There has been an interest to apply neural network as inference engines of the medical consultation system, because the neural expert system is expected to solve some obstacles of the knowledge acquisition. However, some problems remain to be examined in development of neural expert systems. One problem concerns how the data structure influence on the process of the knowledge acquisition and what kind of data structure is desirable in the learning process. Another one concerns that the knowledge embodied in neural network is difficult for medical experts to understand the meaning of the connection weights. The purpose of this study is to elucidate these problems concerning the knowledge acquisition by the neural network.

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We propose here a new theory of a multiple fuzzy set(MFS) defined on the frameworks(=dependent coordinates system as a support set) composed of vectors in a unit circle, which is taken out from a universe of static frameworks(set of support sets). And we propose another new concept of "fuzziness" concerning how to be seen through the spectacles applied to the frameworks. The measures of spectacles are constructed on the basis of relationship. Further, we propose a new methodology to express a MFS in the geometrically measurable form by using the reducing transformation technology. The diagram of transformed MFS(TMFS) is called by the name, COSMOS-DIAGRAM because of the close resemblance of the figures to the several appearances of natural objects such as trees, flowers, fireworks, constellations, cellular segmentations and so on. Lastly, we refer to its capability in several engineering fields as well as the mathematical interest.

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This presentation is consisted of two parts. The first one is the essential consideration about the difference between doctors' diagnostic rules. The second part is the study about the relationship between doctors' diagnostic rule and characteristics of membership functions.

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Fuzzy expert system construction tool "the Hyper brain NORIO", was utilized to develop a fuzzy expert system for orthodontic analysis on the personal computer EPSON PC286LS. The analysis employed the fuzzy logic. Roentgen cephalometrics is a vital tool in the conventional orthodontic diagnosis where by films are traced and measured utilizing the key landmarks, line, and planes. The results are then compare to the norms. The diagnostic results employing the above system were fitted to the diagnosis by the orthodontists.

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An application of the fuzzy logic to diagnoses of ovarian tumors with MRI is proposed. 14 example cases were applied to the system. This inference system is useful to infer the nature of the tumors.

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Medicine is not always an exact science. Previously this factor made the use of automatic control with a computer very difficult. But, if we can utilize the advantage of fuzzy logic we can use a computer for automatic control in this field. Fuzzy logic can be very beneficial in this field if it enables us to use computers. This system can replicate the following method used by the professional aneasthesiologists. Presently, the doctor looks at the blood pressure and changes in systolic blood pressure to determine the amount of medicine to administer to the patient. Then the doctor uses a fuzzy way of thinking. He observes the rise in blood pressure and using a type of fuzzy thinking he adjusts the dosage of medicine that the patient receives.

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