Principal Component Analysis of Triangular Fuzzy Number Data

Principal component analysis (PCA) is a well-known tool often used for the exploratory analysis of a. data set, which can be used to reduce the data dimensionality and also to decrease the dependency among features. The traditional PCA algorithms are designed aiming at numerical data instead of non-numerical data. In this article we propose a generalized PCA algorithm which tackles a problem where data, is linguistic variable represented by triangular fuzzy number. Using the information provided by the centroid and fuzzy boundary of triangular fuzzy number, the proposed method starts with translating triangular fuzzy numbers into real numbers, then PCA is carried out on high-dimensional real number data set. Finally, the application of the proposed algorithm to a triangular fuzzy number data set is described.