Since the optimal construction of a Radial Basis Function Neural Network (RBF-NN) is difficult to determine and plays an important role in predicting performance, we propose a modified RBF-NN, which is integrated with the K-Means clustering based on the Rough sets theory (Rough K-Means), in order to optimize the number of hidden neurons. First, an original RBF-NN that superposes each center to a training set point is built and the network is trained to obtain the potential relationships between the input and output variables. Next, Rough K-Means is employed to optimize the structure and weights of the RBF-NN by clustering the output from the hidden layer that is due to the cluster uncertainty of the hidden output. Further, RBF-NN with Rough K-Means and K-Means, respectively, are employed to develop naphtha dry point soft sensors. The results show that the Rough K-Means is more effective in handling uncertainty and that RBF-NN with Rough K-Means is superior to RBF-NN with K-Means.