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The viewpoint of this paper is based on the hypothesis that human expert know-how is represented and stored in natural fuzzy linguistic terms. Know-how is obtained by the summarization of numerous experiences over a long period of time and expressed with a set of fuzzy IF-THEN rules. This paper describes the electronic circuits, both in current and voltage modes including semiconductor chips that were developed from 1980–1997, and dedicated to fuzzy information processing. A set of fuzzy IF-THEN rules with a fuzzy inference engine has a good ability to describe complicated systems that are nonlinear, time-varying, multivariable, chaotic, unpredictable, etc. The focus of this paper lies not only on a fuzzy inference engine and defuzzifier, but also on a fuzzy memory device, fuzzy PLA, a grade-controllable membership function circuit and time-sweeping mode fuzzy computer hardware. Distinctive features of a fuzzy logic controller are presented by employing benchmark tests, such as an inverted pendulum, wine glass stabilization and mouse stabilization. These experimental results show that fuzzy logic control is effective, even in cases where the mathematical model is not available.

In this paper, we propose a hardware oriented vector quantization algorithm employing rough-winner-take-all neural network. The proposed algorithm is almost same as K-means clustering which is the simplest vector quantization. The only different point is that the proposed method employs rough-winner-take-all as the substitute of ordinary winner-take-all. In a rough-winner-take-all strategy, the winner is roughly selected in the early learning stage and is strictly assigned in the later stage. The simulation results show that the quantization performance of the proposed method is nearly equal to Neural Gas which is an excellent vector quantization. Besides, the proposed method can be realized as an extra mode of existing K-means or Self-Organizing Map hardware by changing its winner-take-all controlling.

A 2−r shape of a membership function generator is presented. The proposed membership function generator requires a bit-shifter and a NOR operation only, and thus suits digital hardware implementation well. A fast defuzzification method employing active units is also presented. It reduces a calculation cost for the defuzzification. In this paper, we have successfully applied proposed methods to a self-organizing relationship network. Simulation results show that the proposed method has as good and approximation ability of nonlinear functions as the ordinary method.

We propose a bit-shifting-based fuzzy inference method for an efficient digital hardware implementation. The proposed fuzzy inference method includes two new techniques which are a membership function generating method and a fast defuzzification method using only “active units”. These techniques reduce a hardware cost and a calculation cost for the membership function and the defuzzification, respectively. In this paper, we apply the proposed method to an execution mode of self-organizing relationship network. Simulation results show that the proposed method has a good approximation ability of a nonlinear I/O relationship as well as the ordinary method.

In this paper, we propose a new updating method considering usability of each element of inputs and apply it to the reproduction of the GA to achieve more effective search than the traditional reproduction. In the proposed updating method, the order of updating elements is decided by averaging the corresponding elements multiplied by fitness values of the chromosomes. To verify the effectiveness of the proposed updating method, the GA with the modified reproduction is applied to 0–1 knapsack problem.

We use a deep mathematical result (namely, aminor modification of Kolmogorov's solution to Hilbert's13th problem) to explain why fundamental physicalequations are of second order. This same result explain why all these fundamental equations naturallylead to nonsmooth solutions likesingularities.

This paper describes a fuzzy rule-based simple interpolation algorithm for discrete data. A simple interpolation algorithm between two noise-free points in the Euclidean space is proposed by taking into account the fuzzy effects of the surrounding points. The advanced algorithm for the noisy points is proposed, where interpolation is done by classifying the neighboring noisy points into some groups. The validity and the effectiveness of these methods have been verified by computer simulations and by applications to the actual time series noisy data. The experimental results have provided substantial proofs for practical use.

In this paper, a new optimization method, which is effective for the problem that the optimum solution should be searched in several solution spaces, is proposed. The proposed method is an extension of distributed genetic algorithm (DGA), in which each sub-population searches a solution in different space. Based on the competition between sub-populations, population sizes are adequately changed. The proposed method is applied to signal source localization, in which the number of sources is unknown, and simulation results show the effectiveness of the method.

This paper proposes a new method of Self-Organizing Map (SOM) in which an input space is represented as a graph by modifications of a distance measure and a updating rule. The distance between input node and reference element is defined by the shortest distance between them in the graph. The reference elements are updated along the shortest path to the input node. The effectiveness of the proposed method is verified by applying it to a Traveling Salesman Problem.

We propose a new image enlargement method employing a codebook-based fuzzy interpolation technique in order to realize simultaneous smoothing and sharpening in image enlargement. In the proposed method, codebooks are generated by using self-organizing maps, and codes of the codebooks are used to determine parameters of Gaussian membership functions in the fuzzy rules. Then, an enlargement of an image is achieved by a fuzzy inference. In this paper, experimental results show the performances of the proposed method superior to other typical image enlargement methods. The calculation time is reduced drastically in comparison with the previous codebook-based method which has been proposed by the authors.

