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A formal approach to fuzzy modeling
J. Lygeros
Dept. of Electr. Eng. & Comput. Sci., MIT, Cambridge, MA, USA
vol. 5, no. 3, pp. 317-27, Aug. 1997

A formalism for coding fuzzy models of dynamical systems is presented. It is shown that the formalism is rich enough to capture the performance of arbitrary conventional discrete time dynamical systems whose transition maps are polynomials with rational coefficients. The proof of this fact provides a constructive algorithm for generating fuzzy models to arbitrarily closely approximate an arbitrary map on a compact set. Our modeling formalism highlights the similarities between fuzzy systems and hybrid control systems. We hope to be able to exploit these similarities by extending results from the area of hybrid systems to the fuzzy domain and vice versa.

A new approach to fuzzy modeling
Kim Euntai, Park Minkee, Ji Seunghwan, Park Mignon
Dept. of Electron. Eng., Yonsei Univ., Seoul, South Korea
vol. 5, no. 3, pp. 328-37, Aug. 1997

This paper proposes a new approach to fuzzy modeling. The suggested fuzzy model can express a given unknown system with a few fuzzy rules as well as Takagi and Sugeno's model (1985), because it has the same structure as that of Takagi and Sugeno's model. It is also as easy to implement as Sugeno and Yasukawa's model (1993) because its identification mimics the simple identification procedure of Sugeno and Yasukawa's model. The suggested algorithm is composed of two steps: coarse tuning and fine tuning. In coarse tuning, fuzzy C-regression model (FCRM) clustering is used, which is a modified version of fuzzy C-means (FCM). In fine tuning, gradient descent algorithm is used to precisely adjust parameters of the fuzzy model instead of nonlinear optimization methods used in other models. Finally, some examples are given to demonstrate the validity of this algorithm.

A fuzzy approach for performance modeling in a batch plant: application to semiconductor manufacturing
C. Azzaro-Pantel, P. Floquet, L. Pibouleau, S. Domenech
Lab. de Genie Chimique, CNRS, Toulouse, France
vol. 5, no. 3, pp. 338-57, Aug. 1997

In the current literature dealing with job shop scheduling, most of the approaches have developed models based on the assumption that the problem domain does not contain any imprecision. However, this hypothesis is strongly challenged in the implementation phase of such models-imprecision is inherent to production systems involving human intervention. The aim of this paper is to demonstrate the advantages of possibilistic production data modeling in a real-world application, i.e., semiconductor manufacturing. In this work, a discrete-event simulation model (MELISSA) for performance evaluation of a batch-manufacturing facility previously developed in our laboratory has been extended to treat uncertainties modeled by fuzzy numbers. Due to the confidential nature of industrial data, an illustrative example, presenting the same typical features as a real problem, is treated and analyzed using fuzzy concepts. Inclusion of fuzzy techniques provides the decision-maker with a range of possible values for completion times, average storage times, and operator workload instead of a unique value (which has little significance due to the variety of human operators). In addition, the negative portion of average waiting times yields useful information for the manager to detect deficient resources in the production system.

A fuzzy classifier with ellipsoidal regions
S. Abe, R. Thawonmas
Dept. of Electr. & Electron. Eng., Kobe Univ., Japan
vol. 5, no. 3, pp. 358-68, Aug. 1997

In this paper, we discuss a fuzzy classifier with ellipsoidal regions which has a learning capability. First, we divide the training data for each class into several clusters. Then, for each cluster, we define a fuzzy rule with an ellipsoidal region around a cluster center. Using the training data for each cluster, we calculate the center and the covariance matrix of the ellipsoidal region for the cluster. Then we tune the fuzzy rules, i.e., the slopes of the membership functions, successively until there is no improvement in the recognition rate of the training data. We evaluate our method using the Fisher iris data, numeral data of vehicle license plates, thyroid data, and blood cell data. The recognition rates (except for the thyroid data) of our classifier are comparable to the maximum recognition rates of the multilayered neural network classifier and the training times (except for the iris data) are two to three orders of magnitude shorter.

