Fuzzy modeling is a method to describe the characteristics of complex systems using fuzzy inference. The method has a distinguishing feature in that it can express complex nonlinear systems linguistically. However in the case where the system has multi-inputs, the acquired fuzzy rules through some sorts of learning are hard to understand. And when it is difficult to obtain sufficient input-output data from the system with multi-inputs, the fuzzy model cannot be made precise. The authors have proposed a hierarchical fuzzy modeling method. The proposed fuzzy modeling method uses fuzzy neural networks(FNNs). The identified fuzzy rules with the new method are easy to understand. The method enables to obtain a precise fuzzy model even with limited number of input-output data. However, there have been some cases where this conventional method was trapped into local minima to model some nonlinear objects. This paper presents a new hierarchical fuzzy modeling using multiple submodels. The new fuzzy modeling method, having the features of the hierarchical fuzzy modeling method, expands the exploratory space for fuzzy models. This proposed method allows multiple submodels in a large and increases the possibility to obtain more adequate fuzzy models. Sumulations using numerical data are done to show the effectiveness of the proposed method.

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In recent years, power systems have been growing and complicating. For such power systems, improvement of the stability has been an important issues. To improve the stability of AC transmission system, the concept of the flexible AC transmission system(FACTS)has been proposed. In this paper, the fuzzy controller which is based on the sliding-mode control is applied to the variable series capacitor(VSrC)which is one of the FACTS equipment so as to improve the stability of power systems. The proposed fuzzy controller has the characteristics such that the fuzzy rules are constructed systematically and simply on the basis of sliding-mode control. The proposed method is applied to a single-machine against infinite bus system with variable series capacitor(VSrC), as well as to a multi-machine system. Simulation results will indicate the validity of the proposed fuzzy controller.

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The purpose of this paper is to combine the ability of fuzzy set to represent more realistic situations with the well-established traditional queueing network model problem. We are forced to employ subjective probabilities when there is no information about a model or some parameters of a model are vague. The information and data are very fuzzy, because they are frequently very little, and may be sometimes obtained from experts subjectively. We also apply fuzzy set theory to the open central server network model with the fuzzy queues and the closed single class BCMP network model in which each node consists of fuzzy queue. Thus, we represent the characteristic and performance of the open central server network model and the closed single class BCMP network model based on the proposed fuzzy queueing system.

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In this paper, first we propose constraints on natural language propositions involving fuzzy quantifiers by truth-qualification. For example, for the proposition"Most tall men are heavy is true", we consider that constrains exist between height and weights of men, so between grade values of the fuzzy set"TALL"and those of the fuzzy set"HEAVY"of the men. Second under the constraints, we propose an inference method for natural language propositions involving fuzzy quantifiers, for example"Most tall men are heavy is true". For the proposition, we can infer a modified proposition "Many tall men are very heavy is true", where the fuzzy quantifier"Many"in the inferred proposition can be resolved analytically, according to the modifier"very". Generally, for natural language propositions involving three types of quantifiers, a monotone nonincreasing type(few, …), a monotone nondecreasing type(most, …)and a convex type(several, …)and monotone truth-qualifiers(true, false, …), we can resolve fuzzy quantifiers analytically for propositions transformed in fuzzy predicates.

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In this paper the case in which the way to an instructed destination is given by linguistic terms is considered as an example of human and computer interaction. Two models are considered. One is a route decision model that understands instructions are goes to the destination. The other is a facial expression model that expresses emotions according to the situation that the route decision model falls into. These two models are implemented on a computer. In the route decision model fuzzy sets are employed in order to deal with fuzziness inherent in linguistic terms. A degree of matching is definied to compare a fuzzy set representing the meaning of linguistic terms and a fuzzy set representing information on visual scene. The route decision model proceeds on its way by the use of the degree of matching. In the facial expression model emotions are inferred from the situation of the route decision model by the use of the fuzzy reasoning. Facial expressions are shown based on values of 6 variables related to eyes, eyedrows and mouth obrained by the use of a neural network model. Some simulation results show that the route decision model can reach an instructed destination in spite of fuzzy and uncertain instructions, the model sometimes loses its way as human does, and that by the facial expression model it becomes clear what emotions the route decision model has when it reaches the destination or loses its way.

