The GMDH(Group Method of Data Handing) family of modeling algorithm emulates the self-organizing activity of the central nervous system, and discovers the structure (functional form) of empirical models that include many input variables.A generalized susccessive projection method for fast learning algorithm of the GMDH type model whose partial descriptions are represented by Radial Basis Function networks is developed and compared with the instantaneous learning algorithms such as the Least mean Square.(1) For the learning of partial descriptions of the perceptron type GMDH, a combined algorithm of the Successive Projection Method and the Orthogonal Projection Method is deveoped. (2) For the learning of the network type GMDH, an algorithm is derived ast he solution of an optimizaiton problem in which the Minkowski norm of distance travelled (step size) is minimized. Several examples show the validity of the methods.

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There have been growing demands of supporting tools for facility management to cope with rapidly increasing and diversifying offices. The authors have proposed a supporting system for office zoning as the first half of the process of the office plane planning. The authors also study a case utilizing system to utilize cases of furniture layouts as the latter half of the plane planning. For the utilization of the cases, the selection of indexs and the method for case retrieval are important.This paper presents new methods for indexation and knowledge acquisition for the case retrieval for the case utilizing system. For the selection of the indexes, a field study of office layouts is done. Important factors for the evaluation of the layouts are chosen and a fuzzy number for each factor is used to index the cases of office layouts. A fuzzy inference is employed to retrieve the cases. For acquiring the weights on the fuzzy rules, the knowledge acquisition support system with a presentation of suggestions proposed by the authors is applied. For demonstrating the feasibility of the proposed methods, simulations are done. Moreover, the supporting system for office zoning and the case utilizing system of furniture layouts are integrated on the CAD-system. Demonstration of the integrated system is shown.

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It is expected that the need for softwae agents for automatic matching and extraction ofdigital images flowing in multi-media networks.Image consists of multiple patterns. It is effective to distinguish vague patterns by interactions with multiple symbols. These symbols correspond to multiple meanings ofpatterns, and the interactions among patterns and symbols can determine meanings of patterns.This paper presents a multi-module network for the inference of a meaning of a combination of vague patterns with multiple meanings through interactions between symbols and patterns. This paper also proposes an attention mechanisms for this multi-module network. Experiments on association of facial expressions consisting of eyebrows, eyes, and mouths are done to show feasibility of the proposed network.

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This paper considers that concepts of objects are sets of vague patterns of multiple attributes. These concepts can be recalled through association among the vague patterns. By the association and recollection of concepts consisting of multiple vague patterns, the concepts under insufficient or imprecise information can be also recolledcted.It has been reported that multistage inference of fuzzy logic explodes vagueness. This explosion will erase all the information in the inputted patterns. This is also the case in the association among vague patterns. Suppression of increase of vaguenness should be studied.This paper proposes a network which can associate and recall concepts on combinations of multi vague patterns. A mechanism for suppression of vagueness is introduced into the association among the vague information. Feasibility of the proposed method is verified by simulations using fruits having the attributes of taste, color, shape, etc.

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This paper proposes a fuzzy-arithmetic-based method for extracting fuzzy if-then rules from a multi-layer feedforward neural network. We assume that the neural network has already been trained for a multi-dimensional pattern classification problem. The proposed method extracts fuzzy if-then rules such as "If x_1 is small and x_2 is large then Class 2 with CF=0.9" where CF is the grade of certainty of this rule. For extracting such a fuzzy if-then rule, first antecedent fuzzy sets of a fuzzy if-then rule are presented to the trained neural network in the proposed method. Next the outputs from the neural network are calculated as fuzzy numbers based on fuzzy arithmetic. Then the consequent class and the grade of certainty of the fuzzy if-then rule are determined by an inequality relation between the fuzzy number outputs. In order to show the effectiveness of the proposed method, we show simulation results on some numerical examples.

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By means of fuzzy c-means clustering algorithm, we propose a neuro-fuzzy learning algorithm for tunning fuzzy rules. In this new approach, firstly, we abstract so-called typical data from given training data by using fuzzy c-means clustering algorithm (FCM) in order to remove the redundant data and resolve conflicts in data whcih are considered disadvantages for the learning time and the convergence, and make them as practical training data. Then, according to these typical data, we tune fuzzy rules based on the neuro-fuzzy learning algorithm proposed by authors. These typical data created by FCM have similar characters and properties with the original training data esentially, and the number of the data is less than the original one, so that the learning time can be expected to be reduced. Also, it will be considered that the fuzzy rules generated by the combination of FCM and neuro-fuzzy technique are more reasonable and suitable for identifying a system than the case of using only the neuro-fuzzy learning algorithm. Moreover, the efficiency of the proposed approach is illustrated by numerical examples.

