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An ART-based fuzzy adaptive learning control network
Jian Lin Cheng, Teng Lin Chin
Dept. of Control Eng., Nat. Chiao Tung Univ., Hsinchu, Taiwan
vol. 5, no. 4, pp. 477-96, Nov. 1997

This paper addresses the structure and an associated online learning algorithm of a feedforward multilayer neural net for realizing the basic elements and functions of a fuzzy controller. The proposed fuzzy adaptive learning control network (FALCON) can be contrasted with traditional fuzzy control systems in network structure and learning ability. An online structure/parameter learning algorithm, FALCON-ART, is proposed for constructing FALCON dynamically. It combines backpropagation for parameter learning and fuzzy ART for structure learning. FALCON-ART partitions the input state space and output control space using irregular fuzzy hyperboxes according to the data distribution. In many existing fuzzy or neural fuzzy control systems, the input and output spaces are always partitioned into "grids". As the number of variables increases, the number of partitioned grids grows combinatorially. To avoid this problem in some complex systems, FALCON-ART partitions the I/O spaces flexibly based on data distribution. It can create and train FALCON in a highly autonomous way. In its initial form, there is no membership function, fuzzy partition, and fuzzy logic rule. They are created and begin to grow as the first training pattern arrives. Thus, the users need not give it any a priori knowledge or initial information. FALCON-ART can online partition the I/O spaces, tune membership functions, find proper fuzzy logic rules, and annihilate redundant rules dynamically upon receiving online data.

Hybrid fuzzy-neural systems in handwritten word recognition
Hsien Chiang Jung, P. D. Gader
Dept. of Comput. Eng. & Comput. Sci., Missouri Univ., Columbia, MO, USA
vol. 5, no. 4, pp. 497-510, Nov. 1997

Two hybrid fuzzy neural systems are developed and applied to handwritten word recognition. The word recognition system requires a module that assigns character class membership values to segments of images of handwritten words. The module must accurately represent ambiguities between character classes and assign low membership values to a wide variety of noncharacter segments resulting from erroneous segmentations. Each hybrid is a cascaded system. The first stage of both is a self-organizing feature map (SOFM). The second stages map distances into membership values. The third stage of one system is a multilayer perceptron (MLP). The third stage of the other is a bank of Choquet fuzzy integrals (FI). The two systems are compared individually and as a combination to the baseline system. The new systems each perform better than the baseline system. The MLP system slightly outperforms the FI system, but the combination of the two outperforms the individual systems with a small increase in computational cost over the MLP system. Recognition rates of over 92% are achieved with a lexicon set having average size of 100. Experiments were performed on a standard test set from the SUNY/USPS CD-ROM database.

An approach to enlarge learning space coverage for robot learning control
Young Young Kuu, Ji Shiah Shaw
Dept. of Control Eng., Nat. Chiao Tung Univ., Hsinchu, Taiwan
vol. 5, no. 4, pp. 511-22, Nov. 1997

In robot learning control, the learning space for executing general motions of multijoint robot manipulators is quite large. Consequently, for most learning schemes, the learning controllers are used as subordinates to conventional controllers or the learning process needs to be repeated each time a new trajectory is encountered, although learning controllers are considered to be capable of generalization. In this paper, we propose an approach for larger learning space coverage in robot learning control. In this approach, a new structure for learning control is proposed to organize information storage via effective memory management. The proposed structure is motivated by the concept of human motor program and consists mainly of a fuzzy system and a cerebellar model articulation controller (CMAC)-type neural network. The fuzzy system is used for governing a number of sampled motions in a class of motions. The CMAC-type neural network is used to generalize the parameters of the fuzzy system, which are appropriate for the governing of the sampled motions, to deal with the whole class of motions. Under this design, in some sense the qualitative fuzzy rules in the fuzzy system are generalized by the CMAC-type neural network and then a larger learning space can be covered. Therefore, the learning effort is dramatically reduced in dealing with a wide range of robot motions, while the learning process is performed only once. Simulations emulating ball carrying under various conditions are presented to demonstrate the effectiveness of the proposed approach.

