Adaptive membership function fusion and annihilation in fuzzy if-then rules

The parameters of the input and output fuzzy membership functions for fuzzy if-then min-max inferencing may be adapted using supervised learning applied to training data. Under the assumption that the inference surface is in some sense smooth, the process of adaptation can reveal overdetermination of the fuzzy system in two ways. First, if two membership functions come sufficiently close to each other, they can be fused into a single membership function. Second, annihilation occurs when a membership function becomes sufficiently narrow. In both cases, the number of if-then rules is reduced. In certain cases, the overall performance of the fuzzy system can be improved by this adaptive pruning. The process of membership function fusion and annihilation is illustrated with two examples