An Interpretation of Geological Map Expression by Means of Fuzzy Measure

Abstract

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.