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Real word data sets often contain many missing elements. Most algorithms that automatically develop a rule-based model are not well suited to deal with incomplete data. The usual technique is to disregard the missing values or substitute them by a best guess estimate, which can bias the results. In this paper we propose a new method for estimating the parameters of a Takagi-Sugeno fuzzy model in the presence of incomplete data. We also propose an inference mechanism that can deal with the incomplete data. The presented method has the added advantage that it does not require imputation or iterative guess-estimate of the missing values. This methodology is applied to fuzzy modeling of a classification and regression problem. The performance of the obtained models are comparable with the results obtained when using a complete data set.