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Linear fuzzy clustering is a technique for local PCA and has been applied to knowledge discovery from database. Fuzzy c-lines (FCL) is a technique for detecting local linear structure and is a modified version of fuzzy c-means (FCM), in which prototypes are replaced with lines. In this paper, we consider the linear fuzzy clustering of data with uncertainties based on intervals, and propose a new clustering algorithm that can handle component-wise uncertainties. The clustering criterion is defined by considering two different metrics, minimum distance and maximum distance, and the optimal prototypes are estimated by using a linear search algorithm. Numerical example shows that the result of the proposed method provides a tool for interpretation of local features of the data with uncertainties.