Forecasting time series with genetic fuzzy predictor ensemble
Kim Daijin, Kim Chulhyun
Dept. of Comput. Eng., Dong-A Univ., Pusan, South Korea
vol. 5, no. 4, pp. 523-35, Nov. 1997

This paper proposes a genetic fuzzy predictor ensemble (GFPE) for the accurate prediction of the future in the chaotic or nonstationary time series. Each fuzzy predictor in the GFPE is built from two design stages, where each stage is performed by different genetic algorithms (GA). The first stage generates a fuzzy rule base that covers as many of training examples as possible. The second stage builds fine-tuned membership functions that make the prediction error as small as possible. These two design stages are repeated independently upon the different partition combinations of input-output variables. The prediction error will be reduced further by invoking the GFPE that combines multiple fuzzy predictors by an equal prediction error weighting method. Applications to both the Mackey-Glass chaotic time series and the nonstationary foreign currency exchange rate prediction problem are presented. The prediction accuracy of the proposed method is compared with that of other fuzzy and neural network predictors in terms of the root mean squared error (RMSE).

Fuzzy model identification for classification of gait events in paraplegic
Kuen Ng San, H. J. Chizeck
Dept. of Syst., Control, & Ind. Eng., Case Western Reserve Univ., Cleveland, OH, USA
vol. 5, no. 4, pp. 536-44, Nov. 1997

Fuzzy system identification was applied to a biomedical system for classification purposes. Gait achieved through functional electrical stimulation (FES) of paraplegics was divided using sensor measurements of kinematic variables as inputs to five discrete events. Two identification algorithms were used to estimate the system model. Both max-min and max-product composition were used. Membership functions were either trapezoidal or triangular and all membership functions in a particular universe of discourse had the same shape and size. The universe of discourse was varied by altering the overlap between membership functions. The classification performance was assessed quantitatively, by measuring the percentage of time steps in which the correct event was found, and qualitatively, by observing types of errors. The identification algorithm affected system performance. No difference in classification was found between max-min and max-product composition. The performance was dependent on membership function overlap. A comparison of the classification found using the fuzzy rule base versus that found using a traditional look-up table demonstrated that the fuzzy approach was superior. It is speculated that the use of fuzzy logic decreased errors stemming from sensor noise and/or small variations in the input signals. The performance of this approach was compared to that of a feedforward neural network and the fuzzy system is found superior.

Fuzzy logic models for ranking process effects
B. Schaible, Xie Hong, Cheng Lee Yung
Dept. of Mech. Eng., Colorado Univ., Boulder, CO, USA
vol. 5, no. 4, pp. 545-56, Nov. 1997

When modeling and analyzing manufacturing processes, it may be helpful to know the relative importance of the various process parameters and their interactions. This ranking has traditionally been accomplished through regression modeling and analysis of variance (ANOVA). In this paper, we develop a fuzzy logic modeling technique to rank the importance of process effects. Several different cases are presented using functions that allow the determination of the actual importance of effects. The impact of noisy data on the results is considered for each case. It is shown that in many cases the fuzzy logic model (FLM) ranking methodology is capable of ranking process effects in the exact order or in an order reasonably close to the exact order. For complex processes where regression modeling and ANOVA techniques fail or require significant knowledge of the process to succeed, it is shown that the FLM-based ranking can be performed successfully with little or no knowledge of the process.

Jobshop scheduling with imprecise durations: a fuzzy approach
P. Fortemps
Dept. of Math. & Oper. Res., Fac. Polytech. de Mons, Belgium
vol. 5, no. 4, pp. 557-69, Nov. 1997

Jobshop scheduling problems are NP-hard problems. The durations in the reality of manufacturing are often imprecise and the imprecision in data is very critical for the scheduling procedures. Therefore, the fuzzy approach, in the framework of the Dempster-Shafer theory, commands attention. The fuzzy numbers are considered as sets of possible probabilistic distributions. After a review of some issues concerning fuzzy numbers, we discuss the determination of a unique optimal solution of the problem and then we cast a meta-heuristic (simulated annealing-SA) to this particular framework for optimization. It should be stressed that the obtained schedule remains feasible for all realizations of the operations durations.

Design and analysis of fuzzy morphological algorithms for image processing
D. Sinha, P. Sinha, E. R. Dougherty, S. Batman
Graduate Center, City Univ. of New York, Staten Island, NY, USA
vol. 5, no. 4, pp. 570-84, Nov. 1997

A general paradigm for lifting binary morphological algorithms to fuzzy algorithms is employed to construct fuzzy versions of classical binary morphological operations. The lifting procedure is based upon an epistemological interpretation of both image and filter fuzzification. Algorithms are designed via the paradigm for various fuzzifications and their performances are analyzed to provide insight into the kind of liftings that produce suitable results. Algorithms are discussed for three image processing tasks: shape detection, edge detection, and clutter removal. Detailed analyses are given for the effect of noise and its mitigation owing to fuzzy approaches. It is demonstrated how the fuzzy hit-or-miss transform can be used in conjunction with a decision procedure to achieve word recognition.