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When we attempt to model a complex system including human as an important component, it may be difficult to represent the system by a deterministic mathematical model. The main reason of this difficulty is that the system itself inherently has some fuzziness concerning subjective judgement of human. In this paper, we propose a fuzzy nonlinear regresion analysis method with RFLN(RCE-based Fuzzy Learning Network), which is capable of extracting knowledge of the experts automatically, RFLN is an extended RCE (Restricted Coulomb Energy) model, hence it needs few iterations in learning and its additional learning is easy. The proposed method has higher flexibility than fuzzy linear regression analysis models. We propose learning algorithms to identify a nonlinear interval model which approximately includes all the given input-output data. The proposed method has characteristics of faster learning and of easier additional learning. The effectiveness of the method is shown by numerical experiments.

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It is known that a fuzzy modeling approach is effective for constructing a fuzzy controller based on some fuzzy models. The asymptotic stability of such a fuzzy system can be assured, when exsisting a common Lyapunov solution to the Lyapunov inequalities for each subsystem. In addition, the stability check of A_iA_j is conventionally used as a necessary condition for searching a common Lyapunov solution, where A_i is a stable system matrix for the i-th subsystem. We sometimes can not conclude whether the fuzzy system is globally asymptotically stable or not, because a common Lyapunov solution does not exist, though A_iA_j is stable.In this paper, we specialize the fuzzy system as a mixed system or a periodically time-varying system, where in the former case the rule confidences p_i(k) are assumed to have 0 < p_i(k) < 1,and in the latter case they are assumed to have p_i(k)=1 or p_i(k)=0 with the fixed configuration of a period L. It is shown that if the fuzzy system is asymptotically stable as a mixed system and a periodically time-varying system with a relatively long period, then the fuzzy system provides a stable behavior in the computer simulation, even though there exist no common Lyapunov solutions. Of course, if there exists a common Lyapunov solution, then the fuzzy system is said to be asymptotically stable as both special systems; in particular, it is asymptotically stable as a periodically time-varying systems with any period L.

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A technique to predict the principal motions of earthquakes using preliminary tremors, has been developed. Taking adventage of the time lag between them, we can take suitable countermeasures against the principal motions that affect the urban structures; e.g. an escape from dangerous zone, stopping elevators and gas supply, and setting up AMD (Active Mass Damper) system. A structured neural network is used to construct the maximum acceleration prediction model, where inputs are fuzzified shaking direction data, power spectrum and maximum acceleration of preliminary tremors. The proposed model has been improved by handling some earthquakes in Ibaraki-ken southwest area that least fit the model as exceptions. Average square error of the improved model is reduced to third of one of the statistical model.

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On a continuous logic system whcih uses AND, OR, NOT and arithmetic operations, one type of infinitelly-valued functions : infinitelly-valued threshold functions were defined in previous papers. It has been shown that the infinitelly-valued functions may be applied to approximate reasoning involving ambiguity, and to process control with high speed, while there remains a fundamental problem of devising and effective scheme to express non-liear approximate reasoning rules by teh infinitelly-valued threshold functions.This paper firstly discusses mathematical aspects of a group of the infinitelly-valued threshold functions, which have range of the interval [0,1] as I/O domain and are denominated the fuzzy threshold functions. Secondly, particular fuzzy threshold functions, which behave as discrete threshold functions when discrete inputs are given, are discussed, Necessary and sufficient conditions are presented. Thirdly, multistage synthesis of the infinitelly-valued threshold functions are discussed showing what type of functions may be generated. Based on these considerations, this section clarifies the applicability of the infinitelly-valued threshold functions to express non-linear approximate reasoning rules. Lastly, a synthesis method of an analogue full-adder is proposed as an application of these considerations.

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This paper constructs a model which infers and expresses the degree of laugh resulting from a funny story. A psychological model analyzing the degree of laugh and fuzzy theory are applied to the presented model. The degree of laugh is expressed by the use of facial and liguistic expressions. The pleasure of surroudings, the degree ofmental strain, amusement of the story and the degree of feelings resulting from the story are considered as inputs of the model. They are expressed by linguistic terms. First of all, an initial face is obtained by the use of the fuzzy reasoning technique from the pleasure and the strain. The face is expressed together with linguistic terms. Next, the condition of laugh is obtained by the use of degrees of unconstrained state of mind and mental strain. The degree of uncostrained state of mind is estimated from the pleasure of surroundings and the degree of feelings resulting from the story. The degree of laugh and that of superiority laugh are estimated by the use of the fuzzy reasoning technique and expressed by facial expressons and linguistic terms. Finally some questionnaires are performed in order to evaluate the presented model.

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It is frequent that irregular-looking time series data may be caused by deterministic dynamics, and also well konwn that it is called deterministic chaos. Nowadays even if the time series data observed from a system has little noise, it is not always easy, by eye, to recognize whether or not it has some noise. To solve this issue, in general, there is a method of extracting some characteristic frequency by FFT(Fast Fourier Transformation). But chaotic time series is composed of infinite number of frequency element, and give rise to broad continuous power spectrum. In this paper, we propose a new method based on the chaos theorem, Trajectory Parallel Measure Method that measures the degree of stochastic process in the time series governed by determinism. One of the features of this method is to examine directions of trajectories sampled randomly from the attractor. And we present the result of the application of this method to 3 types of data ; the chaotic time series data, white noise and the time series data which is added some white noise on the chaotic data, and we also present its usefulness.

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