Representing Complex Fuzzy Membership Functions in a

The problem of deriving membership functions as a means for describing linguistic variables (for some control process) and the choice of fuzzy inference operators and connectives is at the heart of developing fuzzy control systems. Over the years con-nectionist systems have obtained prominence as a means to solve complicated learning tasks. More recently a surge in interest for applying neural systems to fuzzy control problems has occurred. In this paper, it will be shown how complicated fuzzy membership functions can be composed of simpler-shaped functions. The importance lies in the fact, that the decomposition process can be implemented through use of a connectionist representation. Furthermore, it allows augmenting an existing hybrid symbolic/connectionist learning system-SC-net-to incorporate fuzzy variables described by more complicated membership functions than was earlier possible. Finally, it provides the necessary tools for constructing connectionist fuzzy controllers, which by means of machine learning can be trained to adapt to an ever changing environment.