An algorithmic approach for fuzzy inference
C. J. Kim
Dept. of Electr. Eng., Suwon Univ., South Korea
vol. 5, no. 4, pp. 585-98, Nov. 1997

To apply fuzzy logic, two major tasks need to be performed: the derivation of production rules and the determination of membership functions. These tasks are often difficult and time consuming. This paper presents an algorithmic method for generating membership functions and fuzzy production rules; the method includes an entropy minimization for screening analog values. Membership functions are derived by partitioning the variables into the desired number of fuzzy terms and production rules are obtained from minimum entropy clustering decisions. In the rule derivation process, rule weights are also calculated. This algorithmic approach alleviates many problems in the application of fuzzy logic to binary classification.

Fuzzy shell clustering algorithms in image processing: fuzzy C-rectangular and 2-rectangular shells
F. Hoeppner
Inst. for Flight Guidance, German Aerosp. Res. Establ., Braunschweig, Germany
vol. 5, no. 4, pp. 599-613, Nov. 1997

Objective function-based clustering has been generalized recently to detect contours of circles and ellipses or even hyperbolas in a set of binary data vectors. Although there are special algorithms to discover lines, the detection of rectangles needs further treatment. A simple line-detection algorithm is not sufficient for rectangles since for identifying four lines as one rectangle, additional information such as the length of the lines and whether they are parallel or meet at a right angle is necessary. In this paper, a special fuzzy shell-clustering algorithm for rectangular contours is developed. The principal idea behind it can be generalized for other polygons so we also derive an algorithm that is capable of detecting rectangles and other polygons as well as approximating circles, ellipses, and lines.

Using fuzzy partitions to create fuzzy systems from input-output data and set the initial weights in a fuzzy neural network
Lin Yinghua, G. A. Cunningham III, S. V. Coggeshall
Center for Nonlinear Studies, Los Alamos Nat. Lab., NM, USA
vol. 5, no. 4, pp. 614-21, Nov. 1997

We create a set of fuzzy rules to model a system from input-output data by dividing the input space into a set of subspaces using fuzzy partitions. We create a fuzzy rule for each subspace as the input space is being divided. These rules are combined to produce a fuzzy rule based model from the input-output data. If more accuracy is required, we use the fuzzy rule-based model to determine the structure and set the initial weights in a fuzzy neural network. This network typically trains in a few hundred iterations. Our method is simple, easy, and reliable and it has worked well when modeling large "real world" systems.

An integrated approach to fuzzy learning vector quantization and fuzzy c-means clustering
N. B. Karayiannis, J. C. Bezdek
Dept. of Electr. & Comput. Eng., Houston Univ., TX, USA
vol. 5, no. 4, pp. 622-8, Nov. 1997

Derives an interpretation for a family of competitive learning algorithms and investigates their relationship to fuzzy c-means and fuzzy learning vector quantization. These algorithms map a set of feature vectors into a set of prototypes associated with a competitive network that performs unsupervised learning. Derivation of the new algorithms is accomplished by minimizing an average generalized distance between the feature vectors and prototypes using gradient descent. A close relationship between the resulting algorithms and fuzzy c-means is revealed by investigating the functionals involved. It is also shown that the fuzzy c-means and fuzzy learning vector quantization algorithms are related to the proposed algorithms if the learning rate at each iteration is selected to satisfy a certain condition.

Comments on "Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: quadratic stabilizability, H/sup infinity/ control theory, and linear matrix inequalities"
Jin Kang Hyung, Kwon Cheol, Park Mignon, K. Tanaka, T. Ikeda, H. O. Wang
Dept. of Electron. Eng., Yonsei Univ., Seoul, South Korea
vol. 5, no. 4, pp. 629-30, Nov. 1997

The authors state that in the above paper (Tanaka et al., 1996), the derived stability analysis cannot guarantee the norm requirement for necessity and the selection of the G matrix can affect the stability analysis. Therefore, the derived stability analysis cannot avoid conservative results. They illustrate this fact using a simple example and propose a modified stability theorem.