzy inference by means of generalized Dempster-Shafer theory
C. Romer, A. Kandel
Austria
vol. 3, no. 4, pp. 448-53, Nov. 1995

The generalization of Dempster-Shafer (D-S) theory to fuzzy sets provides means for evidential reasoning on basis of fuzzy information. Fuzzy implication operators are used to turn partial fuzzy knowledge about a physical system into an inference engine. Presently there are more than 72 fuzzy implication operators known and investigated, evoking demand for strategies of finding the best performing fuzzy implication operator for the physical system under investigation. In this paper the authors propose such a concept based on generalized D-S theory. A convention to update prior knowledge regarding the applicability of fuzzy implication operators, with respect to fuzzy evidences pertaining to the physical system under consideration, is presented.

Building Sugeno-type models using fuzzy discretization and orthogonal parameter estimation techniques
Wang Liang, R. Langari
vol. 3, no. 4, pp. 454-8, Nov. 1995

This paper develops a new approach to building Sugeno-type models. The essential idea is to separate the premise identification from the consequence identification, while these are mutually related in the previous methods. A fuzzy discretization technique is suggested to determine the premise of the model, and an orthogonal estimator is provided to identify the consequence of the model. The orthogonal estimator can provide information about the model structure, or which terms to include in the model, and final parameter estimates in a very simple and efficient manner. The well-known gas furnace data of Box and Jenkins is used to illustrate the proposed modeling approach and to compare its performance with other statistical and fuzzy modeling approaches. It shows that the performance of the new approach compares favorably with these existing techniques.

Fuzzy logic control of a solar power plant
F. R. Rubio, M. Berenguel, E. F. Camacho
vol. 3, no. 4, pp. 459-68, Nov. 1995

This paper presents an application of fuzzy logic control to the distributed collector field of a solar power plant. The major characteristic of a solar power plant is that the primary energy source, solar radiation, cannot be manipulated. Solar radiation varies throughout the day, causing changes in plant dynamics and strong perturbations in the process. A special subclass of fuzzy inference systems, the TP (triangular partition) and TPE (triangular partition with evenly spaced midpoints) systems, is used to obtain adequate control signals in the whole range of possible operating conditions. The fuzzy logic controller has been tested in the real plant and results obtained are shown. A comparison with other control approaches widely used in the plant is performed using a nonlinear computer model of the field.

On a fuzzy difference equation
E. Y. Deeba, A. de Korvin
vol. 3, no. 4, pp. 469-73, Nov. 1995

Difference equations arise in the modeling of many interesting problems. "Measurements" of data or specified information for an underlying problem may be imprecise or only partially specified. This motivates us to initiate a study of "fuzzy difference equations". In this paper, we formulate and solve a given difference equation in the fuzzy setting and give a general method for dealing with any second-order difference equation. This work is motivated by considering an important problem in computer science, namely, the polyphase merging problem.

Probably approximately correct learning in fuzzy classification systems
F. Bergadano, V. Cutello
vol. 3, no. 4, pp. 473-8, Nov. 1995

An efficient method for learning (trapezoidal) membership functions for fuzzy predicates is presented. Positive and negative examples of one class are given together with a system of classification rules. The learned membership functions can be used for the fuzzy predicates occurring in the given rules to classify further examples. We show that the obtained classification is approximately correct with high probability. This justifies the obtained fuzzy sets within one particular classification problem, instead of relying on a subjective meaning of fuzzy predicates as normally done by a domain expert.