On the Efficiency of Fuzzy Logic for Stochastic Modeling

The properties of fuzzy modeling is investigated for statistical signals. The research makes explicit comparative investigations to position fuzzy modeling in the statistical signal processing domain next to nonlinear dynamic system modeling. It is found that, the nonlinear system dynamics with exogenic inputs can adequately be represented by fuzzy modeling, including the stochastic, as well as deterministic inputs. From the statistical pattern recognition viewpoint, it is interesting to note that, fuzzy modeling has conspicuous ability to represent such input/output relations adequately with relatively small number of fuzzy sets compared to other possibilities, like RBF networks. However, for pattern recognition case, the fuzzy sets determined by data driven methods and approximated by predetermined fuzzy set functions may result in inadequate representations. While such representations can still be used for interpretability reasons, the unshaped data driven projected fuzzy sets remain the essential representation of the fuzzy sets