The certainty of identifying to geological unit in geological map is interpreted by means of fuzzy measure, and the information sum of the certainty as well as the expression of geological map are examined for a practical application.
Geological map is a kind of thematic maps, which is classified to plane data map. The difference from the other distribution maps is that the geological unit is expressed not in a nominal scale but in an ordinal scale, and that each point on the map has various certainty of belonging to the unit. On the latter, a fuzzy measure makes it possible to express the certainty. The fuzzy measure g becomes g=1 at an actual outcrop, and it decrease with an increasing distance from the outcrop. The fuzzy measure is possible to represent complexities including anisotropy of the geologic body, and the subject or the judgement of the author of the map.
An integral of fuzzy measure of a domain enables us not only to get information sum of the certainty but also to evaluate increased information after exploration. About the geological map expression, features with higher measure points such as outcrops should be shown on the map, and the degree of certainty should be defined. By utilizing fuzzy measure, both the possibilities of the information sum and the certainty can be expressed.

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Crustal shear zones are believed to have formed at deeper levels under high ductile, high PT, conditions. Subsequent rise of the shear zone rocks up to the surface, involves a series of deformational and metamorphic processes which leave their effects/imprints in the form of new structures, textures, fabric, and the related petrographic, mineralogical and geochemical features, all of which can be observed and measured. All these elements can be restructured or reorganized to develop quantitative models.
Depending upon the type of available data, only one or some specific models for a shear zone can be developed. Amathematical modelcan be developed when the measurable variables (or the controlling factors) of a shear zone can be approximated by some limited range. A mathematical model can be made more realistic if some random components of the shear zone (or the system) - e.g. vertical uplift, rise or fall of temperature, etc-can be considered. This gives rise to astochastic modelfor a shear zone. If the present-day tectonic set-up of a shear zone can be considered in terms of the sum total of a few structural processes (as outlined in the paper) together with one or two random components (outlined in the paper) operative in the system, astochastic processmodel can be developed for the shear zone. Aprocess-response model can be developed when the structural/tectonic factors that constitute the “causes” - i.e. process elements - and those constituting the “effects” - i.e. response elements - for a shear zone are known. A shear zone may take up alinear modelwhen all the associated structural data that have given rise to the development of the shear zone are directly observable and measurable in field sections, such that the observational data yield a certain linear relation of the type y=a+bx.
The method of developing a quantitative model for a shear zone has been demonstrated in the paper by taking the actual situation of a shear zone.

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[in Japanese]

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