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In a healthy state, the human heart beat shows an extensive spectrum and its attractor has a chaotic orbit. However, in a damaged state, fluctuations in the heart beat become periodical. An, Implantable Cardioverter / Difibrillator(ICD), along with an implanted pace maker unit in either the subcutaneous chest wall, or subpectoral or subcutaneous abdomen, or sub-muscles rectus abdomen serve to detect abnormalities as follows and eliminate them quickly. The abnormalities affected include : ventricular fibrillation(non-regulated electrical activity in a ventricle)and other arrhythmia, such as, ventricular tachycardia(VT)or supra ventricular tachycardia(SVT). There are two methods for detecting arrhythmia available with the present ICD. One is to investigate the heart beat or period, and the other is to investigate the electrocardiographic wave. However, the employment of these techniques, either singly or in combination doesn't always reach the accuracy that is needed. At first, this paper describes traditional analysis methods and the problems of ICD in brief. Subsequently, it covers the chaotic approach. Finally, the results suitable for real testing, as well as future topics, are given.

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In this paper, by considering the experts' imprecise or fuzzy understanding of the nature of the parameters in the problem-formulation process, large-scale multiobjective block-angular linear programming problems involving fuzzy numbers are formulated. By using the α-level sets of fuzzy numbers, the corresponding nonfuzzy α-programming problem is introduced. The fuzzy goals of the decision makes for the objective functions are quantified by eliciting the corresponding membership functions including nonlinear ones. Through the introduction of an extended Pareto optimality concept, if the decision maker specifies the degree α and the reference membership values, the corresponding extended Pareto optimal solution can be obtained by solving the minimax problems for which the Dantzig-Wolfe decomposition method is applicable. Then a linear programming-based interactive fuzzy satisficing method for deriving a satisficing solution for the decision maker efficiently from an extended Pareto optimal solution set is presented. An illustrative numerical example are provided to demonstrate the feasibility of the proposed method.

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In this paper, we describe a method of scratched-look expression of our calligraphy system. Scratched-look has very various patterns. Our system makes acratched-look patterns by using fractals. In this system, a scratched-look expression is expressed by white points which are plotted with affine transformations on a calligraphy character. Thus, the system realizes scratched-look patterns which resemble real calligraphy scratched-look pattterns. More-over, the system evaluates user writing speed and pen pressure, and decides the degree of scratchiness(s_degree). The density of plotted points corresponds to s_degree, the shade of scratchiness is expressed. All 4 types of scratched-look patterns which are made in this system are close to real calligraphy scratched-look. Furthermore, besides visusal evaluation, fractal dimensions of scratched-look patterns in both the system and real calligraphy are evaluated and compared, these results reveal that fractal dimension is similar value.

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The paper proposes a diagnostic method employing Possibility theory. There has been a way to solve the inverse problem of fuzzy relational equation as a diagnostic method using fuzzy causal relations between causes and symptoms. The causalities between fuzzy set A on possible causes U and B on possible symptoms V are given as a fuzzy relation R on U×V. Then, the diagnosis is to obtain A by solving a fuzzy relational equation B=A○R under the conditions of given R and B. In the diagnostic process, the membership values of fuzzy set B are interpreted as degrees or intensities of symptoms, while those of fuzzy set A are done as possibilities or certainties of causes. This interpretation, however, shows that different measures of fuzziness-intensity and possibility-are confusingly mixed in a equation. According to Possibility theory, fuzzy sets A, B and fuzzy relation R in a fuzzy relational equation could be understood as possibility distributions π_U(u_i), π_V(v_i)on U, V and a conditonal possibility distribution π_<V|U>(v_i|u_i)on U×V, respectively. Therefore, in this paper, we define diagnostic problem as a problem to obtain possibility that any crisp subset of U is the set of causes of a given crisp subset of V as symptoms, where possibility distribution π_U(u_i)on U and conditional possibility distribution π_<Y|U>(v_i|u_i)are given as a priori knowledge. Then, the way to solve the problem is discussed and proposed.

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To expand and to improve the ability of fuzzy control inference system, we have analyzed the characteristic of fuzzy control rules in the unstable system with multi-degrees of freedom using computer simulation. In this study we have managed to control the inverted double pendulum. From our experiences, we have adopted a two-stage inference method, in which first, we infer the force to control the each arm of the double pendulum independently, and then we unify and infer the actural value of the force from the values that was infered in the first step. To make the control system more flexible and more robust, we proposed a simple and strong adaptive control method of range scaling method in which the system reduces or expands the scale of the range of fuzzy variables dynamically. This method resolves the conflict of requests such as to make the inverted pendulum standibng with the wide range of the initial values and to control the pendulum more precisely. We could the inverted double pendulum using the fuzzy control rule sets and adapting the range scaling method by a computer simulation. The fuzzy control system reveals an accurate control and also achieves a robust control by the simple range scaling method proposed in this paper.

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