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It is an urgent desire for all the education institutions to predict the student’s academic performance at the earliest. Though, there are many factors are involved in discovering their performance, the most important factor focused in this paper is learning style of the individual student. In this work a novel method is constructed to cluster students learning style and with other facilities available to the students. The inconsistencies and impreciseness in identifying students by standard clustering models as Assimilator /Divergent / Converger / Accomadator is overcome by applying the intuitionistic fuzzy Mean shift clustering (IFMSC). This algorithm will intelligently tackle the outliers and the students whom lies in the border of the clusters by defining each student in terms of intuitionistic fuzzification with the assistance of mean shift method. The standard clustering models selects the centroids in an arbitrary manner which may have the possibility of failing to select the optimal instances as centroids during the initial stage itself. This problem is overcome in this proposed work by inheriting the Chaotic Cheetah Chase Algorithm(C3A) , which in turn is optimized by the chaotic theory while choosing the parameters and centroids. Thus, by applying the proposed IFMSC-C3A, the prediction of learning style of the students which influence their academic performance is accomplished more precisely while comparing the other clustering models.