There are two main methods to deal with belief in intelligent systems : a logical approach using modal logic and a numerical approach using probability, fuzzy measures, and so on. To study a theoretical relationship between the two approaches, an extended fuzzy-measure-based model as a family of minimal models for modal logic is defined where each minimal model corresponds to an intermediate value of a fuzzy measure. Then, graded modal operators can be defined in the model, which is an extension of our previous model which only deals with the value 1 of a fuzzy measure. Soundness and completeness results of several systems of modal logic are proved with respect to classes of these new models based on intermediate values of fuzzy, possibility, necessity, and Dirac measures. The inclusion relation between the classes of models as well as their corresponding systems is also shown.

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In this paper, we present an interactive fuzzy satisficing method for large-scale multiobjective linear programming problems with the block angular structure. By considering the imprecise nature of human judgements, we assume that the decision maker (DM) may have a fuzzy goal for each of the objective functions. Having elicited the corresponding linear membership functions, if the DM specifies the reference membership levels for all the membership functions, the corresponding Pareto optimal solution which is, in the minimax sense, nearest to the requirement or better than that if the reference membership levels are attainable can be obtained by solving the minimax problem. Here it is shown that the formulated minimax problem can be reduced to one master problem and a number of linear subproblems and the Pareto optimal solution together with the trade-off rate information between the membership functions can be obtained by applying the Dantzig-Wolfe decomposition method. In this way, the satisficing solution for the DM can be derived from Pareto optimal solutions by updating the current reference membership levels on the basis of the current levels of the membership functions together with the trade-off rates between the membership functions.

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Recently, fuzzy reasonings are used in many fields and places. In order to apply the reasoning methods to the various fields, the tuning method of the fuzzy reasoning is the key issue. Some self-tuning methods were proposed. However these conventional self-tuning methods do not have sufficient capability of learning. In this paper, we propose a new self-tuning fuzzy reasoning, which consists of some membership function expressed by the spline function. Delta rule is utilized for tuning the shapes of membership function and consequent parts. The effectiveness of the proposed methods is shown by some numerical examples.

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It is desirable to be able to express behavioral sequences which include the ambiguous state recognition when trying to represent "human-like" behavior-decision abilities, for example, in the intelligent robot. We have already proposed the macro behavior-decision algorithm close to the one which humans use every day by utilizing fuzzy algorithms capable of expressing sequence flow and handling both crisp and fuzzy processing. In this paper, we try to express the flowchart of a fuzzy algorithm based on Fuzzy Petri Nets (FPN) and evaluate the fuzzy state transition in the system by the marking change of fuzzy truth tokens. By using this method, we can design the fuzzy algorithm that explosions of the fuzziness do not occur and analyze the system behavior. Finally, we report results of computer simulations using this method performed for an example of the behavior-decision fuzzy algorithm for an autonomous mobile robot.

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Ordinary social system simulation depends on mathematical models based on numerical information. When we forecast the future trend of a social system, we often use this model. However, there are many cases where social scientists can get a better result of a simulation than that of a simulation based on a mathematical model. We assume that this is because they can translate all information into linguistic information in their heads and can use them for forecasting the trend of a social system. In this paper, we argue that linguistic information plays a very important role in the information processing. Therefore, we try to model the human ability of information processing based on language. We call this framework intelligent computing. To realize the information processing based on language, we need a framework of understanding the meaning of language. We apply the idea of systemic functional linguistic theory to this computing. Depending on the concept of this linguistic theory, we propose a linguistic model which expresses the human thinking process. Moreover, taking care of the natures of language, we show an information fusion based on language; various kinds of information are unified with language. As an example of our proposed methods for simulating a social system, we show a simulation estimating the future trend of the yen-dollar rate.

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Fuzzy modeling, based on input-output(I/O) data pairs, is a method for identifying an unknown 'black-box system'. With a fuzzy model humans can qualitatively understand a system's I/O relationship. Usually we have some knowledge about a system we wish to model. Hence we can say that almost all systems are 'grey-boxes'. In effect fuzzy modeling enables a human to achieve a deeper understanding of grey-box system. In this paper we propose a method of qualitative system description based on both knowledge and numerical data. First we identify a numerical data-based I/O model and a knowledge-based model. Then the two models are combined by comparing each others structure. At this point we can make an abduction to settle our lack of knowledge. A description of the system will be generated, with the users register level in consideration, by simulating the combined model. We apply our method to a fuzzy controller design by first constructing a control model of the combined model and then designing a fuzzy feedback controller based on some control description. Finally we apply our technique to a helicopter system.

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L.A. Zadeh has proposed a principle of incompatibility in purport : It is inadequate to apply a mathematical model to a human-oriented system, and therefore a language model should intrinsically be used. A human behavior such as an outfielder of baseball tracing a ball to catch it can be said to be a typical human-oriented system that Zadeh insists. The outfielder catches without any difficulty a ball flying by far rapidlier than he runs keenly watching the locus of the flying ball with just his skillfulness he has acquired as a weapon. S. Chapman has found a simple rule for catching a ball from the observation of outfielder's such behaviors of ball catching. Complying with such affairs, the author of this paper has developed a fuzzy expert system, BS-SIM, to simulate the outfielder's ball catching actions in a manner of fuzzy control by composing Chapman's experience law as fuzzy production rules. An outfielder robot settled in the system has ability to fuzzy-observe the motion of the ball changing itself second by second, to estimate adequate running speed utilizing many of fuzzy production rule groups including Chapman's experience law, and to reach the point onto which the ball is falling. The robot possessing such ability was able to, it was understood, catch a ball with a remarkably high probability (somtimes the probability has reached 100%) in a 3-dimensional environment quite close to reality (e.g. an environment where wind blows). With an outfielder robot, whose ball-catching actions are based upon a language model, simulation of human ball-catching actions can be said to be done by such a robot when judgment is made from a widely-ranging viewpoint.

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The purpose of this paper is to identify a pulse rate prediction model for an activity sensing pacer by SOFIA (Self-Organizing Fuzzy Identification Algorithm), which is a simplified method of fuzzy modeling proposed by Sugeno and Kang. Input and output variables of the pulse rate prediction model are workload and pulse rate, respectively. First, it is pointed out by comparing identfication result of SOFIA with that of a linear model that the input-output relation between workload and pulse rate is highly nonlinear. Finally, as a result of compairing prediction result by the identified fuzzy model with those by other pacers, it is shown that SOFIA is useful for predicting pulse rate for activity sensing pacers.

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In this paper, a chaotic fuzzy associative memory system is proposed, in which the chaotic memory search is applied to a fuzzy associative memory system in order to support human creative thinking. It is shown by means of simulation results for examples that this system has the following functions. (1)The function that the patterns which are memorized and within a limited distance from an input pattern are retrieved dynamically. (2)The function that the patterns which are not memorized but available as a fuzzy rule are retrieved. Lastly, it is showed that even if a retrieved pattern is not desirable one for users, other desirable ones can be retrieved by function (1), and it becomes easy for users to think creatively since they are given hints for creative thinking by function (2).

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