Identification of Enhanced Fuzzy Models with Multidimensional Fuzzy Membership Functions

Identification of enhanced data-driven fuzzy models with multidimensional fuzzy membership functions is considered. The enhancement of fuzzy modeling is important since it can be used for modeling nonlinear, uncertain, and complex systems. For this aim a number of proposals appear in the literature. In these works some of the general concerns are local models, global models or the combination of both. The common approach in these works is the use of decomposed fuzzy membership functions from the multidimensional membership functions counterpart. However, because of such decomposition, inevitably a decomposition error creeps in the model development process thereby degrading the model performance. To avoid this error, it is desirable to work with multidimensional membership functions directly, to determine the final fuzzy model outcome. The motivation of this research is due to fuzzy modeling of architectural design data for the development of intelligent design processes where the data are multidimensional and highly nonlinear. From this starting point, this research deals with multidimensional membership functions to form a fuzzy model where the membership functions are modeled by radial basis functions (RBF) network. Comparisons are made with the results presented in the literature and the enhanced fuzzy modeling of this approach is demonstrated