This paper addresses the design of a robust set-based interval observer for a nonlinear discrete-time system affected by system uncertainty (state disturbance and measurement noise) using a Takagi-Sugeno (TS) fuzzy model including an unmeasurable premise variable. The effect of unmeasurable premise variable and uncertainties is considered as of unknown but bounded nature, i.e., in the set-membership framework. A zonotopic representation of a set towards reducing set operations to simple matrix calculations is used to bound the state estimation provided by the interval observer-based approach. Furthermore, the criterion-based approach and H∞ performance technique are considered in order to compute the observer gain to achieve robustness. Finally, an example is employed to both illustrate and discuss the effectiveness of the proposed approach.