Chen et al., have proposed a new estimation method for the membership values in fuzzy sets. The proposed scheme takes input from empirical/experimental data, which reflect the expert's knowledge on the relative degree of belonging of the members, and then searches for the best fit membership values of the element. Through the estimation of the practical case (Sect. 3 in [1]) the algorithm suggests to normalize the estimated membership values if there is any among them more than one and change some condition to guarantee its positiveness. In this paper, we show how to use the same imposed condition to guarantee that the estimated membership values will be within the unit interval without normalization.

In two- or more-dimensional systems where the components of the sample data are strongly correlated, it is not proper to divide the input space into several subspaces without considering the correlation. In this paper, we propose the usage of the method of principal component in order to uncorrelate and remove any redundancy from the input space of the adaptive neuro-fuzzy inference system (ANFIS). This leads to an effective partition of the input space to the fuzzy model and significantly reduces the modeling error. A computer simulation for two frequently used benchmark problems shows that ANFIS with the uncorrelation process performs better than the original ANFIS under the same conditions.