Back-driving a truck with suboptimal distance trajectories: a fuzzy logic control approach
Chen Guanrong, Zhang Delin
Dept. of Electr. & Comput. Eng., Houston Univ., TX, USA
vol. 5, no. 3, pp. 369-80, Aug. 1997

This paper provides a suboptimal solution to the problem of automatically back-driving a truck using the natural parabolic paths as the shortest moving distance requirement. By applying fuzzy logic control techniques, a controller with nine rules is developed, which works well even without using a mathematical system model. As long as the states (position and orientation) of the truck are measurable at each discrete-time step during the control process, this controller can drive the truck to follow any feasible trajectories (their smallest radii are no less than the smallest radius of the curve along which the truck can travel), and to move successfully into a prescribed parking lot. In addition to the design of the controller, controllability and stability of the control system are briefly discussed under the condition that only partial information about the current states of the system are available. Simulation results are presented, to demonstrate the accuracy and effectiveness of this new fuzzy logic controller and to compare its control performance with other fuzzy logic controllers that were designed for the same purpose under the same conditions but without using any optimality criterion.

Predictive modular fuzzy systems for time-series classification
V. Petridis, A. Kehagias
Div. of Electron. & Comput. Eng., Aristotelian Univ. of Thessaloniki, Greece
vol. 5, no. 3, pp. 381-97, Aug. 1997

We introduce the so-called predictive modular fuzzy system (PREMOFS) which performs time-series classification. A PREMOFS consists of 1) a bank of prediction modules and 2) a fuzzy decision module. It is assumed that the time series is generated by a source belonging to a finite search set (universal set); then the classification problem is to select the source that best represents the observed data, Classification is based on a membership function which is updated recursively according to the predictive accuracy of each model. Two algorithms are presented for updating the membership function. The first is based on sum/product fuzzy inference and the second on max/min fuzzy inference. In short, PREMOFS is a fuzzy modular system that classifies time series to one of a finite number of classes using the full set of past data (without preprocessing) to perform a recursive competitive computation of membership function based on predictive accuracy. Convergence proofs are given for both PREMOFS algorithms; in both cases the membership grade tends to one for the source that best predicts the observed data and to less than one for the remaining sources; hence, correct classification is guaranteed. Simulation results are also presented: PREMOFS are applied to signal detection, system identification, and phonemeMM>quit classification tasks.

Checking the coherence and redundancy of fuzzy knowledge bases
D. Dubois, H. Prade, L. Ughetto
Inst. de Recherche en Inf., Univ. Paul Sabatier, Toulouse, France
vol. 5, no. 3, pp. 398-417, Aug. 1997

Checking the coherence of a set of rules is an important step in knowledge base validation. Coherence is also needed in the field of fuzzy systems. Indeed, rules are often used regardless of their semantics, and it sometimes leads to sets of rules that make no sense. Avoiding redundancy is also of interest in real-time systems for which the inference engine is time consuming. A knowledge base is potentially inconsistent or incoherent if there exists a piece of input data that respects integrity constraints and that leads to logical inconsistency when added to the knowledge base. We more particularly consider knowledge bases composed of parallel fuzzy rules. Then, coherence means that the projection on the input variables of the conjunctive combination of the possibility distributions representing the fuzzy rules leaves these variables completely unrestricted (i.e., any value for these variables is possible) or, at least, not more restrictive than integrity constraints. Fuzzy rule representations can be implication-based or conjunction-based; we show that only implication-based models may lead to coherence problems. However, unlike conjunction-based models, they allow to design coherence checking processes. Some conditions that a set of parallel rules has to satisfy in order to avoid inconsistency problems are given for certainty or gradual rules. The problem of redundancy, which is also of interest for fuzzy knowledge bases validation, is addressed for these two kinds of rules.

A subjective methodology for safety analysis of safety requirements specifications
J. Wang
Centre of Maritime & Offshore Oper., Liverpool John Moores Univ., UK
vol. 5, no. 3, pp. 418-30, Aug. 1997

This paper presents a methodology for subjective safety analysis of safety requirements specifications of software for safety-critical systems. The methodology incorporates fuzzy set modeling and evidential reasoning to assess the safety associated with safety requirements specifications. Three basic parameters-failure likelihood, consequence severity, and failure consequence probability are used to analyze a safety rule in terms of membership functions. The subjective safety description associated with the safety rule is then mapped back to the defined safety expressions which are also characterized in terms of membership functions. Such a mapping results in the production of the safety evaluation associated with the safety rule. The information produced for all safety rules can then be synthesised using an evidential reasoning approach to obtain the safety evaluation associated with the safety requirements specifications. The developed methodology is capable of dealing with multiple safety analysts who make judgements on each safety rule. A case study based on a train-set crossing is used to demonstrate the methodology.

