Fuzzy fractal dimensions and fuzzy modeling

摘要: Fractal dimensions describe self-similarity (structural complexity) of various phenomena (such as e.g., temporal signals, images). Their determination (through box counting or a correlation method) is inherently associated with the use information granules--sets. The intent this study to generalize idea domain fuzzy sets and reveal associations between mechanisms fractal analysis granular computing (including modeling). First, we introduce concept itself discuss role vehicle for constructing dimensions. Second, propose an algorithmic framework necessary carry out all computing, experimentally quantify performance regression models used determine contrast it existing in set-based environment. It shown that set approach produces more consistent (in terms their performance). We also postulate power law granularity its direct implications form variable modeling. In particular, show how helps construct mappings system's variables rule-based models. Experimental studies involving several frequently categories illustrate main features approach.