Fractal fuzzy decision-making: what is the adequate dimension for self-organizing maps?

We describe a new methodology, based on resources of fractal dimension theory and fuzzy approximated reasoning, to determine the adequate dimension for the output space of self-organizing maps (SOM). This approach considers the dataset under analysis and proposes the dimension that best satisfies the dilemma: to maximize the reduction of dimension and to minimize the topographic distortions - measured with the topographic product. In order to reach this objective, we create the "significant fractal fuzzy dimension measure" as a variation of a fractal dimension measure.