Firstly, we consider modes of reasoning and show that fuzzy reasoning is performed depending on the knowledge of plural rules. Secondly, we introduce an extended logic system employing arithmetic operations together with AND, OR and NOT. On the logic system introduced, we consider infinite multiple-valued switching functions satisfying monotonicity, and then define fuzzy threshold functions. Thirdly we assume monotonicity in modes of reasoning, and represent rule tables of reasoning by means of the fuzzy threshold functions. Next, we propose a method of approximate reasoning using these rule tables. Fourthly, we apply the reasoning method to process control. Through experimental studies by a computer, we show advantages of the control method employing fuzzy threshold functions to the MAX-MIN-CG method which is one of the often used fuzzy-logic-based process control methods. In theoretical discussions, it is shown that fuzzy threshold functions include multiple-valued threshold functions as a special case. This implies that any multiple-valued threshold function may easily be expressed in an extended logical form.

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In this paper, by introducing a degree of satisfaction represented by a fuzzy set for an n-person cooperative game, the game is defined by a three-tuple(N, μ, G), where N is a set of players, μis a membership function of a fuzzy set representing a degree of satisfaction with respect to a payoff and G is the amount of payoff. For the game(N, μ, G)we propose a new solution concept on the basis of the fuzzy decision by Bellman & Zadeh. Then we further consider how to construct the membership functions through characteristic functions υ in a traditional game(N, υ). This means that the game(N, υ)is extended to the game(N, μ, G). When all of the membership functions are linear functions or hyperbolic functions, the proposed solution can be obtained through the formulated linear programming problems respectively. We also consider to adopt one of the five types of membership functions, which include linear, hyperbolic, exponential, hyperbolic inverse and piecewise linear functions, to each coalition. In this case, the proposed solution can be obtained by combined use of the bisection method and the phase one of linear programming. An illustrative numerical example is presented and the proposed solution and the nucleolus which is a related solution concept are compared.

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It is well known that there are two types of method in approximate reasoning systems. One is the 'direct approach' which was originally proposed by Zadeh, and the other is the 'truth space approach', as Baldwin called it, which has several ways. It is shown by Tong that these two approaches give the same conclusion under the strict condition. However we shall show that these are exactly the same without such a condition and that the 'direct approach' includes the 'truth space approach'. The main discussion is in four parts. First, we consider the 'direct approach'. Second, we consider the 'truth space approach'. Third, we show that these approaches give the same conclusion and finally we clear the relation between the study of Tong and the study of ours.

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The determination of the suitable fuzzy control rules and membership functions is the most important but not so easy. Hitherto, to determine the fuzzy control rules and mambership functions, the system designer abstructs the knowhow of the skilled operator by a means of interviews and etc, . So, no one knows the abstructed fuzzy control rules and membership functions are the best or not. This paper proposes the fuzzy clustering method by the discretionary fuzzy performance function and the generation method of fuzzy rules and membership functions automatically for the construction of the fuzzy control system. And this paper reports the availability of this method by applying to the practical process.

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Nowadays, there are needs for information systems that allow to deal with ambiguous information. For instance, a lot of fuzzy database systems are proposed, which can handle ambiguous or fuzzy data to manage our fuzzy queries. However, with regard to access interface to database management systems it is said that there are rare systems with easy-to-use interface for people who are not accustomed to use such database systems. Therefore, we analyze the ambiguity which queries issued by users essentially have, and we study how human-oriented queries should be expressed. This paper proposes new and/or operations based on averaging operators for fitting our intuition. Furthermore, it proposes Compound Fuzzy Attribute : an ambiguous attribute derived from multiple rigid attributes, and describes the generating scheme of such ambiguous attributes. When ambiguity is included in the query, the retrieval time shows extension because of mass calculation. In our system, the retrieval time is shortened by using the cluster-seeking technique. Such a fuzzy querying system is implemented on Sun3 workstation using C language. Finally, the configuration and the user interface of this system is reported.

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The authors proposed a natural language interface that is possible to do a fuzzy database retrieval by natural language. This paper makes a matter what class of natural language the interface can accept clear. For this we classify natural language queries into several classes, and then evaluate the ability of acceptance of the interface for each class. The new extended method is added to the original interface for the unacceptable classes.

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Robot manipulators PD feedback is a PTP(Point To Point)control from which can handle nonlinearity of robot manipulators with the simple linear feedback and guarantees system stability strictly. In this paper, we propose a method of trajectory tracking control for robot manipulators with fuzzy adaptation rule based on PD feedback. The result of an experiment using a 2-degree-of-freedom manipulator shows the effectiveness of this trajectory tracking control method for robot manipulators. A advantage of this method is that control algorithm is simple and small in calculation quantity.

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It is necessary to tune inference rules whenever fuzzy reasoning is employed to control an object. Some self-tuning methods which can tune inference rules automatically were proposed. But, these conventional methods don't have sufficient generalization capability. We propose a new selftuning method of fuzzy inference rules using delta rule, which is a learning algorithm of neural network. This method have high generalization capability, because this method optimizes antecedent parts which are arranged each rule. In this paper, formulation of the proposed method is described first, and its applications to some numerical examples and a moving obstacle avoidance are reported to show its advantages.

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