The qualitative data which contain human consciousness and mental states involve human vagueness, but applications of fuzzy systems theory are effective on such data. In this paper, by using Zadeh's probability concept of fuzzy events, we define the fuzzy interval data and introduce the Bayesian posterior distribution by fuzzy data. However, the method with direct usage of the membership functions of fuzzy interval data treating the membership functions precisely is inefficient from a view point of calculation. But our method treating the middle points of membership functions as the representative points can settle such problems. Here, we suppose that the fuzzy interval data are obtained from normal population. When prior distribution of population parameter θ is normal distribution, we can show that the posterior distribution forms the normal distribution approximately by using our proposed method. As a result, even if we obtain fuzzy interval data, we can explain that the approximate Bayesian interval estimation which is not so far different from the usual Bayesian interval estimation of population parameter θ is possible. In real situations, we do not always obtain ideal symmetrical membership functions. Then, we perform the computer simulations under relistic situations which do not satisfy completely the condition of the symmetry of trapezoidal membership function and examine the practicability of our method. As a result, we can show the practicability.

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In this paper, we propose an inference method for natural language propositions involving fuzzy quantifiers. For example, from "Most tall men are heavy", we can infer a modified proposition "Many tall men are very heavy", where the fuzzy quantifier "Many" in the inferred proposition can be resolved analytically. Generally, for natural language propositions involving three types of quantifiers : a monotone nonincreasing type (few, …), a monotone nondecreasing type (most, …) and a triangular type (several, …), we can resolve fuzzy quantifiers analytically for inferred propositions.

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Recently many research studies using fuzzy theory have been done for the modelings of complex systems including human beings. Especially in the field of decision-makings, and human emotions, the researches have been developing. The authors have proposed a multi-attlibute decision making model based on fuzzy inference and realized the model with a fuzzy neural network (FNN). In this paper, we compare our model with the conjoint analysis which is a practical tool for measuring consumers' perception of the products, and clarify the remarkable points as well as the limits of our model.In multi-attribute decision making, human beings influenced with various factors often change their decisions. There have been few researches that studied the change of human decisions. This paper presents a new approach to identify the change in a decision making process. The new approach is based on the model which the authors have proposed. The FNN identifies the weights to the attributes with the back propagation learning.Through experiments, it is shown that the changes of subjects' decisions can be described by the changes of their weights to the attributes. It is also studied how the change will be when some new information are added during the decision making.

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This paper studies knowledge finding for fuzzy inference system with multiple inputs. Recently many research studies on Classifier System (CS) which is a new paradigm of machine learning have been reported. This system is a production system which generates production rules using genetic algorithms. Fuzzy Classifier System (FCS), which uses a fuzzy inference system and a fuzzy rule base in place of the production system and the rule base of the CS, can handle continuous variables. The FCS uses a chromosome into which a fuzzy rule of fuzzy rule table is encoded, and it does not increase the size of the chromosome exponentially in dealing with multi-input systems. However, the FCS was applied to a single input-single output function approximation problem, and only its capability to handle continuous variables was shown. No study on methods of credit apportionment which is very important for multi-input systems has been reported.This paper shows that the feature of the FCS is its capability to find fuzzy rules by applying the FCS to a multi-input system. Simulations of collision avoidance of a ship are done to show that the FCS can find fuzzy control rules from payoffs based on only successes/failures of the steering. This paper also studies a method of credit apportionment for this problem. With this method, the fuzzy rules which describe knowledge in mutually related variables can be obtained.

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We characterize the problem of detecting edges in images as a fuzzy reasoning problem. The edge detection problem is divided into three stages : filtering, detection, and tracing. Images are filtered by applying fuzzy reasoning based on local pixel characteristics to control the degree of Gaussian smoothing. Filtered images are then subjected to a simple edge detection algorithm which evaluates the edge fuzzy membership value for each pixel, based on local image characteristics. Finally, pixels having high edge membership are traced and assembled into structures, again using fuzzy reasoning to guide the tracing process. The filtering, detection, and tracing algorithms are tested on several test images. Comparison is made with a standard edge detection technique.

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In fractal block coding technique, an image is divided into blocks and codes of the image are made by searching similar blocks. Chotic images that are not suitable for conventional compression techniques are processed at high compression rate by using fractal coding. However, this technique is too time consuming to use practically. This paper proposes a method to improve the processing time.Because it is necessary that no perceptible defect generates in the reconstructed image, the ability of the visual sense is considered in the algorithm. Edge information extracted by using a ▽^2G filter is used to make a quadtree that represents a variable block division of the image. However, edge blocks are divided into the smallest blocks because edge blocks are important to the visual sense. Similar blocks are searched adaptively on this variable block structure. Moreover, flat blocks are searched in the permitted error by using the established threshold.This method achieves the 1/2.75 reduction in processing time and the 1/1.29 reduction in compression rate. The S/N ratio is 0.7 dB worse, but the degradation is not noticeable.

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We propose an intelligent interface using an on-line human motion recognition method by means of associative inference. The proposed interface carries out recognizing by means of a) a fuzzy rule set whose fuzzy labels express human motion features, and of b) situation dependent rule sets additional to a)'s a rule set. So the proposed interface improves two conventional untouched interface problems explained ; 1) it's impossible to recognize any human motions, 2) It's impossible to distinguish same human motions in dependence on a situation or on a context.We apply the proposed interface both to a robot interface and to a Japanese sign language interface. As results of experiments, the rate of recognition average on the robot interface is 98.1%, the rate of recognition average on the Japanese sign language interface is 85.9%. So we verified that the proposed interface improves two problems shown as 1) and 2), shows its usefulness for untouched human interfaces.

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As is well known, there are two typical approaches to the noise evaluation problems as follows : (1) The first approach is by the physical noise evaluation method, where attention is mainly paid to the valuation indices such as the equivalent soud level, median, etc., which can be objectively measured and/or predicted. (2) The second approach is by the psychological noise evaluation method, where attention is mainly paid to the evaluation indices such as loudness, noisness and annoyance that can be subjectively measured.In the engineering field of the practical noise counterplan, it is very important to grasp quantitatively the mutual relationship between the physical sound insulation system and the psychological impression. On the other hand, in the psychological noise evaluation, the fuzziness caused by the human subjective judgment for the acoustical stimulus is inevitably obscure.From the above viewpoints, in this paper the relationship between the physical sound insulation method and the psychological noise evaluation method for fluctuating random noise is considered, by using the fuzzy set theory. That is, a new systematical method for estimating and/or predicting the psychological impression is proposed, in the case when the two physical characteristics of noise stimulus (the sound pressure level probability distribution and the power spectral density) being changed by the erection of the sound insulation barrier. The validity and usefulness of the proposed method are confirmed experimentally by application to the actually observed data.

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A method of computerized tomography using the neuro-fuzzy model was proposed for the reconstruction of smooth distribution of some material parameters. Unfortunately, detailed pictures of the spatial distribution is hard to reconstruct from very small number of projection data. In this paper we discuss the effectiveness of regularization conditions in the neuro-fuzzy computerized tomography.

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