ABSTRACT
Natural phenomena may be roughly divided into two categories: one is determinacy, and the other is indeterminacy. Indeterminacy can also be divided into randomness and fuzziness. Today one can investigate some irregular phenomena with determinacy and randomness by fractal geometry. However, so far, the fractal geometric theory and its applications have only been confined to these two natural phenomena. In order to describe indeterminate fuzzy phenomena by the fractal geometric theory, it is very important to define new fractal concepts and construct new fractal sets. In this chapter, we introduce our recent work in this respect (Zhang & Xie, 1989).
