Simulation and analysis of fuzzy-parameterized models with the extended transformation method

The transformation method has been proposed as a practical tool for the simulation and the analysis of systems with uncertain, fuzzy-valued model parameters using fuzzy arithmetic. Up to now, this method has been available in two forms: in a general form, which can be used for the simulation and the analysis of arbitrarily non-monotonic problems, and in a reduced form, which reduces the computational costs of the method to a large extent, requiring, instead, some additional conditions to be fulfilled. In this paper, the extended transformation method will be introduced as an advanced version of the previously presented formulations of the transformation method. This extended version includes the former versions as marginal cases and allows a pre-adjustment of the method, subject to the number of model parameters that are expected to cause non-monotonic behavior of the model output. Finally, to set up the method properly, a novel approach, again based on the transformation method, is presented to practically detect those parameters that are responsible for a non-monotonic behavior of the model output.