In recent years, rough set theory has become one of the powerful solutions in solving the problem of artificial intelligence and data mining. But the classic version of the Raff set theory is not very suitable for discussing feature reduction in imperfect information systems. An incomplete information system refers to data tables that do not have a value in some attribute directories. Feature selection based on fuzzy rough sets is an effective approach to select the best subset of features. Fuzzy set theory and rough set theory are two distinct but complementary theories that deal with uncertainty in data. The salient features of both theories are within the scope of fuzzy rough tuning theory. This hybrid theory is useful as a potential tool for data mining, especially for feature selection. However, there are relatively few studies on incomplete data with time intervals. The purpose of this paper is to present a fuzzy set approach based on overcoming information systems with incomplete value. Since feature reduction is an NP-hard problem, a fast and effective approximation algorithm is required.. In this paper A new optimization approach known as water cycle algorithm has been used to solve this problem. The presented method was tested on the known UCI dataset. The results of the experiments show that the fuzzy rough and the proposed algorithm gave appropriate results, which is reasonable.