Analysis of probabilistic fuzzy systems' parameters in conditional density estimation

Probabilistic fuzzy systems (PFS) are shown to be valuable methods for conditional density estimation that combine fuzziness or linguistic uncertainty and probabilistic uncertainty. Several PFS applications have shown the added value of the different reasoning mechanisms of PFS and gains from incorporating two types of uncertainty. The effects of parametrization and parameter estimation on the function or conditional density approximations of PFS have not been documented in the literature. This paper aims to fill this gap in the literature by analyzing the parameters of PFS in conditional density estimation and point forecast using synthetic and real data applications. We show that both in-sample and out-of-sample results depend on PFS parametrization and the results deteriorate when the probability parameters of PFS are not optimized correctly, since these parameters allow the system to be fine tuned.