There are various types of information divergence measures considered in theoretical data of information theory, which compares two probability distributions and has operations in statistics and engineering. They are valuable and have effects in various fields such as sensor coordination, sequential testing in the Markov chain, the risk for binary experiments, region segmentation, and prediction, etc. In this article, we will create some fuzzy inequalities of fuzzy chi-square divergence measures that impose properties of convex functions and fuzzy new f-divergence measures. Also, observe the application of an intuitionistic fuzzy set.