Fuzzy interpolation enhances the robustness of fuzzy systems and helps to reduce systems complexity. Although a number of important fuzzy rule interpolation approaches have been proposed in the literature, most of these approaches cannot be expressed in a closed form. This is usually caused by the effort to avoid possible invalid interpolated results. This paper proposes a different fuzzy rule interpolation approach. It not only can be represented in a closed form but also guarantees that the interpolated results are valid fuzzy sets. This approach is based on a direct use of the extension principle which has been widely utilised for the development of a variety of fuzzy systems. The mathematical properties of the proposed approach are analysed by taking the advantage of the closed form representation. This approach has been applied to a practical problem of predicting diarrhoeal disease rates in remote villages. The results demonstrate the potential of the proposed work in enhancing the robustness of fuzzy interpolation.