Statistical data including personal subjectivity or vagueness can be regarded as fuzzy observations. The treatment for the fuzzy observations was developed by Okuda, et al. In this fuzzy observation model, concerning the identification of membership functions, it is impossible to apply the conventional subjective methods because the membership functions must be restricted so that the frequencies of fuzzy data accord with the population distribution. In this paper, a method of identifying the membership functions based on fuzzy observation data is presented.

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The grouping of n objects into g groups is equivalent to the assignment of the every membership α_<ij> of ith object to jth group. When these α_<ij>'s are un-known, a criterion to get optimal α_<ij>'s from obtained date is proposed. Making use of the hypothesis decomposition for the contingency table, the change in the amount of information by grouping I_g is defined as I_g=n log n+Σ__iΣ__j α_<ij>logα_<ij>-Σ__j n_jlogn_j, 0≦α_<ij>≦1,Σ__j α__ij=1,where n_j is the number of members in jth group. On the other hand, we also have the parallel hypothesis decomposition with that for the contingency table, if the object data is assumed to be drawn from the normal population. Then from a geometrical viewpoint a new criterion FGC (Fuzzy Group Criterion) is proposed in order to search for an optimal grouping such as FGC=S_W/S_T+I_g/I_n, where S_T and S_W denote the total S.S. and the within S.S., respectively, and I_n=nlog n which denotes the change in the amount of information by grouping of n objects into n non-fuzzy groups. An optimal grouping is then selected to have the minimum FGC. This grouping strategy is intended to have the small within S.S. without a clear-cut grouping, that is, with small I_g. It may lead to a fuzzy grouping optimal. The application of this strategy to the fuzzy k-means method is described, where the optimal number of clusters and the parameter value which controls the degree of separation between clusters are searched for. An example to two artificial two-dimensional data sets is also given in which we get a result that the fuzzy clusters are optimal if the boundary between clusters seems obscure and that the non-fuzzy ones are optimal if it seems clear.

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This paper presents a study on the intelligent vehicle that has the driver's subjective evaluation model. In this system, inferring driver's subjective evaluation for drivability, the vehicle changes the control characteristics of the engine, the automatic transmission, etc. This study is the first step towards designing an intelligent vehicle capable of operating under specified driving conditions. The subject's driving task is to follow the car in front of subject and to keep the headway distance between the two cars consistent. In order to carry outthis driving task, drivers are asked to center the first car within the boundaries indicated on the windshield of the test car. The relationship between the error of headway distance and the accelerator of the subject who follows the first car are expressed by auto regressive and moving average models (ARMA model). Fuzzy data result from this relationship are generated from the coefficients of the ARMA model. Because each driver performs the given task differently, the data are difficult to analyze with conventional methodology. I applied techniques similar to that of type-2 fuzzy sets analysis to this data. This model are applied to predict subjective evaluation of the driver performing the driving task with a "control" car which has an unknown characteristic of automatic transmission, and the inference remains true.

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Some methods for acquiring fuzzy reasoning rules by neural network have been proposed. These methods, however, use multi-layered neural network which contains hidden units corresponding to all combinations of membership functions, so the number of hidden units (i.e., reasoning rules) increase exponentially as the number of input variables and their membership function increase. In order to solve this problems, in this paper we propose a new acquisition method of fuzzy reasoning rules. The neural network used in this method have a dynamic creative function of hidden units, so the only necessary rules to express the characteristics of controlled object are created in the network. The process of rule acquisition by this method resembles closely the process that a man makes fuzzy reasoning rules by trial and error. We demonstrate the effectiveness of this method by applying it two fuzzy control problems.

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The concept of rough sets, which was proposed by Z.Pawlak in 1982,can be employed to discuss the consistency of the classification given by human experts with the observed attribute values of each sample. Z.Pawlak proposed a method of reducing attributes, i.e., removing redundant attributes based on the equivalence relation defined by the attribute values of each sample. Tanaka et al. modified the Pawlak's method to remove more attributes by considering the given classification. They also constructed a fuzzy expert system based on the reduced attributes and applied it to a diagnosis problem of liver troubles. This paper aims to improve the performance of their fuzzy expert system by proposing a new fuzzy inference method. While only the most fitting fuzzy rule is usually used in their method, we take account of all fuzzy rules for classifying unknown samples. In order to consider all fuzzy rules, we use the average-product combination in classification process. The classification power of the proposed method is demonstrated by an application to the same diagnosis problem as in Tanaka et al.