We propose new method of the independent component analysis (ICA), which doesn't require to know the classes of the distribution of the sources beforehand in contrast with conventional methods and achieves separation of sources with higher precision than the conventional methods. The proposed method employs the self-organizing maps (SOM) to the Bell-Sejnowski's method (1995) for the purpose of making use of the ability of SOM to approximate the probability density. SOM grasps the probability density of the input signals by nature. It can also track the changes of the probability density of the input signal adaptively. In this paper, the effectiveness and validity of the proposed method are verified by applying it to the separation of linearly mixed sounds and linearly mixed pictures by the computer simulations.

We propose novel FIR-OS hybrid type filter employing the neo fuzzy neuron, and frameworks of a linear FIR filter and an order statistic (OS) filter, aiming at elimination of a Gaussian noise and an impulsive noise at the same time, and high restoration of the signal, simultaneously. The proposed filter is synthesized by learning method which guarantees optimal design caused by employing the neo fuzzy neuron (NFN) model. In this paper, the effectiveness and validity of the proposed filter are verified by applying it to the filtering of the noisy images.

The authors describe a design algorithm for extraction of membership functions of a fuzzy neuron based on example-based learning with optimization of cross-detecting lines. This algorithm facilitates design without the knowledge of experts. The algorithm was verified by recognition of hand-written characters. Using this algorithm, a fuzzy neuron can be designed very easily without knowledge about the features of the character, and optimum membership functions can be extracted. >

The paper describes a scale factor controller, presented by the authors, which is a modification of a voltage-driven weighted current mirror with feedback. It is applied for a current multiplier/divider and also a defuzzifier circuit.

In early learning stage of a self-organizing map (SOM), the weight vectors are arranged to interpolate among the input vectors. A new interpolation method employing the transient characteristics of the SOM is proposed in this paper. In order to realize a smooth interpolation, a modified updating equation based on compensation vector is used in the proposed method. Furthermore, we define the criterion of smoothness, and the reasonable number of learning iterations for the desired arrangement of the weight vectors can be decided. The performance of the proposed method is confirmed by the interpolation results in 2-dimensional and 3-dimensional spaces.

In this paper, we propose a new method of the shape detection by using a self-organizing method with input vector transformation. It is difficult to detect a shape from a noisy image by the conventional Hough Transform. The proposed method enables to detect the shape automatically. Two SOMs are used in the proposed method, the first SOM determines the number of typical shapes included in the image and the second SOM determines the parameters of the shapes. The performance of the proposed method is confirmed by detection of lines and circles from noisy images.

Adaptive-Subspace Self-Organizing Map (ASSOM) is a variant of Self-Organizing Map, where each computational unit defines a linear subspace. The subspace in a unit is represented by a set of basis vectors. After training, these units result in a set of subspace detectors. In numerous cases, however, these are not enough to describe a class of patterns because of a linearity. In this letter, the ASSOM on the high-dimensional space with kernel method is proposed in order to achieve efficient classification. By using the kernel method, linear subspaces in the ASSOM can be extended to non-linear subspaces easily. This improves the representation of subspace. The effectiveness of the proposed method is verified by applying it to a well-known problem, or two spirals classification.

In this tutorial, the utility of a fuzzy system is demonstrated by providing a broad overview, emphasizing analog mode hardware, along with a discussion of the author's original work. First, the difference between deterministic words and fuzzy words is explained as well as fuzzy logic. The description of the system using mathematical equations, linguistic rules, or parameter distributions (e.g., neural networks) is discussed. Fuzzy inference and defuzzification algorithms are presented, and their hardware implementation is discussed. The fuzzy logic controller was used to stabilize a glass with wine balanced on a finger and a mouse moving around a plate on the tip of an inverted pendulum. >

This paper describes a fuzzy sets method which is very useful for handling uncertainties and essential for knowledge acquisition of a human expert. Kinetics of a reactor is often complex and not trivial to describe by mathematical equations. Reactor control by traditional control technology is therefore difficult. A novel technology is presented. In the following a fuzzy inference (approximate reasoning) is used for decision making in analogy to human thinking, facilitating a more sophisticated control. Readers of this paper do not need any advanced mathematics beyond the four basic operations in arithmetic (+,−, ×, ÷) and using the maximum and minimum values. This fuzzy inference is introduced to construct a fuzzy logic controller which is suitable for a nonlinear, multivariable and time variant system applied to a bioreactor.

A new filter based on the statistical independence between signals is presented. The original signal is estimated by the weighted sum of each harmonic of the observation corrupted by noise. The filter is synthesised by adjusting the weighting parameters by learning with the use of higher order moments of observation noise without any information about the dynamics of a target system.