This paper proposes a method to design interval observers for nonlinear systems by making use of the Takagi-Sugeno fuzzy model. The Takagi-Sugeno model has properties which general nonlinear systems do not posses. This paper demonstrates how such properties allow interval observers to handle nonlinearities in unmeasured variables. Instead of computing some intervals only, this paper puts emphasis on clarifying guarantees the observer can provide for a reasonable length of computed intervals in terms of convergence and attractiveness.