Calibrating the membership functions of the fuzzy inference system: instantiated by car-following data

The fuzzy rule based inference is known to be a useful tool to capture the behavior of an approximate system in transportation. One of the obstacles of implementing the fuzzy rule based inference, however, has been to calibrate the membership functions of the fuzzy sets used in the rules. This paper proposes a way to calibrate the membership function when a set of input and output data is given for the system. First, the mathematical operations of the fuzzy rule based inference system are represented by a neural network construction. The operations of each node of this neural network are designed so that they correspond to specific logical operations of the fuzzy rule based inference system. The values of the weights of this neural network are set to correspond to the parameters that control the shape and location of each membership function. Second, given a set of input-output data, the weights are corrected sequentially using the principle of the generalized delta rule based back-propagation mechanism. After correction, the values of the weights are used to specify the exact shape of the membership functions of the fuzzy sets in the rules. The procedure implements a set of logical rules that can be applied when calibrating the shapes of the membership functions of a fuzzy inference system. An example, in which the membership functions of a fuzzy inference model for car-following behavior are calibrated using the real world data, is shown. (C) 2002 Elsevier Science Ltd. All rights reserved.