Fuzzy regression analysis using fuzzy clustering

Proposes an estimation method for fuzzy cluster loading using the kernel method. Fuzzy cluster loading was proposed in order to interpret the result of fuzzy clustering by obtaining the relationship between the obtained fuzzy clusters and the variables of the given data. From the structure of the model for fuzzy cluster loading, it is known that the estimate is obtained using the estimate of the weighted regression analysis. We propose a method to obtain the estimate in a higher space then the space in the given data using the idea of the kernel method. The significant properties of this technique are: (1) we use high dimension space to estimate the fuzzy cluster loading, due to this, we can get a better result to extract the data structure; and (2) through the cluster structure of given data, we can extract a clearer structure of the given data. Several numerical examples show the validity of the proposed technique and the efficiency of the use of the cluster structure in the given data.