Sampled-analog implementation of application-specific fuzzy controllers
U. Cilingiroglu, B. Pamir, Z. S. Gunay, F. Dulger
ETA Design Centre, Istanbul Tech. Univ., Turkey
vol. 5, no. 3, pp. 431-42, Aug. 1997

Sampled-analog circuit techniques are exploited in an application-specific integrated fuzzy controller design. A circuit library comprising a sample-and-hold amplifier, positive and negative ramp amplifiers, an inference cell, adder, and weighted adder amplifiers, and a divider unit was developed for this purpose. Any expert system of piecewise linear input membership functions, conjunctive rules and singleton output classes can be implemented with this library. The library was implemented in a 1.2 mu m double-metal double-poly CMOS technology. Test results indicate excellent linearity and accuracy in full 5 V rail-to-rail operation in all units. A controller of four inputs, 16 rules, and two outputs fabricated with these library units occupies 1.76 mm/sup 2/ silicon. Test results indicate full functionality. The measured speed, 85 k samples per second, is limited by the unbuffered outputs. Sampling rate can be increased by 50% in those applications where pipelining is permissible.

Inference, inquiry, evidence censorship, and explanation in connectionist expert systems
R. J. Machado, A. F. Da Rocha
Catholic Univ. of Rio de Janeiro, Brazil
vol. 5, no. 3, pp. 443-59, Aug. 1997

The combination of the techniques of expert systems and neural networks has the potential of producing more powerful systems, for example, expert systems able to learn from experience. In this paper, we address the combinatorial neural model (CNM), a kind of fuzzy neural network able to accommodate in a simple framework the highly desirable property of incremental learning, as well as the usual capabilities of expert systems. We show how an interval-based representation for membership grades makes CNM capable of reasoning with several types of uncertainty: vagueness, ignorance, and relevance commonly found in practical applications. In addition, we show how basic functions of expert systems such as inference, inquiry, censorship of input information, and explanation may be implemented. We also report experimental results of the application of CNM to the problem of deforestation monitoring of the Amazon region using satellite images.

A self-learning fuzzy logic controller using genetic algorithms with reinforcements
Knan Chiang Chih, Yuan Chung Hung, Lin Jin Jye
Dept. of Electr. Eng., Nat. Central Univ., Chung-Li, Taiwan
vol. 5, no. 3, pp. 460-7, Aug. 1997

This paper presents a new method for learning a fuzzy logic controller automatically. A reinforcement learning technique is applied to a multilayer neural network model of a fuzzy logic controller. The proposed self-learning fuzzy logic control that uses the genetic algorithm through reinforcement learning architecture, called a genetic reinforcement fuzzy logic controller, can also learn fuzzy logic control rules even when only weak information such as a binary target of "success" or "failure" signal is available. In this paper, the adaptive heuristic critic algorithm of Barto et al. (1987) is extended to include a priori control knowledge of human operators. It is shown that the system can solve more concretely a fairly difficult control learning problem. Also demonstrated is the feasibility of the method when applied to a cart-pole balancing problem via digital simulations.

Approximation capability of fuzzy systems using translations and dilations of one fixed function as membership functions
Hong Mao Zhi, Da Li Yan, Feng Zhang Xue
Dept. of Autom., Tsinghua Univ., Beijing, China
vol. 5, no. 3, pp. 468-73, Aug. 1997

This paper reports on a related study on approximation theory of fuzzy systems. First, some basic principles are presented to construct membership functions. Then, an approach is proposed to form membership functions by using translations and dilations of one fixed function (called a basis function) which is very similar to that in wavelets analysis. The properties of this type of membership function reflect the advantages of the given approach. Finally, it is proved that fuzzy systems based on such membership functions are universal approximators under certain mild conditions on the basis function. This conclusion expands the family of fuzzy systems which can be universal approximators.