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Rough set theory (RST) is an important tool to find feature subset selection. One of the most important and challenging issues in RST is to find reducts and core. Most of the problems in many areas, including machine learning, involve high dimensional descriptions of input features. Therefore, it is not surprising to mention that several studies have been conducted on the dimensionality reduction. Feature selection refers to the problem of selecting those input features that are mostly predictive of a given result. RST can be used as a tool to discover data dependency and reduce the number of attributes contained in a data set via the data alone that require no extra information. There have been several studies in the area of finding reducts with minimal cardinal. In this paper, we have proposed the hybrid information system, in which their attributes consist of crisp and fuzzy variables. Fuzzy variables appear as linguistic variables. We first define the degree of separation between fuzzy numbers and then choose a threshold-level (γ) to clarify the objects based on attributes. Considering the threshold-level, we use discernibility matrices to find reducts and core. Experimental results show that the proposed algorithm can improve the feature selection.