Since interval output data can be regarded as distributions of possibility, interval regression analysis is proposed by possibilistic interval systems. Interval data are given by fuzzy observa tion or expert knowledge and it becomes recently important to deal with interval data implying our partial ignorance on the phenomenon. In our formulations, possibility and necessity measures, which are dual each other, are used to construct several formulations of interval regression models, depending on different situations under consideration. Our approach for obtaining a possibilistic interval model which fits to given interval output data can be reduced to LP problems. Thus, merits of our approach are to be able to obtain interval parameters by LP methods and to add expert knowledge on parameters in interval models to constraint conditions in LP problems. Some examples are depicted to illustrate these new techniques.

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In disaster-prevention plans, the way of role sharing is important. There are many things to do for the laders. So, they are required to share these roles and the planner should consider who should share a role and who should share another. And also, they have to consider that in disasters some people obey the leaders and others do not. In this study a simulation model of human behavior considering these points was built and an experiment with this simulation model was executed. The results of experiment were: 1. This simulation model reflects the differencee between subjects. 2. The subjects considered many different things and what they consiered was independent from the situation set by the model. 3. The subjects'action became similor when the situation became severe. 4. The sbjects considered another leader when there is one.

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This paper critically reviews the economics of uncertainty and information, one of the most important subjects in economics today. An economic man has to choose the best good or service among alternatives. The presence of uncertainty or risk affects his decision in various ways. For one thing, he may be risk averse or risk preferred. For another, his knowledge about the states of the world may be different from others'. In this paper, we pay special attention to the following three topics. The first topic is concerned with the question of how to measure risk aversion. When there is only one stochastic variable, the degree of risk aversion is uniquely measured by the concavity of the utility function, the value of a risk premium or a probability premium. With many variables present, however, the uniqueness of the risk aversion measure is not guaranteed. Second, when information is not evenly distributed among decision-making units, there arise some difficulties at to the working and performance of a market. Among those difficulties are adverse selection and moral hazard. The third topic is related to the role of information played in an oligopolistic market. In the above, we have adopted the expected utility theory of von Neumann and Morgenstern. If, however, the status quo effect and other psycho-socio-anthropological factors are taken into consideration, the effectiveness of the expected utility theory is lessened to a considerable extent. This shows the need to introduce a completely new approach to decision making under uncertainty, by recognizing the basic difference between a vertical society of the East and a horizontal society of the West.

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In order to win the election, a politician has to appeal himself to a number of different voters in the electorate. As a means to do so, the use of ambiguity may be effective. In this paper two notions of ambiguity are introduced. One notion of ambiguity is equated with voter uncertainty: a politician takes an ambiguous stance on an issue by announcing to the voters a lottery over the positions he might take on that issue. The other notion of ambiguity is equated with multiple meanings: a politician takes an ambiguous stance on an issue if his rhetoric admits of different meanings in different contexts. These notions of ambiguity are formalized, and their effects on the decision problems of voter and politician are formally analyzed. Some further problems are also discussed.

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The purpose of this paper is to discuss what rationality in probability judgment is. We argued that rationality should be discussed by axioms which rational persons should obey. Coherent rules can be derived from the axioms and they can be used to check whether each judgment is coherent or not. It seems to us that only Bayesian approach has had an adequate axiomatic development, although the same kind of axiomization for other fuzzy measures seem to be possible. Next, we examined ordinary and intuitive probability judgments, especially in terms of the results obtained from three evaluation problems, which are called;Alarm set and Theft;Two Urns, and;Three Prisoners Problems. Our conclusion is that, even when the subjects responses appear to be very different from the numerical value calculated by Bayes theorem and the like, it can be explained why the subjects modified coherent probability judgment. We believe that by being educated suitably, they can be more coherent evaluator of probabilities.

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Several characteristics of physicians'decision making are disucussed. As a model, history taking and the selection among various diagnostic/therapeutic strategies for a patient with probable common cold is analyzed. A decision tree analysis shows that the best choice wound vary from observation to order lab test and then to prescribe antibiotics, as the prior probability or the risk of pneumonia increases. Thus the quantitative assessment of the risk of pneumonia is required for each patient before choosing the best strategy. The series of initial questions followed by a short physical examination, such as an experienced physician would do, is probably the most efficient way of assessing the risk of pneumonia, although its would be very difficult for a physician to define his algorithm. The answer to the questions or the presence of signs revealed by physical examination has the same value in estimating the risk of pneumonia as a chest X-ray film or the result of a blood test. Thus, the efficacy of each question or sign in the differential diagnosis should be investigat ed to know precisely which questions are to be asked and which signs are to be examined. Unfortunately, the current health insurance system in Japan employs a per item payment policy and thus the length of time used in the interview or in the physical examination is not evaluated at all.This payment system leads physicians to order unnecessary tests and drugs, instead of allowing them to spend more time for hhistory taking or physical exam.The authoris afraid that physicians, who uses a battery of test results rather than the answers and signs, might forget the skill of constructing the most valuable algorithm.

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Uncertainties in systems engineering are discussed from a viewpoint of fuzzy theory. It is emphasized that the existence of a man plays an essential role in systems engineering and so fuzziness characterizing a man is a key problem to be dealt with. An idea of fuzzy control is introduced as a typical example where fuzzy logic is applied. In order to show wider applicability of fuzzy theory than probability theory, modal classification of uncertainties is made, and some fields of applying fuzzy theory are shown according to the modalities of uncertainties.

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