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A kind of optimal membership function is decided experimentally, which generates a fuzzy feature from the mesh pattern of character. This decision is based on the fact that the meshes with smaller number of black pixels is greater than those meshes with bigger one. According to experiments, it is confirmed that some of handwriting variations can be absorbed by fuzzification of the mesh feature. And the recognition rate can be improved about 4.9% by setting bigger membership value to those meshes with smaller number of black pixels when a character includes more of such kind of meshes. Moreover, when the fuzzy feature is applied to the near degree method with cutting value, the recogniton rate is additionally enhanced about 4.4%.

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Many papers of image processing have been published until now, most of which dealt with the pattern recognition, boundary detection, noise elimination and three-dimensional understanding. Few paper treated the meaning of image. Considering the rapid progress of multi-media information systems, the problem of communication between human and image must be very essential in near future. The problem of the impact of image on human mind has been studied in psychology. On the other hand, almost nothing has been studied about the transmission of mental image of human to picture. In this paper, the authors develop a system where a colorless landscape (line drawing) is painted automatically in accordance with the seasonal image of human. Since the image in human mind is abstract, it is difficult to trasnform it to computer command. And color is not only a physical variable but also a psychological one, therefore mathematical representation is almost impossible. The authors first express the seasonal color image by natural language as to each element. Next, the rules which translate the linguistic expression to RGB component are introduced. The variables in the above rules are all sensory and qualitative, which are conveniently represented by fuzzy sets. By using these rules and approximate reasoning very delicate coloring is realized. Moreover, some additional rules of modification are considered, in order to adjust the color image when the season and the time are different from the standard. Approximate reasoning is applied too for the modification. Some different kinds of landscape are colored by this method, and most of the results can express human image satisfactorily.

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The work which forms the basis of this paper is aimed at solving the following two problem areas of support systems for shape creation in product design : a. Expression of complex design viewpoints for the creation of new proposals of shape. b. Relating abstract words to concrete shapes by use of meaning. Firstly, in order to solve (a), development of a fuzzy reasoning model was under taken, for the purpose of generating new proposals of shape using a complex evaluation plane of an arrangement of sample shapes. The results of simulation by the model was compared from the viewpoint of obtaining new shape proposals, and a reasonable degree of success was observed. Secondly, in order to solve (b), development of a further fuzzy reasoning model for relating words to shapes. The results of simulation by the model were compared to designer's judgment feeling of shapes, and again a reasonable degree of success was observed. Finally, for application of the two models, an experiment was conducted, based on proposals of shape obtained by processing input words. The practicality of the results was considered from a designer's viewpoint and it is considered that the system may be useful.

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A new fuzzy control method for an inverted pole installed on a cart is proposed. The controller can upswing the pole from the dangling state and then stabilize the inverted pole, including control of cart position. Two kinds of 2 dimensional formalized fuzzy rule tables are used in this control. One consists of 49 articles of fuzzy rule which are used for control of both the pole upswing from the dangling state and the stabilization of inverted pole. The other is a fuzzy rule table for indirectly positioning the cart location by controlling the slant angle of inverted pole after stabilization. 7 kinds of fuzzy sets are used for constructing the rules and a triangle type membership function is used for reasoning. A new high-speed reasoning method is proposed. By contriving several ideas to make these rules work effectively, a reliable control method is established. The control of nondimensionalized system is studied in order to prove the propriety of this fuzzy control for the entire cart/pole system, and several new observations are introduced concerning design of and tuning of the control system and the upswing limit of the pole.

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A Basic Oxygen Furnace (BOF) has an important role in the steel making process. The amounts of impurities in the pig iron from the blast furnace should be controlled in the process of the BOF. Through the operation of the BOF, some portion of manganese (Mn), which should remain in the steel adequately, is also removed. It is required to control the density of the residual Mn in the steel in the desired level. However, it has been difficult to estimate and control the density of the residual Mn effectively mainly because the chemical reactions in the BOF are quite complicated. This paper presents a fuzzy modeling of the residual Mn in the BOF for realizing practicalestimation and control. A fuzzy neural network was used for the fuzzy modeling. Two modeling procedures were used : one is the method of increasing variables for identifying the premise part of the fuzzy model and the other is the method of increasing the number of input variables with the fixed membership functions for each input variable. The former method identified a fuzzy model which clarifies main parameters regarding the residual Mn and the latter method identified another fuzzy model with useful input variables for controlling the BOF. The accuracies of the obtained models were sufficient for practical use in the field.

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